[ { "text": "A Fermion Doublet With Chiral Gauge Interaction On A Lattice: We present a new staggered discretization of the Dirac operator. Doubling\ngives only a doublet of Dirac fermions which we propose to interpret as a\nphysical (lepton or quark) doublet. If coupled with gauge fields, an\n$(1+\\gamma^5)$ chiral interaction appears in a natural way. We define a\ngeneralization for curved background which does not require tetrad variables.\nThe approach suggests a natural explanation for the three fermion families.", "category": "hep-lat" }, { "text": "Strong-coupling effective action(s) for SU(3) Yang-Mills: We apply strong-coupling expansion techniques to finite-temperature lattice\npure gauge theory, obtaining dimensionally reduced $Z_N$-symmetric effective\ntheories. The analytic mappings between the effective couplings and the\noriginal one, viz. $\\beta$, allow to estimate the transition point $\\beta_c$ of\nthe 4D theory for a large range of the imaginary-time extent $N_\\tau$ of the\nlattice. We study the models for SU(3) via Monte Carlo simulation, finding\nsatisfactory agreement with the critical point of the original theories\nespecially at low $N_\\tau$. We have fixed an error in the group measure used in\narXiv:1010.0951 and provide here the correct numerical results.", "category": "hep-lat" }, { "text": "Topological susceptibility in two-flavor QCD: We compute the topological susceptibility in QCD with two flavors of\ndynamical fermions using numerical simulation with overlap fermions.", "category": "hep-lat" }, { "text": "Hadron Spectrum with Wilson fermions: We present results of a high statistics study of the quenched spectrum using\nWilson fermions at $\\beta=6.0$ on $32^3 \\times 64$ lattices. We calculate the\nmasses of mesons and baryons composed of both degenerate and non-degenerate\nquarks. Using non-degenerate quark combinations allows us to study baryon mass\nsplittings in detail. We find significant deviations from the lowest order\nchiral expansion, deviations that are consistent with the expectations of\nquenched chiral perturbation theory. We find that there is a $\\sim 20%$\nsystematic error in the extracted value of $m_s$, depending on the meson mass\nratio used to set its value. Using the largest estimate of $m_s$ we find that\nthe extrapolated octet mass-splittings are in agreement with the experimental\nvalues, as is $M_\\Delta - M_N$, while the decuplet splittings are 30% smaller\nthan experiment. Combining our results with data from the GF11 collaboration we\nfind considerable ambiguity in the extrapolation to the continuum limit. Our\npreferred values are $M_N / M_\\rho = 1.38(7)$ and $M_\\Delta / M_\\rho =\n1.73(10)$, suggesting that the quenched approximation is good to only $\\sim\n10-15%$. We also analyze the $O(ma)$ discretization errors in heavy quark\nmasses.", "category": "hep-lat" }, { "text": "Progress applying density of states for gravitational waves: Many models of composite dark matter feature a first-order confinement\ntransition in the early Universe, which would produce a stochastic background\nof gravitational waves that will be searched for by future gravitational-wave\nobservatories. We present work in progress using lattice field theory to\npredict the properties of such first-order transitions. Targeting SU(N)\nYang--Mills theories, this work employs the Logarithmic Linear Relaxation (LLR)\ndensity of states algorithm to avoid super-critical slowing down at the\ntransition.", "category": "hep-lat" }, { "text": "$I=0$ $\u03c0\u03c0$ $s$-wave scattering length from lattice QCD: We deliver lattice results for the $I=0$ $\\pi\\pi$ elastic $s$-wave scattering\nlength calculated with the MILC $N_f=3$ flavors of the Asqtad-improved\nstaggered fermions. The scattering phase shifts are determined by L\\\"uscher's\nformula from the energy-eigenvalues of $\\pi\\pi$ systems at one center of mass\nframe and four moving frames using the moving wall source technique. Our\nmeasurements are good enough to resolve the scattering length $a$ and effective\nrange $r$, moreover, it allows us to roughly estimate the shape parameter $P$.\nUsing our lattice results, the scattering length $a$ and effective range $r$ at\nthe physical point are extrapolated by chiral perturbation theory. Our results\nare reasonably consistent with the Roy equation determinations and the newer\nexperimental data. Numerical computations are carried out with two MILC fine\n($a\\approx0.09$~fm, $L^3 \\times T = 40^3\\times 96$) and one MILC superfine\n($a\\approx0.06$~fm, $L^3 \\times T = 48^3\\times 144$) lattice ensembles at three\npion masses of $m_\\pi\\sim247~{\\rm MeV}$, $249~{\\rm MeV}$, and $314~{\\rm MeV}$,\nrespectively.", "category": "hep-lat" }, { "text": "On meson spectral functions at high temperature and nonzero momentum: In the high-temperature phase of QCD meson spectral functions at nonzero\nmomentum are expected to have a nontrivial and interesting structure. In order\nto provide a reference point for lattice studies employing e.g. the Maximal\nEntropy Method, we discuss several characteristics of meson spectral functions\nin the infinite-temperature limit. We report on ongoing work in quenched QCD\nwith staggered fermions.", "category": "hep-lat" }, { "text": "Vacuum Entanglement Harvesting in the Ising Model: The low-energy states of quantum many body systems, such as spin chains, are\nentangled. Using tensor network computations, we demonstrate a protocol that\ndistills Bell pairs out of the ground state of the prototypical\ntransverse-field Ising model. We explore the behavior of rate of entanglement\ndistillation in various phases, and possible optimizations of the protocol.\nFinally, we comment on the protocol as we approach quantum criticality defining\na continuum field theory.", "category": "hep-lat" }, { "text": "Magnetic and electric screening masses from Polyakov-loop correlations: Screening properties of the quark gluon plasma are studied from Polyakov-loop\ncorrelation in lattice QCD simulations with two flavors of improved Wilson\nquarks at temperatures $T/\\Tpc \\simeq 1$--4 where $\\Tpc$ is the pseudocritical\ntemperature. Using the Euclidean-time reflection symmetry and the charge\nconjugation symmetry, we introduce various types of Polyakov-loop correlation\nfunctions and extract screening masses in magnetic and electric sectors. We\nfind that the temperature dependence of the screening masses are well described\nby the weak coupling expansion. We also find that a ratio of the screening\nmasses in the electric sector to the magnetic sector shows qualitative\nagreement with a prediction from the dimensionally-reduced effective field\ntheory and the N=4 supersymmetric Yang-Mills theory at $1.3 < T/\\Tpc < 3$.", "category": "hep-lat" }, { "text": "The quark-mass dependence of the potential energy between static colour\n sources in the QCD vacuum with light and strange quarks: The low-lying energy spectrum of the static-colour-source-anti-source system\nin a vacuum containing light and strange quarks is computed using lattice QCD\nfor a range of different light quark masses. The resulting levels are described\nusing a simple model Hamiltonian and the parameters in this model are\nextrapolated to the physical light-quark masses. In this framework, the QCD\nstring tension is found to be $\\sqrt{\\sigma}=445(3)_{\\rm stat}(6)_{\\rm sys}$\nMeV.", "category": "hep-lat" }, { "text": "Determinant Calculations Using Random Walk Worldline Loops: We use statistical ensembles of worldline loops generated by random walk on\nhypercubic lattices to calculate matter determinants in background Yang-Mills\nfields.", "category": "hep-lat" }, { "text": "Scaling test of quenched Wilson twisted mass QCD at maximal twist: We present the results of an extended scaling test of quenched Wilson twisted\nmass QCD. We fix the twist angle by using two definitions of the critical mass,\nthe first obtained by requiring the vanishing of the pseudoscalar meson mass\nm_PS for standard Wilson fermions and the second by requiring restoration of\nparity at non-zero value of the twisted mass mu and subsequently extrapolating\nto mu=0. Depending on the choice of the critical mass we simulate at values of\nbeta in [5.7,6.45], for a range of pseudoscalar meson masses 250 MeV < m_PS < 1\nGeV and we perform the continuum limit for the pseudoscalar meson decay\nconstant f_PS and various hadron masses (vector meson m_V, baryon octet m_oct\nand baryon decuplet m_dec) at fixed value of r_0 m_PS. For both definitions of\nthe critical mass, lattice artifacts are consistent with O(a) improvement.\nHowever, with the second definition, large O(a^2) discretization errors present\nat small quark mass with the first definition are strongly suppressed. The\nresults in the continuum limit are in very good agreement with those from the\nAlpha and CP-PACS Collaborations.", "category": "hep-lat" }, { "text": "Capillary Waves in Binder's Approach to the Interface Tension: In Binder's approach the reduced interface tension sigma of the Ising model\nin the broken phase is determined from the finite volume effects of the\npartition function Z(M) at fixed total magnetization M. For small |M| the\npartition function of a system of size L^d with periodic boundary conditions is\ndominated by configurations with two interfaces, such that Z(M) ~ exp(- 2 sigma\nL^{d-1}). Capillary wave fluctuations of the interfaces correct this result to\nZ(M) ~ exp(- 2 sigma L^{d-1}) with x = -1. The knowledge of the pre-exponential\nbehavior allows an improved fit of numerical data, and a determination of the\ninterface stiffness.", "category": "hep-lat" }, { "text": "Development of Lattice QCD Tool Kit on Cell Broadband Engine Processor: We report an implementation of a code for SU(3) matrix multiplication on\nCell/B.E., which is a part of our project, Lattice Tool Kit on Cell/B.E.. On\nQS20, the speed of the matrix multiplication on SPE in single precision is\n227GFLOPS and it becomes 20GFLOPS {this vaule was remeasured and corrcted.}\ntogether with data transfer from main memory by DNA transfer, which is 4.6% of\nthe hardware peak speed (460GFLOPS), and is 7.4% of the theoretical peak speed\nof this calculation (268.77GFLOPS). We briefly describe our tuning procedure.", "category": "hep-lat" }, { "text": "Tensor renormalization group approach to (1+1)-dimensional SU(2)\n principal chiral model at finite density: We apply the tensor renormalization group method to the (1+1)-dimensional\nSU(2) principal chiral model at finite chemical potential with the use of the\nGauss-Legendre quadrature to discretize the SU(2) Lie group. The internal\nenergy at vanishing chemical potential $\\mu=0$ shows good consistency with the\nprediction of the strong and weak coupling expansions. This indicates an\neffectiveness of the Gauss-Legendre quadrature for the partitioning of the\nSU(2) Lie group. In the finite density region with $\\mu\\ne 0$ at the strong\ncoupling we observe the Silver-Blaze phenomenon for the number density.", "category": "hep-lat" }, { "text": "Color superconductivity in a small box: a complex Langevin study: It is expected that the color superconductivity (CSC) phase appears in QCD at\nlow temperature and high density. On the basis of the lattice perturbation\ntheory, a possible parameter region in which the CSC occurs has been predicted.\nIn this work, we perform complex Langevin simulation on an $8^3\\times 128$\nlattice using four-flavor staggered fermions. We find, in particular, that the\nquark number has plateaux with respect to the chemical potential similar to our\nprevious study, indicating the formation of the Fermi sphere. A\ndiquark-antidiquark operator, which is an order parameter of color\nsuperconductivity, is formulated on the lattice using the U(1) noise. Our\nresult for this operator is found to fluctuate violently when the Fermi surface\ncoincides with the energy levels of quarks. We also discuss partial restoration\nof the chiral symmetry at high density.", "category": "hep-lat" }, { "text": "Surface operator study in SU(2) gauge field theory: The surface operator in an SU(2) gauge field theory is studied. We analyze\nAbelian projection of the SU(2) symmetry to the U(1) group calculating the\nsurface parameter. The surface parameter dependence on the surface area and\nvolume is studied in confinement and deconfinement phases. It is shown the\nspatial and temporal surface operators exhibit nontrivial area dependence in\nthe confinement and deconfinement phases. It is shown also that there is no\nvolume law for the operators defined on a cubic surface.", "category": "hep-lat" }, { "text": "Non-Perturbative Renormalization of Lattice Four-Fermion Operators\n without Power Subtractions: A general non-perturbative analysis of the renormalization properties of\n$\\Delta I=3/2$ four-fermion operators in the framework of lattice\nregularization with Wilson fermions is presented. We discuss the\nnon-perturbative determination of the operator renormalization constants in the\nlattice Regularization Independent (RI or MOM) scheme. We also discuss the\ndetermination of the finite lattice subtraction coefficients from Ward\nIdentities. We prove that, at large external virtualities, the determination of\nthe lattice mixing coefficients, obtained using the RI renormalization scheme,\nis equivalent to that based on Ward Identities, in the continuum and chiral\nlimits. As a feasibility study of our method, we compute the mixing matrix at\nseveral renormalization scales, for three values of the lattice coupling\n$\\beta$, using the Wilson and tree-level improved SW-Clover actions.", "category": "hep-lat" }, { "text": "Probing hadron wave functions in Lattice QCD: Gauge-invariant equal-time correlation functions are calculated in lattice\nQCD within the quenched approximation and with two dynamical quark species.\nThese correlators provide information on the shape and multipole moments of the\npion, the rho, the nucleon and the $\\Delta$.", "category": "hep-lat" }, { "text": "The Anderson transition in QCD with $N_f=2+1+1$ twisted mass quarks:\n overlap analysis: Chiral Random Matrix Theory has proven to describe the spectral properties of\nlow temperature QCD very well. However, at temperatures above the chiral\nsymmetry restoring transition it can not provide a global description. The\nlevel-spacing distribution in the lower part of the spectrum of the Dirac\noperator is Poisson-like. There the eigenmodes are localized in space-time and\nseparated from the rest of the spectrum by a so-called mobility edge. In\nanalogy to Anderson localization in condensed-matter systems with random\ndisorder this has been called the QCD-Anderson transition. Here, we study the\nlocalization features of the low-lying eigenmodes of the massless overlap\noperator on configurations generated with $N_f=2+1+1$ twisted mass Wilson sea\nquarks and present results concerning the temperature dependence of the\nmobility edge and the mechanism of the quark-mode localization. We have used\nvarious methods to fix the spectral position of the delocalization transition\nand verify that the mobility edge extrapolates to zero at a temperature within\nthe chiral transition region.", "category": "hep-lat" }, { "text": "Determining the chiral condensate from the distribution of the winding\n number beyond topological susceptibility: The first two non-trivial moments of the distribution of the topological\ncharge (or gluonic winding number), i.e., the topological susceptibility and\nthe fourth cumulant, can be computed in lattice QCD simulations and exploited\nto constrain the pattern of chiral symmetry breaking. We compute these two\ntopological observables at next-to-leading order in three-flavour Chiral\nPerturbation Theory, and we discuss the role played by the eta propagation in\nthese expressions. For hierarchies of light-quark masses close to the physical\nsituation, we show that the fourth cumulant has a much better sensitivity than\nthe topological susceptibility to the three-flavour quark condensate, and thus\nconstitutes a relevant tool to determine the pattern of chiral symmetry\nbreaking in the limit of three massless flavours. We provide the complete\nformulae for the two topological observables in the isospin limit, and predict\ntheir values in the particular setting of the recent analysis of the RBC/UKQCD\ncollaboration. We show that a combination of the topological susceptibility and\nthe fourth cumulant is able to pin down the three-flavour condensate in a\nparticularly clean way in the case of three degenerate quarks.", "category": "hep-lat" }, { "text": "Semileptonic decays $B\\rightarrow D^{(*)}l\u03bd$ at nonzero recoil: We have analyzed the semileptonic decays $B\\rightarrow D\\ell\\nu$ and\n$B\\rightarrow D^*\\ell\\nu$ on the full suite of MILC (2+1)-flavor asqtad\nensembles with lattice spacings as small as 0.045 fm and light-to-strange-quark\nmass ratios as low as 1/20. We use the Fermilab interpretation of the clover\naction for heavy valence quarks and the asqtad action for light valence quarks.\nWe compute the hadronic form factors for $B\\rightarrow D$ at both zero and\nnonzero recoil and for $B\\rightarrow D^*$ at zero recoil. We report our results\nfor $|V_{cb}|$.", "category": "hep-lat" }, { "text": "Beauty mesons in $N_f=2+1+1+1 $ lattice QCD with exact chiral symmetry: We present the first study of $N_f=2+1+1+1$ lattice QCD with domain-wall\nquarks. The $(b, c, s)$ quarks are physical, while the $(u, d)$ quarks are\nheavier than their physical masses, with the pion mass $ \\sim 700 $ MeV. The\ngauge ensemble is generated by hybrid Monte Carlo simulation with the Wilson\ngauge action for the gluons, and the optimal domain-wall fermion action for the\nquarks. Using point-to-point quark propagators, we measure the time-correlation\nfunctions of quark-antiquark meson interpolators with quark contents $\\bar b\nb$, $\\bar b c$, $\\bar b s$, and $ \\bar c c$, and obtain the masses of the\nlow-lying mesons. They are in good agreement with the experimental values, plus\nsome predictions which have not been observed in experiments. Moreover, we also\ndetermine the masses of $(b, c, s)$ quarks.", "category": "hep-lat" }, { "text": "Improved Lattice Renormalization Group Techniques: We compute the bare step-scaling function $s_b$ for SU(3) lattice gauge\ntheory with $N_f = 12$ massless fundamental fermions, using the\nnon-perturbative Wilson-flow-optimized Monte Carlo Renormalization Group\ntwo-lattice matching technique. We use a short Wilson flow to approach the\nrenormalized trajectory before beginning RG blocking steps. By optimizing the\nlength of the Wilson flow, we are able to determine an $s_b$ corresponding to a\nunique discrete $\\beta$ function, after a few blocking steps. We carry out this\nstudy using new ensembles of 12-flavor gauge configurations generated with\nexactly massless fermions, using volumes up to $32^4$. The results are\nconsistent with the existence of an infrared fixed point (IRFP) for all\ninvestigated lattice volumes and number of blocking steps. We also compare\ndifferent renormalization schemes, each of which indicates an IRFP at a\nslightly different value of the bare coupling, as expected for an IR-conformal\ntheory.", "category": "hep-lat" }, { "text": "Instanton Distribution in Quenched and Full QCD: In order to optimize cooling as a technique to study the instanton content of\nthe QCD vacuum, we have studied the effects of alternative algorithms, improved\nactions and boundary conditions on the evolution of single instantons and\ninstanton anti-instanton pairs. Using these results, we have extracted and\ncompared the instanton content of quenched and full QCD.", "category": "hep-lat" }, { "text": "Compactified N=1 supersymmetric Yang-Mills theory on the lattice:\n Continuity and the disappearance of the deconfinement transition: Fermion boundary conditions play a relevant role in revealing the confinement\nmechanism of N=1 supersymmetric Yang-Mills theory with one compactified\nspace-time dimension. A deconfinement phase transition occurs for a\nsufficiently small compactification radius, equivalent to a high temperature in\nthe thermal theory where antiperiodic fermion boundary conditions are applied.\nPeriodic fermion boundary conditions, on the other hand, are related to the\nWitten index and confinement is expected to persist independently of the length\nof the compactified dimension. We study this aspect with lattice Monte Carlo\nsimulations for different values of the fermion mass parameter that breaks\nsupersymmetry softly. We find a deconfined region that shrinks when the fermion\nmass is lowered. Deconfinement takes place between two confined regions at\nlarge and small compactification radii, that would correspond to low and high\ntemperatures in the thermal theory. At the smallest fermion masses we find no\nindication of a deconfinement transition. These results are a first signal for\nthe predicted continuity in the compactification of supersymmetric Yang-Mills\ntheory.", "category": "hep-lat" }, { "text": "The static quark self-energy at large orders from NSPT: Using Numerical Stochastic Perturbation Theory (NSPT), we calculate the\nstatic self-energy of SU(3) gauge theory up to order \\alpha^{20}. Simulations\non a large set of different lattice volumes allow for a careful treatment of\nfinite size effects. The resulting infinite volume perturbative series of the\nstatic self-energy is in remarkable agreement with the predicted asymptotic\nbehaviour of high order expansions, namely with a factorial growth of\nperturbative coefficients known as renormalon.", "category": "hep-lat" }, { "text": "Form and index of Ginsparg-Wilson fermions: We clarify the questions rised by a recent example of a lattice Dirac\noperator found by Chiu. We show that this operator belongs to a class based on\nthe Cayley transformation and that this class on the finite lattice generally\ndoes not admit a nonvanishing index, while in the continuum limit, due to\noperator properties in Hilbert space, this defect is no longer there. Analogous\nobservations are made for the chiral anomaly. We also elaborate on various\naspects of the underlying sum rule for the index.", "category": "hep-lat" }, { "text": "A library of extended high-temperature expansions of basic observables\n for the spin S Ising models on two- and three-dimensional lattices: We present an on-line library of unprecedented extension for high-temperature\nexpansions of basic observables in the Ising models of general spin S, with\nnearest-neighbor interactions.\n We have tabulated through order beta^{25} the series for the nearest-neighbor\ncorrelation function, the susceptibility and the second correlation moment in\ntwo dimensions on the square lattice, and, in three dimensions, on the\nsimple-cubic and the body-centered cubic lattices. The expansion of the second\nfield derivative of the susceptibility is also tabulated through beta^{23} for\nthe same lattices. We have thus added several terms (from four up to thirteen)\nto the series already published for spin\n S=1/2,1,3/2,2,5/2,3,7/2,4,5,infinity.", "category": "hep-lat" }, { "text": "Gribov copies, Lattice QCD and the gluon propagator: We address the problem of Gribov copies in lattice QCD. The gluon propagator\nis computed, in the Landau gauge, using 302 ($\\beta = 5.8$) $12^4$\nconfigurations gauge fixed to different copies. The results of the simulation\nshows that: i) the effect of Gribov copies is small (less than 10%); ii) Gribov\ncopies change essentially the lowest momenta components ($q < 2.6$ GeV); iii)\nwithin the statistical accuracy of our simulation, the effect of Gribov copies\nis resolved if statistical errors are multiplied by a factor of two or three.\nMoreover, when modelling the gluon propagator, different sets of Gribov copies\nproduce different sets of parameters not, necessarily, compatible within one\nstandard deviation. Finally, our data supports a gluon propagator which, for\nlarge momenta, behaves like a massive gluon propagator with a mass of 1.1 GeV.", "category": "hep-lat" }, { "text": "Quenched scalar meson correlator with Domain Wall Fermions: We study the singlet and non-singlet scalar-meson masses using domain wall\nfermions and the quenched approximation. The singlet mass is found to be\nsmaller than the non-singlet mass and indicates that the lowest singlet meson\nstate could be lighter than 1 GeV. The two-point functions for very small quark\nmasses are compared with expectations from the small-volume chiral perturbation\ntheory and the presence of fermionic zero modes.", "category": "hep-lat" }, { "text": "The sign problem and the Lefschetz thimble: Recently, we have proposed a novel approach (arxiv:1205.3996) to deal with\nthe sign problem that hinders Monte Carlo simulations of many quantum field\ntheories (QFTs). The approach consists in formulating the QFT on a Lefschetz\nthimble. In this paper we concentrate on the application to a scalar field\ntheory with a sign problem. In particular, we review the formulation and the\njustification of the approach, and we also describe the Aurora Monte Carlo\nalgorithm that we are currently testing.", "category": "hep-lat" }, { "text": "Finite Temperature Phase Transition in SU(2) Lattice Gauge Theory with\n Extended Action: We study the three dimensional fundamental-adjoint $SU(2)$ lattice gauge\ntheory at finite temperature by Monte Carlo simulations. We find that the\nfinite temperature deconfinement phase transition line joins the first order\nbulk phase transition line at its endpoint. Moreover, across the bulk\ntransition line, the Polyakov loop undergoes a discontinuous jump implying the\nexistence of both confining and deconfining phases on its two sides.\nImplications for universality and the nature of the confining-deconfining\ntransition are discussed.", "category": "hep-lat" }, { "text": "Investigation of Doubly Heavy Tetraquark Systems using Lattice QCD: We search for possibly existent bound states in the heavy-light tetraquark\nchannels with quark content $ \\bar{b}\\bar{b}ud $, $ \\bar{b}\\bar{b}us $ and $\n\\bar{b}\\bar{c}ud $ using lattice QCD. We carry out calculations on several\ngauge link ensembles with $ N_f=2+1 $ flavours of domain-wall fermions and\nconsider a basis of local and non-local interpolators. Besides extracting the\nenergy spectrum from the correlation matrices, we also perform a L\\\"uscher\nanalysis to extrapolate our results to infinite volume.", "category": "hep-lat" }, { "text": "Width of the flux tube in compact U(1) gauge theory in three dimensions: We study the squared width and the profile of flux tubes in compact U(1)\nlattice gauge theory in three spacetime dimensions. The results obtained from\nnumerical calculations in the dual formulation of this confining theory are\ncompared with predictions from an effective bosonic-string model and from the\ndual-superconductor model: it is found that the former fails at describing the\nquantitative features of the flux tube, while the latter is in good agreement\nwith Monte Carlo data. The analytical interpretation of these results (in the\nlight of the semi-classical analysis by Polyakov) is pointed out, and a\ncomparison with non-Abelian gauge theories in four spacetime dimensions is\ndiscussed.", "category": "hep-lat" }, { "text": "Ising description of the transition region in SU(3) gauge theory at\n finite temperature: We attempt the numerical construction of an effective action in three\ndimensions for Ising spins which represent the Wilson lines in the\nfour-dimensional SU(3) gauge theory at finite temperature. For each\nconfiguration of the gauge theory, each spin is determined by averaging the\nWilson lines over a small neighborhood and then projecting the average to +/-1\naccording to whether the neighborhood is ordered or disordered. The effective\nIsing action, determined via the lattice Schwinger-Dyson equations, contains\neven (two-spin) and odd (one- and three-spin) terms with short range. We find\nthat the truncation to Ising degrees of freedom produces an effective action\nwhich is discontinuous across the gauge theory's phase transition. This\ndiscontinuity may disappear if the effective action is made more elaborate.", "category": "hep-lat" }, { "text": "Domain decomposition and multilevel integration for fermions: The numerical computation of many hadronic correlation functions is\nexceedingly difficult due to the exponentially decreasing signal-to-noise ratio\nwith the distance between source and sink. Multilevel integration methods,\nusing independent updates of separate regions in space-time, are known to be\nable to solve such problems but have so far been available only for pure gauge\ntheory. We present first steps into the direction of making such integration\nschemes amenable to theories with fermions, by factorizing a given observable\nvia an approximated domain decomposition of the quark propagator. This allows\nfor multilevel integration of the (large) factorized contribution to the\nobservable, while its (small) correction can be computed in the standard way.", "category": "hep-lat" }, { "text": "THE QCD ABACUS: A New Formulation for Lattice Gauge Theories: A quantum Hamiltonian is constructed for SU(3) lattice QCD entirely from\ncolor triplet Fermions --- the standard quarks and a new Fermionic\n``constituent'' of the gluon we call ``rishons''. The quarks are represented by\nDirac spinors on each site and the gauge fields by rishon-antirishon bilinears\non each link which together with the local gauge transforms are the generators\nof an SU(6) algebra. The effective Lagrangian for the path integral lives in\n$R^4 \\times S^1$ Euclidean space with a compact ``fifth time'' of circumference\n($\\beta$) and non-Abelian charge ($e^2$) both of which carry dimensions of\nlength. For large $\\beta$, it is conjectured that continuum QCD is reached and\nthat the dimensionless ratio $g^2 = e^2/\\beta$ becomes the QCD gauge coupling.\nThe quarks are introduced as Kaplan chiral Fermions at either end of the finite\nslab in fifth time. This talk will emphasize the gauge and algebraic structure\nof the rishon or link Fermions and the special properties that may lead to fast\ndiscrete dynamics for numerical simulations and new theoretical insight.", "category": "hep-lat" }, { "text": "The principle of indirect elimination: The principle of indirect elimination states that an algorithm for solving\ndiscretized differential equations can be used to identify its own\nbad-converging modes. When the number of bad-converging modes of the algorithm\nis not too large, the modes thus identified can be used to strongly improve the\nconvergence. The method presented here is applicable to any standard algorithm\nlike Conjugate Gradient, relaxation or multigrid. An example from theoretical\nphysics, the Dirac equation in the presence of almost-zero modes arising from\ninstantons, is studied. Using the principle, bad-converging modes are removed\nefficiently. Applied locally, the principle is one of the main ingredients of\nthe Iteratively Smooting Unigrid algorithm.", "category": "hep-lat" }, { "text": "Fermion RG blocking transformations and IR structure: We explore fermion RG block-spinning transformations on the lattice with the\naim of studying the IR structure of gauge theories and, in particular, the\nexistence of IR fixed points for varying fermion content. In the case of light\nfermions the main concern and difficulty is ensuring locality of any adopted\nblocking scheme. We discuss the problem of constructing a local blocked fermion\naction in the background of arbitrary gauge fields. We then discuss the\ncarrying out of accompanying gauge field blocking. In the presence of the\nblocked fermions implementation of MCRG is not straightforward. By adopting\njudicious approximations we arrive at an easily implementable approximate RG\nrecursion scheme that allows quick, inexpensive estimates of the location of\nconformal windows for various groups and fermion representations. We apply this\nscheme to locate the conformal windows in the case of SU(2) and SU(3) gauge\ngroups. Some of the reasons for the apparent efficacy of this and similar\ndecimation schemes are discussed.", "category": "hep-lat" }, { "text": "Onium Masses with Three Flavors of Dynamical Quarks: We have greatly extended an earlier calculation of the charmonium spectrum on\nthree flavor dynamical quark ensembles by using more recent ensembles generated\nby the MILC collaboration. The heavy quarks are treated using the Fermilab\nformulation. The charmonium state masses are in reasonable agreement with the\nobserved spectrum; however, some of the spin splittings may still be too small.", "category": "hep-lat" }, { "text": "The Euclidean two-point correlation function of the topological charge\n density: We study the Euclidean two-point correlation function $G_q(x)$ of the\ntopological charge density in QCD. A general statement based on reflection\npositivity tells us that $G_q(x)<0$ for $x\\neq 0 $. On the other hand the\ntopological susceptibility $\\chi_q=\\int d^d x G_q(x)$ is a positive quantity.\nThis indicates that $G_q(x)$ developes a positive contact term at $x=0$, that\ncontributes to the determination of the physical value of $\\chi_q$. We show\nexplicitly these features of $G_q(x)$ in a solvable nontrivial continuum model,\nthe two-dimensional $CP^{N-1}$ model in the large-N limit. A similar analysis\nis done on the lattice.", "category": "hep-lat" }, { "text": "Performance of lattice QCD programs on CP-PACS: The CP-PACS is a massively parallel MIMD computer with the theoretical peak\nspeed of 614 GFLOPS which has been developed for computational physics\napplications at the University of Tsukuba, Japan. We report on the performance\nof the CP-PACS computer measured during recent production runs using our\nQuantum Chromodynamics code for the simulation of quarks and gluons in particle\nphysics. With the full 2048 processing nodes, our code shows a sustained speed\nof 237.5 GFLOPS for the heat-bath update of gluon variables, 264.6 GFLOPS for\nthe over-relaxation update, and 325.3 GFLOPS for quark matrix inversion with an\neven-odd preconditioned minimal residual algorithm.", "category": "hep-lat" }, { "text": "Infrared behavior of the Faddeev-Popov operator in Coulomb gauge QCD: We calculate the eigenvalue distribution of the Faddeev-Popov operator in\nCoulomb gauge QCD using quenched SU(3) lattice simulation. In the confinement\nphase, the density of the low-lying eigenvalues increases with lattice volume,\nand the confinement criterion is satisfied. Moreover, even in the deconfinement\nphase, the behavior of the FP eigenvalue density is qualitatively the same as\nin the confinement phase. This is consistent with the fact that the\ncolor-Coulomb potential is not screened in the deconfined phase.", "category": "hep-lat" }, { "text": "Understanding Parton Distributions from Lattice QCD: Present Limitations\n and Future Promise: This talk will explain how ground state matrix elements specifying moments of\nquark density and spin distributions in the nucleon have been calculated in\nfull QCD, show how physical extrapolation to the chiral limit including the\nphysics of the pion cloud resolves previous apparent conflicts with experiment,\nand describe the computational resources required for a definitive comparison\nwith experiment.", "category": "hep-lat" }, { "text": "(Approximate) Low-Mode Averaging with a new Multigrid Eigensolver: We present a multigrid based eigensolver for computing low-modes of the\nHermitian Wilson Dirac operator. For the non-Hermitian case multigrid methods\nhave already replaced conventional Krylov subspace solvers in many lattice QCD\ncomputations. Since the $\\gamma_5$-preserving aggregation based interpolation\nused in our multigrid method is valid for both, the Hermitian and the\nnon-Hermitian case, inversions of very ill-conditioned shifted systems with the\nHermitian operator become feasible. This enables the use of multigrid within\nshift-and-invert type eigensolvers. We show numerical results from our MPI-C\nimplementation of a Rayleigh quotient iteration with multigrid. For\nstate-of-the-art lattice sizes and moderate numbers of desired low-modes we\nachieve speed-ups of an order of magnitude and more over PARPACK. We show\nresults and develop strategies how to make use of our eigensolver for\ncalculating disconnected contributions to hadronic quantities that are noisy\nand still computationally challenging. Here, we explore the possible benefits,\nusing our eigensolver for low-mode averaging and related methods with high and\nlow accuracy eigenvectors. We develop a low-mode averaging type method using\nonly a few of the smallest eigenvectors with low accuracy. This allows us to\navoid expensive exact eigensolves, still benefitting from reduced statistical\nerrors.", "category": "hep-lat" }, { "text": "Constraining $1+\\mathcal{J}\\to 2$ coupled-channel amplitudes in\n finite-volume: Whether one is interested in accessing the excited spectrum of hadrons or\ntesting the standard model of particle physics, electroweak transition\nprocesses involving multi-hadron channels in the final state play an important\nrole in a variety of experiments. Presently the primary theoretical tool with\nwhich one can study such reactions is lattice QCD, which is defined in a finite\nspacetime volume. In this work, we investigate the feasibility of implementing\nexisting finite-volume formalism in realistic lattice QCD calculation of\nreactions in which a stable hadron can transition to one of several two-hadron\nchannels under the action of an external current. We provide a conceptual\ndescription of the coupled-channel transition formalism, a practical roadmap\nfor carrying out a calculation, and an illustration of the approach using\nsynthetic data for two non-trivial resonant toy models. The results provide a\nproof-of-principle that such reactions can indeed be constrained using\nmodern-day lattice QCD calculations, motivating explicit computation in the\nnear future.", "category": "hep-lat" }, { "text": "First experiences with HMC for dynamical overlap fermions: We describe an HMC algorithm for dynamical overlap fermions which makes use\nof their good chiral properties. We test the algorithm in the Schwinger model.\nTopological sectors are readily changed even in the massless case.", "category": "hep-lat" }, { "text": "Fixed-scale approach to finite-temperature lattice QCD with shifted\n boundaries: We study the thermodynamics of the SU(3) gauge theory using the fixed-scale\napproach with shifted boundary conditions. The fixed-scale approach can reduce\nthe numerical cost of the zero-temperature part in the equation of state\ncalculations, while the number of possible temperatures is limited by the\ninteger $N_t$, which represents the temporal lattice extent. The shifted\nboundary conditions can overcome such a limitation while retaining the\nadvantages of the fixed-scale approach. Therefore, our approach enables the\ninvestigation of not only the equation of state in detail, but also the\ncalculation of the critical temperature with increased precision even with the\nfixed-scale approach. We also confirm numerically that the boundary conditions\nsuppress the lattice artifact of the equation of state, which has been\nconfirmed in the non-interacting limit.", "category": "hep-lat" }, { "text": "Spectrum of the Dirac Operator and Multigrid Algorithm with Dynamical\n Staggered Fermions: Complete spectra of the staggered Dirac operator $\\Dirac$ are determined in\nquenched four-dimensional $SU(2)$ gauge fields, and also in the presence of\ndynamical fermions.\n Periodic as well as antiperiodic boundary conditions are used.\n An attempt is made to relate the performance of multigrid (MG) and conjugate\ngradient (CG) algorithms for propagators with the distribution of the\neigenvalues of~$\\Dirac$.\n The convergence of the CG algorithm is determined only by the condition\nnumber~$\\kappa$ and by the lattice size.\n Since~$\\kappa$'s do not vary significantly when quarks become dynamic,\n CG convergence in unquenched fields can be predicted from quenched\nsimulations.\n On the other hand, MG convergence is not affected by~$\\kappa$ but depends on\nthe spectrum in a more subtle way.", "category": "hep-lat" }, { "text": "Radiative improvement of the lattice NRQCD action using the background\n field method and application to the hyperfine splitting of quarkonium states: We present the first application of the background field method to\nNon-Relativistic QCD (NRQCD) on the lattice in order to determine the one-loop\nradiative corrections to the coefficients of the NRQCD action in a manifestly\ngauge-covariant manner. The coefficient of the $\\sigma\\cdot B$ term in the\nNRQCD action is computed at the one-loop level; the resulting shift of the\nhyperfine splitting of bottomonium is found to bring the lattice predictions in\nline with experiment.", "category": "hep-lat" }, { "text": "Light quark correlators in a mixed-action setup: We report our progress in simulating Neuberger valence fermions on N_f=2\nWilson O(a)-improved sea quarks. We compute correlators with valence quark\nmasses both in the p- and in the epsilon-regime, and we match the results with\nthe predictions of the Chiral Effective Theory in the mixed regime. This allows\nus to extract the Low Energy Couplings (LECs) of the N_f=2 theory and to test\nthe validity of the approach.", "category": "hep-lat" }, { "text": "Microscopic Origin of \\boldmath{$U_A(1)$} Symmetry Violation in the High\n Temperature Phase of QCD: We investigate the low-lying eigenmodes of the Dirac matrix with the aim to\ngain more insight into the temperature dependence of the anomalous $U_A(1)$\nsymmetry. We use the overlap operator to probe dynamical QCD configurations\ngenerated with (2+1)-flavors of highly improved staggered quarks. We find no\nevidence of a gap opening up in the infrared region of the eigenvalue spectrum\neven at $1.5\\,T_c$, $T_c$ being the chiral crossover temperature. Instead, we\nobserve an accumulation of near-zero eigenmodes. We argue that these near-zero\neigenmodes are primarily responsible for the anomalous breaking of the axial\nsymmetry still being effective. At $1.5\\,T_c$, these near-zero eigenmodes\nremain localized and their distribution is consistent with the dilute instanton\ngas picture. At this temperature, the average size of the instantons is\n$0.223(8)\\,\\text{fm}$ and their density is $0.147(7)\\,\\text{fm}^{-4}$.", "category": "hep-lat" }, { "text": "The Coulomb flux tube revisited: We perform $SU(2)$ Yang-Mills lattice simulation of the electric field\ndistribution in the Coulomb gauge for different values of $\\beta$ to further\ninvestigate the nature of the Coulomb flux tube.", "category": "hep-lat" }, { "text": "Critical Behavior of the Schwinger Model with Wilson Fermions: We present a detailed analysis, in the framework of the MFA approach, of the\ncritical behaviour of the lattice Schwinger model with Wilson fermions on\nlattices up to $24^2$, through the study of the Lee-Yang zeros and the specific\nheat. We find compelling evidence for a critical line ending at $\\kappa = 0.25$\nat large $\\beta$. Finite size scaling analysis on lattices $8^2,12^2,16^2,\n20^2$ and $24^2$ indicates a continuous transition. The hyperscaling relation\nis verified in the explored $\\beta$ region.", "category": "hep-lat" }, { "text": "Lattice study of the Schwinger model at fixed topology: At small lattice spacing QCD simulations are expected to become stuck in a\nsingle topological sector. Observables evaluated in a fixed topological sector\ndiffer from their counterparts in full QCD, i.e. at unfixed topology, by volume\ndependent corrections. We investigate these corrections in the two-flavor\nSchwinger model, which is in several aspects similar to QCD, using Wilson\nfermions. We also try to remove these corrections by suitable extrapolations to\ninfinite volume.", "category": "hep-lat" }, { "text": "The static energy of a quark-antiquark pair from Laplacian eigenmodes: We test a method for computing the static quark-antiquark potential in\nlattice QCD, which is not based on Wilson loops, but where the trial states are\nformed by eigenvector components of the covariant lattice Laplace operator. The\nruntime of this method is significantly smaller than the standard Wilson loop\ncalculation, when computing the static potential not only for on-axis, but also\nfor many off-axis quark-antiquark separations, i.e., when a fine spatial\nresolution is required. We further improve the signal by using multiple\neigenvector pairs, weighted with Gaussian profile functions of the eigenvalues,\nproviding a basis for a generalized eigenvalue problem (GEVP), as it was\nrecently introduced to improve distillation in meson spectroscopy. We show\nresults with the new method for the static potential with dynamical fermions\nand demonstrate its efficiency compared to traditional Wilson loop\ncalculations. The method presented here can also be applied to compute hybrid\nor tetra-quark potentials and to static-light systems.", "category": "hep-lat" }, { "text": "Fisher's zeros as boundary of RG flows in complex coupling space: We discuss the possibility of extending the RG flows to complex coupling\nspaces. We argue that the Fisher's zeros are located at the boundary of the\ncomplex basin of attraction of IR fixed points. We support this picture with\nnumerical calculations at finite volume for2D O(N) models in the large-N limit\nand the hierarchical Ising model using the two-lattice matching method. We\npresent numerical evidence supporting the idea that, as the volume increases,\nthe Fisher's zeros of 4-dimensional pure gauge SU(2) lattice gauge theory with\na Wilson action, stabilize at a distance larger than 0.1 from the real axis in\nthe complex beta=4/g^2 plane. We show that when a positive adjoint term is\nadded, the zeros get closer to the real axis. We compare the situation with the\nU(1) case. We discuss the implications of this new framework for proofs of\nconfinement and searches for nontrivial IR fixed points in models beyond the\nstandard model.", "category": "hep-lat" }, { "text": "A study of center and chiral symmetry realization in thermal\n $\\mathcal{N}=1$ super Yang-Mills theory using the gradient flow: The realization of center and chiral symmetries in $\\mathcal{N}=1$ super\nYang-Mills theory (SYM) is investigated on a four-dimensional Euclidean lattice\nby means of Monte Carlo methods. At zero temperature this theory is expected to\nconfine external fundamental charges and to have a non-vanishing gaugino\ncondensate, which breaks the non-anomalous Z$_{2\\textrm{N}_{c}}$ chiral\nsymmetry. In previous studies at finite temperatures, the phase transitions\ncorresponding to deconfinement and chiral restoration were observed to occur at\nroughly the same critical temperature for SU(2) gauge group. We find further\nevidences for this observation from new measurements at smaller lattice\nspacings using the fermion gradient flow, and we discuss the agreement of our\nfindings with conjectures from superstring theory. The implementation of the\ngradient flow technique allows us also to estimate, for the first time, the\ncondensate at zero temperatures and zero gaugino mass with Wilson fermions.", "category": "hep-lat" }, { "text": "Lattice QCD calculation of the electroweak box diagrams for the kaon\n semileptonic decays: We present a lattice QCD calculation of the axial $\\gamma W$-box diagrams\nrelevant for the kaon semileptonic decays. We utilize a recently proposed\nmethod, which connects the electroweak radiative corrections in Sirlin's\nrepresentation to that in chiral perturbation theory. It allows us to use the\naxial $\\gamma W$-box correction in the SU(3) limit to obtain the low energy\nconstants for chiral perturbation theory. From first principles our results\nconfirm the previously used low energy constants provided by the minimal\nresonance model with a significant reduction in uncertainties.", "category": "hep-lat" }, { "text": "Leading order mesonic and baryonic SU(3) low energy constants from $N_f\n = 3$ lattice QCD: We determine the leading order mesonic~($B_0$ and $F_0$) and baryonic~($m_0$,\n$D$ and $F$) SU(3) chiral perturbation theory low energy constants from lattice\nQCD. We employ gauge ensembles with $N_f=3$ (i.e., $m_u=m_d=m_s$)\nnon-perturbatively improved Wilson fermions at six distinct values of the\nlattice spacing in the range $a\\approx (0.039 - 0.098)$ fm, which constitute a\nsubset of the Coordinated Lattice Simulations (CLS) gauge ensembles. The\npseudoscalar meson mass $M_\\pi$ ranges from around $430$ MeV down to $240$ MeV\nand the linear spatial lattice extent $L$ from $6.4\\,M_{\\pi}^{-1}$ to\n$3.3\\,M_{\\pi}^{-1}$, where $ L M_\\pi \\geq 4$ for the majority of the ensembles.\nThis allows us to perform a controlled extrapolation of all the low energy\nconstants to the chiral, infinite volume and continuum limits. We find the\nSU(3) chiral condensate and $F_0$ to be smaller than their SU(2) counterparts\nwhile the Gell-Mann--Oakes--Renner parameters $B_0\\approx B$ are similar.\nRegarding baryonic LECs, we obtain $F/D = 0.612^{(14)}_{(12)}$.", "category": "hep-lat" }, { "text": "Canonical Transformations and Loop Formulation of SU(N) Lattice Gauge\n Theories: We construct canonical transformations to reformulate SU(N) Kogut-Susskind\nlattice gauge theory in terms of a set of fundamental loop & string flux\noperators along with their canonically conjugate loop & string electric fields.\nWe show that as a consequence of SU(N) Gauss laws all SU(N) string degrees of\nfreedom become cyclic and decouple from the physical Hilbert space ${\\cal\nH}^p$. The canonical relations between the initial SU(N) link operators and the\nfinal SU(N) loop & string operators over the entire lattice are worked out in a\nself consistent manner. The Kogut-Susskind Hamiltonian rewritten in terms of\nthe fundamental physical loop operators has global SU(N) invariance. There are\nno gauge fields. We further show that the $(1/g^2)$ magnetic field terms on\nplaquettes create and annihilate the fundamental plaquette loop fluxes while\nthe $(g^2)$ electric field terms describe all their interactions. In the weak\ncoupling ($g^2 \\rightarrow 0$) continuum limit the SU(N) loop dynamics is\ndescribed by SU(N) spin Hamiltonian with nearest neighbour interactions. In the\nsimplest SU(2) case, where the canonical transformations map the SU(2) loop\nHilbert space into the Hilbert spaces of hydrogen atoms, we analyze the special\nrole of the hydrogen atom dynamical symmetry group $SO(4,2)$ in the loop\ndynamics and the spectrum. A simple tensor network ansatz in the SU(2) gauge\ninvariant hydrogen atom loop basis is discussed.", "category": "hep-lat" }, { "text": "Improved actions and lattice coarsening effects in MCRG studies in SU(2)\n LGT: We study decimation procedures and effective (improved) actions in the\nframework of Monte Carlo Renormalization Group (MCRG). Particular attention is\npaid to matching the form of the effective action to the decimation procedure\nparameters. Using the static quark-antiquark potential in SU(2) LGT we probe\ndifferent distance scales and find that an effective action containing multiple\ngroup representations is capable of reproducing long distance physics well. In\nparticular, appropriate matching results in the practical elimination of the\ncoarsening/fining effect of the lattice spacing under decimation. The short\ndistance regime of the effective theory is also studied. We next carry out\nstudies of effective actions involving both multiple representations and loops\nbeyond the single plaquette towards determining an improved action good over a\nwide length scale regime.", "category": "hep-lat" }, { "text": "Nucleon form factors and root-mean-square radii on a (10.8 fm$)^4$\n lattice at the physical point: We present the nucleon form factors and root-mean-square (RMS) radii measured\non a (10.8 fm$)^4$ lattice at the physical point. We compute the form factors\nat small momentum transfer region in $q^2\\le 0.102$ GeV$^2$ with the standard\nplateau method choosing four source-sink separation times $t_{\\rm sep}$ from\n0.84 to 1.35 fm to examine the possible excited state contamination. We obtain\nthe electric and magnetic form factors and their RMS radii for not only the\nisovector channel but also the proton and neutron ones without the disconnected\ndiagram. We also obtain the axial-vector coupling and the axial radius from the\naxial-vector form factor. We find that these three form factors do not show\nlarge $t_{\\rm sep}$ dependence in our lattice setup. On the other hand, the\ninduced pseudoscalar and pseudoscalar form factors show the clear effects of\nthe excited state contamination, which affect the generalized\nGoldberger-Treiman relation.", "category": "hep-lat" }, { "text": "Derivation of Chiral Lagrangians from Random Lattice QCD: In our work we extend the ideas of the derivation of the chiral effective\ntheory from the lattice QCD [1] to the case of the random lattice\nregularization of QCD. Such procedure allows in principle to find contribution\nof any order into the chiral effective lagrangian. It is shown that an infinite\nsubseries of the chiral perturbation can be summed up into tne Born-Infeld term\nand the logarithmic correction to them.", "category": "hep-lat" }, { "text": "Supersymmetric Yang-Mills Theories from Domain Wall Fermions: We present work in progress on employing domain wall fermions to simulate N=1\nsupersymmetric Yang-Mills theories on the lattice in d=4 and d=3 dimensions.\nThe geometrical nature of domain wall fermions gives simple insights into how\nto construct these theories. We also discuss the obstacles associated with\nsimulating the N=2 theory in d=4.", "category": "hep-lat" }, { "text": "Ginsparg-Wilson relation and lattice Weyl fermions: We demonstrate that in the topologically trivial gauge sector the\nGinsparg-Wilson relation for lattice Dirac operators admits an exactly gauge\ninvariant path integral formulation of the Weyl fermions on a lattice.", "category": "hep-lat" }, { "text": "Probing the Region of Massless Quarks in Quenched Lattice QCD using\n Wilson Fermions: We study the spectrum of $H(m)=\\gamma_5 W(-m)$ with $W(m)$ being the\nWilson-Dirac operator on the lattice with bare mass equal to $m$. The\nbackground gauge fields are generated using the SU(3) Wilson action at\n$\\beta=5.7$ on an $8^3\\times 16$ lattice. We find evidence that the spectrum of\n$H(m)$ is gapless for $1.02 < m < 2.0$, implying that the physical quark is\nmassless in this whole region.", "category": "hep-lat" }, { "text": "Comment on \"The QCD axion beyond the classical level: A lattice study\": We rebut the claim by Nakamura and Schierholz [1] that the mass of a\npotential axion needs to be no less than ~230MeV pointing out errors in both\ntheir analytic argument and numerical simulations.", "category": "hep-lat" }, { "text": "Gluon gravitational structure of hadrons of different spin: The gravitational form factors (GFFs) of hadrons encode the matrix elements\nof the energy momentum tensor of QCD. These quantities describe how energy,\nspin, and various mechanical properties of hadrons are carried by their quark\nand gluon constituents. We present the gluon GFFs of the pion, nucleon, $\\rho$\nmeson, and $\\Delta$ baryon as functions of the squared momentum transfer $t$ in\nthe region $0 \\leq -t < 2 \\; \\text{GeV}^2$, as determined in a lattice QCD\nstudy with pion mass $m_{\\pi} = 450(5) \\; \\text{MeV}$. By fitting the extracted\nGFFs using multipole and z-parameter expansion functional forms, we extract\nvarious gluon contributions to the energy, pressure, and shear force\ndistributions of the hadrons in the 3D and 2D Breit frames as well as in the\ninfinite momentum frame. We also obtain estimates for the corresponding gluon\nmechanical and mass radii, as well as the forward-limit gluon contributions to\nthe momentum fraction and angular momentum of the hadrons.", "category": "hep-lat" }, { "text": "Spontaneous supersymmetry breaking in the two-dimensional N=1\n Wess-Zumino model: We study the phase diagram of the two-dimensional N=1 Wess-Zumino model on\nthe lattice using Wilson fermions and the fermion loop formulation. We give a\ncomplete nonperturbative determination of the ground state structure in the\ncontinuum and infinite volume limit. We also present a determination of the\nparticle spectrum in the supersymmetric phase, in the supersymmetry broken\nphase and across the supersymmetry breaking phase transition. In the\nsupersymmetry broken phase we observe the emergence of the Goldstino particle.", "category": "hep-lat" }, { "text": "B Meson Decay Constants Using NRQCD: Recent results for B meson decay constants with NRQCD b-quarks and clover\nlight quarks are discussed. Perturbative matching factors through O($\\alpha/M$)\nare now available and incorporated into the analyses. An O($\\alpha a$)\nimprovement term to the heavy-light axial current is identified and included.\nThe slope of $f_{PS}\\sqrt{M_{PS}}$ versus $1/M_{PS}$ is significantly reduced\nby these corrections.", "category": "hep-lat" }, { "text": "Flavor Twisted Boundary Conditions, Pion Momentum, and the Pion\n Electromagnetic Form Factor: We investigate the utility of partially twisted boundary conditions in\nlattice calculations of meson observables. For dynamical simulations, we show\nthat the pion dispersion relation is modified by volume effects. In the isospin\nlimit, we demonstrate that the pion electromagnetic form factor can be computed\non the lattice at continuous values of the momentum transfer. Furthermore, the\nfinite volume effects are under theoretical control for extraction of the pion\ncharge radius.", "category": "hep-lat" }, { "text": "Topological susceptibility of $2d~\\mathrm{CP}^1$ or $\\mathrm{O}(3)$\n non-linear $\u03c3$-model: is it divergent or not?: The topological susceptibility of $2d$ $\\mathrm{CP}^{N-1}$ models is\nexpected, based on perturbative computations, to develop a divergence in the\nlimit $N \\to 2$, where these models reduce to the well-known non-linear\n$\\mathrm{O}(3)$ $\\sigma$-model. The divergence is due to the dominance of\ninstantons of arbitrarily small size and its detection by numerical lattice\nsimulations is notoriously difficult, because it is logarithmic in the lattice\nspacing. We approach the problem from a different perspective, studying the\nbehavior of the model when the volume is fixed in dimensionless lattice units,\nwhere perturbative predictions are turned into more easily checkable behaviors.\nAfter testing this strategy for $N = 3$ and $4$, we apply it to $N = 2$,\nadopting at the same time a multicanonic algorithm to overcome the problem of\nrare topological fluctuations on asymptotically small lattices. Our final\nresults fully confirm, by means of purely non-perturbative methods, the\ndivergence of the topological susceptibility of the $2d$ $\\mathrm{CP}^1$ model.", "category": "hep-lat" }, { "text": "Monopole Loop Distribution and Confinement in SU(2) Lattice Gauge Theory: The abelian-projected monopole loop distribution is extracted from maximal\nabelian gauge simulations. The number of loops of a given length falls as a\npower of the length nearly independent of lattice size. This power increases\nwith $\\beta=4/g^2$, reaching five around $\\beta=2.85$, beyond which loops any\nfinite fraction of the lattice size vanish in the infinite lattice limit,\nsuggesting the continuum theory lacks confinement.", "category": "hep-lat" }, { "text": "Weak Coupling Limit of U(1) Lattice Model in Fourier Basis: The transfer-matrix of the U(1) lattice model is considered in the Fourier\nbasis and in the weak coupling limit. The issues of Gauss law constraint and\ngauge invariant states are addressed in the Fourier basis. In particular, it is\nshown that in the strong coupling limit the gauge invariant Fourier states are\neffectively the finite size closed loop currents. In the weak coupling limit,\nhowever, the link-currents along periodic or infinite spatial directions find\ncomparable roles as gauge invariant states. The subtleties related to the\nextreme weak coupling of the transfer-matrix in the Fourier basis are\ndiscussed. A careful analysis of the zero eigenvalues of the matrix in the\nquadratic action leads to a safe extraction of the diverging group volume in\nthe limit $g\\to 0$. By means of the very basic notions and tools of the lattice\nmodel, the spectrum at the weak coupling limit for any dimension and size of\nlattice is obtained analytically. The spectrum at the weak coupling limit\ncorresponds to the expected one by the continuum model in the large lattice\nlimit.", "category": "hep-lat" }, { "text": "Running coupling in SU(2) with adjoint fermions: We present a measurement of the Schr\\\"odinger Functional running coupling in\nSU(2) lattice gauge theory with adjoint fermions. We use HEX smearing and\nclover improvement to reduce the discretization effects. We obtain a robust\ncontinuum limit for the step scaling, which confirms the existence of a\nnon-trivial fixed point.", "category": "hep-lat" }, { "text": "Spectral Analysis of Causal Dynamical Triangulations via Finite Element\n Method: We examine the dual graph representation of simplicial manifolds in Causal\nDynamical Triangulations (CDT) as a mean to build observables, and propose a\nnew representation based on the Finite Element Methods (FEM). In particular,\nwith the application of FEM techniques, we extract the (low-lying) spectrum of\nthe Laplace-Beltrami (LB) operator on the Sobolev space $H^1$ of scalar\nfunctions on piecewise flat manifolds, and compare them with corresponding\nresults obtained by using the dual graph representation. We show that, besides\nfor non-pathological cases in two dimensions, the dual graph spectrum and\nspectral dimension do not generally agree, neither quantitatively nor\nqualitatively, with the ones obtained from the LB operator on the continuous\nspace. We analyze the reasons of this discrepancy and discuss its possible\nimplications on the definition of generic observables built from the dual graph\nrepresentation.", "category": "hep-lat" }, { "text": "The dependence of observables on action parameters: Many applications in Lattice field theory require to determine the Taylor\nseries of observables with respect to action parameters. A primary example is\nthe determination of electromagnetic corrections to hadronic processes. We show\ntwo possible solutions to this general problem, one based on reweigting, that\ncan be considered a generalization of the RM123 method. The other based on the\nideas of Numerical Stochastic Perturbation Theory (NSPT) in the Hamiltonian\nformulation. We show that 1) the NSPT-based approach shows a much reduced\nvariance in the determination of the Taylor coefficients, and 2) That both\napproaches are related by a change of variables. Numerical results are shown\nfor the case of $\\lambda-\\phi^4$ in 4 dimensions, but we expect these\nobservations to be general. We conclude by commenting on the possible use of\nMachine Learning techniques to find similar change of variables that can\npotentially reduce the variance in Taylor coefficients.", "category": "hep-lat" }, { "text": "$\u03c1$ meson decay on asymmetrical lattices: We present a lattice QCD calculation of the characteristics of the $\\rho$\nmeson decay. The study is carried out on spatially asymmetric boxes using\nnHYP-smeared clover fermions in the quenched approximation. The resonance mass\nand coupling constant are calculate using the P-wave scattering phaseshifts, of\nthe isospin I=1 two-pion system. We use pion masses m_{\\pi}= 418 MeV and\nm_{\\pi}=312 MeV. In both cases, the $\\rho$ decay is kinematically feasible. We\nwork on lattice sizes N_z X 24^2 X 48 with lattice spacing a=0.1 fm and\nN_z=24,30,34,48.", "category": "hep-lat" }, { "text": "Dynamical quantum phase transitions in a noisy lattice gauge theory: Lattice gauge theories (LGTs) form an intriguing class of theories highly\nrelevant to both high-energy particle physics and low-energy condensed matter\nphysics with the rapid development of engineered quantum devices providing new\ntools to study e.g. dynamics of such theories. The massive Schwinger model is\nknown to exhibit intricate properties of more complicated theories and has\nrecently been shown to undergo dynamical quantum phase transitions out of\nequilibrium. With current technology, noise is inevitable and potentially fatal\nfor a successful quantum simulation. This paper studies the dynamics subject to\nnoise of a $(1+1)$D U$(1)$ quantum link model following a quench of the sign of\nthe mass term. We find that not only is the system capable of handling noise at\nrates realistic in NISQ-era devices, promising the possiblity to study the\ntarget dynamics with current technology, but the effect of noise can be\nunderstood in terms of simple models. Specifically the gauge-breaking nature of\nbit-flip channels results in exponential dampening of state amplitudes, and\nthus observables, which does not affect the structures of interest. This is\nespecially important as it demonstrates that the gauge theory can be\nsuccessfully studied with devices that only exhibit approximate gauge\ninvariance.", "category": "hep-lat" }, { "text": "Dynamics of the 2d Potts model phase transition: The dynamics of 2d Potts models, which are temperature driven through the\nphase transition using updating procedures in the Glauber universality class,\nis investigated. We present calculations of the hysteresis for the (internal)\nenergy and for Fortuin-Kasteleyn clusters. The shape of the hysteresis is used\nto define finite volume estimators of physical observables, which can be used\nto study the approach to the infinite volume limit. We compare with equilibrium\nconfigurations and the preliminary indications are that the dynamics leads to\nconsiderable alterations of the statistical properties of the configurations\nstudied.", "category": "hep-lat" }, { "text": "Study of Chiral Symmetry and $U(1)_A$ using Spatial Correlators for\n $N_f=2+1$ QCD at finite temperature with Domain Wall Fermions: Based on simulations of 2+1 flavor lattice QCD with M\\\"obius domain wall\nfermions at high temperatures, we compute a series of spatial correlation\nfunctions to study the screening masses in mesonic states. We compare these\nmasses with the symmetry relations for various quark masses and lattice sizes\nat temperatures above the critical point. Using these spatial correlation\nfunctions we examine the $SU(2)_L \\times SU(2)_R$ symmetry as well as the\nanomalously broken axial $U(1)_A$ symmetry. Additionally we explore a possible\nand emergent chiral-spin symmetry $SU(2)_{CS}$.", "category": "hep-lat" }, { "text": "Decomposition of the static potential in SU(3) gluodynamics: After fixing the Maximal Abelian gauge in SU(3) lattice gluodynamics we\ndecompose the nonabelian gauge field into the Abelian field created by Abelian\nmonopoles and the modified nonabelian field with monopoles removed. We then\ncalculate respective static potentials in the fundamental representation and\nshow that the sum of these potentials approximates the nonabelian static\npotential with good precision at all distances considered. Comparison with\nother ways of decomposition is made.", "category": "hep-lat" }, { "text": "Higher moments of charge fluctuations in QCD at high temperature: We present lattice results for baryon number, strangeness and electric charge\nfluctuations as well as their correlations at finite temperature and vanishing\nchemical potentials, i.e. under conditions relevant for RHIC and LHC. We find\nthat the fluctuations change rapidly at the transition temperature $T_c$ and\napproach the ideal quark gas limit already at approximately $1.5T_c$. This\nindicates that quarks are the relevant degrees of freedom that carry the\nquantum numbers of conserved charges at $T\\geq 1.5T_c$. At low temperature,\nqualitative features of the lattice results are well described by a hadron\nresonance gas model.", "category": "hep-lat" }, { "text": "SU(2) Flux Distributions on Finite Lattices: We studied SU(2) flux distributions on four dimensional euclidean lattices\nwith one dimension very large. By choosing the time direction appropriately we\ncan study physics in two cases: one is finite volume in the zero temperature\nlimit, another is finite temperature in the the intermediate to large volume\nlimit. We found that for cases of beta > beta crit there is no intrinsic string\nformation. Our lattices with beta > beta crit belong to intermediate volume\nregion, and the string tension in this region is due to finite volume effects.\nIn large volumes we found evidence for intrinsic string formation.", "category": "hep-lat" }, { "text": "2018 Update on $\\varepsilon_K$ with lattice QCD inputs: We present updated results for $\\varepsilon_K$ determined directly from the\nstandard model (SM) with lattice QCD inputs such as $\\hat{B}_K$, $|V_{cb}|$,\n$|V_{us}|$, $\\xi_0$, $\\xi_2$, $\\xi_\\text{LD}$, $F_K$, and $m_c$. We find that\nthe standard model with exclusive $|V_{cb}|$ and other lattice QCD inputs\ndescribes only 70% of the experimental value of $|\\varepsilon_K|$ and does not\nexplain its remaining 30%, which leads to a strong tension in $|\\varepsilon_K|$\nat the $4\\sigma$ level between the SM theory and experiment. We also find that\nthis tension disappears when we use the inclusive value of $|V_{cb}|$ obtained\nusing the heavy quark expansion based on QCD sum rules.", "category": "hep-lat" }, { "text": "Polarized and Unpolarized Nucleon Structure Functions from Lattice QCD: We report on a high statistics quenched lattice QCD calculation of the\ndeep-inelastic structure functions $F_1$, $F_2$, $g_1$ and $g_2$ of the proton\nand neutron. The theoretical basis for the calculation is the operator product\nexpansion. We consider the moments of the leading twist operators up to spin\nfour. Using Wilson fermions the calculation is done for three values of\n$\\kappa$, and we perform the extrapolation to the chiral limit. The\nrenormalization constants, which lead us from lattice to continuum operators,\nare calculated in perturbation theory to one loop order.", "category": "hep-lat" }, { "text": "Negative moment of inertia and rotational instability of gluon plasma: Using first-principle numerical simulations of the lattice SU(3) gauge\ntheory, we calculate the isothermal moment of inertia of the rigidly rotating\ngluon plasma. We find that the moment of inertia unexpectedly takes a negative\nvalue below the \"supervortical temperature\" $T_s = 1.50(10) T_c$, vanishes at\n$T = T_s$, and becomes a positive quantity at higher temperatures. The negative\nmoment of inertia indicates a thermodynamic instability of rigid rotation. We\nderive the condition of thermodynamic stability of the vortical plasma and show\nhow it relates to the scale anomaly and the magnetic gluon condensate. The\nrotational instability of gluon plasma shares a striking similarity with the\nrotational instabilities of spinning Kerr and Myers-Perry black holes.", "category": "hep-lat" }, { "text": "Coulomb gauge studies of SU(3) Yang-Mills theory on the lattice: We study the infrared behaviour of lattice SU(3) Yang-Mills theory in Coulomb\ngauge in terms of the ghost propagator, the Coulomb potential and the\ntransversal and the time-time component of the equal-time gluon propagator. In\nparticular, we focus on the Gribov problem and its impact on the observables.\nWe observe that the simulated annealing method is advantageous for fixing the\nCoulomb gauge in large volumes. We study finite size and discretization\neffects. While finite size effects can be controlled by the cone cut, and the\nghost propagator and the Coulomb potential become scaling functions with the\ncylinder cut, the equal-time gluon propagator does not show scaling in the\nconsidered range of the inverse coupling constant. The ghost propagator is\ninfrared enhanced. The Coulomb potential is now extended to considerably lower\nmomenta and shows a more complicated infrared regime. The Coulomb string\ntension satisfies Zwanziger's inequality, but its estimate can be considered\nonly preliminary because of the systematic Gribov effect that is particularly\nstrong for the Coulomb potential.", "category": "hep-lat" }, { "text": "Making chiral fermion actions (almost) gauge invariant using Laplacian\n gauge fixing: Straight foreward lattice descriptions of chiral fermions lead to actions\nthat break gauge invariance. I describe a method to make such actions gauge\ninvariant (up to global gauge transformations) with the aid of gauge fixing. To\nmake this prescription unambiguous, Laplacian gauge fixing is used, which is\nfree from Gribov ambiguities.", "category": "hep-lat" }, { "text": "Continuum Results for Light Hadronic Quantities using Domain Wall\n Fermions with the Iwasaki and DSDR Gauge Actions: We present preliminary continuum results for light hadronic quantities\nobtained by the RBC/UKQCD collaboration using domain wall fermions with both\nthe Iwasaki and the novel Dislocation Suppressing Determinant Ratio (DSDR)\ngauge actions. The DSDR action allows us to simulate at near physical quark\nmasses on a larger, coarser lattice (a^-1 = 1.4 GeV, L = 4.6 fm) while\nretaining good chiral symmetry properties. We discuss our ongoing combined\nanalysis of the three ensemble sets and give early results for the pion and\nkaon decay constants, quark masses and B_K.", "category": "hep-lat" }, { "text": "Solitons and spontaneous symmetry breaking in 2 and 4 dimensions: We show that mass generation in 1+1 and 3+1 dimensions may occur together\nwith spontaneous symmetry breaking.", "category": "hep-lat" }, { "text": "Aspects of Chiral Symmetry and the Lattice: I explore the non-perturbative issues entwining lattice gauge theory,\nanomalies, and chiral symmetry. After briefly reviewing the importance of\nchiral symmetry in particle physics, I discuss how anomalies complicate lattice\nformulations. Considerable information can be deduced from effective chiral\nLagrangians, helping interpret the expectations for lattice models and\nelucidating the role of the CP violating parameter $\\Theta$. I then turn to a\nparticularly elegant scheme for exploring this physics on the lattice. This\nuses an auxiliary extra space-time dimension, with the physical world being a\nfour dimensional interface.", "category": "hep-lat" }, { "text": "The Polyakov Loop and the Eigenvalues of the Dirac Operator: Aiming at the link between confinement and chiral symmetry the Polyakov loop\nrepresented as a spectral sum of eigenvalues of the Dirac operator was subject\nof recent studies. We analyze the volume dependence as well as the continuum\nbehavior of this quantity for quenched QCD using staggered fermions.\nFurthermore, we present first results using dynamical configurations.", "category": "hep-lat" }, { "text": "Expressing the three-particle finite-volume spectrum in terms of the\n three-to-three scattering amplitude: In this article we complete our formalism relating the finite-volume energy\nspectrum of a scalar quantum field theory to the three-to-three scattering\namplitude, ${\\cal M}_3$. In previous work we found a quantization condition\nrelating the spectrum to a non-standard infinite-volume quantity, denoted\n${\\cal K}_{{\\rm df},3}$. Here we present the relation between ${\\cal K}_{{\\rm\ndf},3}$ and ${\\cal M}_3$. We then discuss briefly how our now completed\nformalism can be practically implemented to extract ${\\cal M}_3$ from the\nfinite-volume energy spectrum.", "category": "hep-lat" }, { "text": "$B\\to D^{(\\ast)}\\ell\u03bd$ at non-zero recoil: $B$ anomalies play a prominent role in Beyond the Standard Model (BSM)\nphysics searches. In particular, the long standing tension between the\ninclusive and the exclusive determinations of the CKM matrix element $|V_{cb}|$\nand the current tensions in the $R(D)$--$R(D^\\ast)$ plane between theory and\nexperiment have brought the $B\\to D^{(\\ast)}\\ell\\nu$ semileptonic processes to\nthe spotlight. Existing lattice-QCD calculations of the $B\\to D\\ell\\nu$ form\nfactors at non-zero recoil are being complemented with very recent developments\nin the $B\\to D^\\ast\\ell\\nu$ channel. In this review I discuss recent progress\nin lattice calculations of $B\\to D^{(\\ast)}\\ell\\nu$, as well as the\nimplications of these results for high precision determinations of $|V_{cb}|$\nand the Lepton Flavor Universality (LFU) ratios $R(D^{(\\ast)})$.", "category": "hep-lat" }, { "text": "Lattice QCD at non-zero baryon number: We discuss the quenched limit of lattice QCD at non-zero baryon number\ndensity. We find evidence for a mixed phase that becomes broader with\nincreasing baryon number. Although the action is explicitly Z(3) symmetric the\nPolyakov loop expectation value becomes non-zero already in the low temperature\nphase. It indicates that the heavy quark potential stays finite at large\ndistances, i.e. the string between static quarks breaks at non-zero baryon\nnumber density already in the hadronic phase. This behaviour is validated by\ncalculating the heavy quark potential using Polyakov loop correlations.", "category": "hep-lat" }, { "text": "Lattice Gauge Fields Topology Uncovered by Quaternionic sigma-model\n Embedding: We investigate SU(2) gauge fields topology using new approach, which exploits\nthe well known connection between SU(2) gauge theory and quaternionic\nprojective sigma-models and allows to formulate the topological charge density\nentirely in terms of sigma-model fields. The method is studied in details and\nfor thermalized vacuum configurations is shown to be compatible with\noverlap-based definition. We confirm that the topological charge is distributed\nin localized four dimensional regions which, however, are not compatible with\ninstantons. Topological density bulk distribution is investigated at different\nlattice spacings and is shown to possess some universal properties.", "category": "hep-lat" }, { "text": "On the fractal structure of two-dimensional quantum gravity: We provide evidence that the Hausdorff dimension is 4 and the spectral\ndimension is 2 for two-dimensional quantum gravity coupled the matter with a\ncentral charge $c \\leq 1$. For $c > 1$ the Hausdorff dimension and the spectral\ndimension monotonously decreases to 2 and 1, respectively.", "category": "hep-lat" }, { "text": "Overlap Fermion in External Gravity: On a lattice, we construct an overlap Dirac operator which describes the\npropagation of a Dirac fermion in external gravity. The local Lorentz symmetry\nis manifestly realized as a lattice gauge symmetry, while the general\ncoordinate invariance is expected to be restored only in the continuum limit.\nThe lattice index density in the presence of a gravitational field is\ncalculated.", "category": "hep-lat" }, { "text": "Energies and radial distributions of B_s mesons - the effect of\n hypercubic blocking: This is a follow-up to our earlier work for the energies and the charge\n(vector) and matter (scalar) distributions for S-wave states in a heavy-light\nmeson, where the heavy quark is static and the light quark has a mass about\nthat of the strange quark. We study the radial distributions of higher angular\nmomentum states, namely P- and D-wave states, using a \"fuzzy\" static quark. A\nnew improvement is the use of hypercubic blocking in the time direction, which\neffectively constrains the heavy quark to move within a 2a hypercube (a is the\nlattice spacing).\n The calculation is carried out with dynamical fermions on a 16^3 times 32\nlattice with a lattice spacing approximately 0.10 fm generated using the\nnon-perturbatively improved clover action. The configurations were generated by\nthe UKQCD Collaboration using lattice action parameters beta = 5.2, c_SW =\n2.0171 and kappa = 0.1350.\n In nature the closest equivalent of this heavy-light system is the B_s meson.\nAttempts are now being made to understand these results in terms of the Dirac\nequation.", "category": "hep-lat" }, { "text": "Lattice gauge theory and gluon color-confinement in curved spacetime: The lattice gauge theory for curved spacetime is formulated. A discretized\naction is derived for both gluon and quark fields which reduces to the\ngenerally covariant form in the continuum limit. Using the Wilson action, it is\nshown analytically that for a general curved spacetime background, two\npropagating gluons are always color-confined. The fermion-doubling problem is\ndiscussed in the specific case of Friedman-Robertson-Walker metric. Lastly, we\ndiscussed possible future numerical implementation of lattice QCD in curved\nspacetime.", "category": "hep-lat" }, { "text": "$\u03c0\u03c0$ scattering in partially-quenched twisted-mass chiral\n perturbation theory: We study pion-pion scattering in partially-quenched twisted-mass lattice QCD\nusing chiral perturbation theory. The specific partially-quenched setup\ncorresponds to that used in numerical lattice QCD calculations of the $I=0$\nscattering length. We study the discretization errors proportional to $a^2$,\nwith $a$ the lattice spacing, and the errors that arise due to the use of\nL\\\"uscher's two-particle quantization condition in a theory that is not\nunitary. We argue that the former can be as large as $\\sim 100\\%$, but explain\nhow they can be systematically subtracted using a calculation of the $I=2$\nscattering amplitude in the same partially-quenched framework. We estimate the\nerror from the violation of unitarity to be $\\sim 25\\%$, and argue that this\nerror will be difficult to reduce in practice.", "category": "hep-lat" }, { "text": "Why the overlap formula does not lead to chiral fermions: We describe a conceptually simple, but important test for the overlap\napproach to the construction of lattice chiral gauge theories. We explain the\nequivalence of the overlap formula with a certain waveguide model for a simple\nset of gauge configurations (the trivial orbit). This equivalence is helpful in\ncarrying out the test, and casts serious doubts on the viability of the overlap\napproach. A recent note by Narayanan and Neuberger which points out a mistake\nin our previous work is irrelevant in this context.", "category": "hep-lat" }, { "text": "Naive Lattice Fermion without Doublers: We discuss the naive lattice fermion without the issue of doublers. A local\nlattice massless fermion action with chiral symmetry and hermiticity cannot\navoid the doubling problem from the Nielsen-Ninomiya theorem. Here we adopt the\nforward finite-difference deforming the $\\gamma_5$-hermiticity but preserving\nthe continuum chiral-symmetry. The lattice momentum is not hermitian without\nthe continuum limit now. We demonstrate that there is no doubling issue from an\nexact solution. The propagator only has one pole in the first-order accuracy.\nTherefore, it is hard to know the avoiding due to the non-hermiticity. For the\nsecond-order, the lattice propagator has two poles as before. This case also\ndoes not suffer from the doubling problem. Hence separating the forward\nderivative from the backward one evades the doublers under the field theory\nlimit. Simultaneously, it is equivalent to breaking the hermiticity. In the\nend, we discuss the topological charge and also demonstrate the numerical\nimplementation of the Hybrid Monte Carlo.", "category": "hep-lat" }, { "text": "Topological Susceptibility and Zero Mode Size in Lattice QCD: We use the overlap formalism to define a topological index on the lattice. We\nstudy the spectral flow of the hermitian Wilson-Dirac operator and identify\nzero crossings with topological objects. We determine the topological\nsusceptibility and zero mode size distribution, and we comment on the stability\nof our results.", "category": "hep-lat" }, { "text": "Universality and Scaling at the chiral transition in two-flavor QCD at\n finite temperature: The order of the phase transition in finite-temperature QCD with two\ndegenerate light quarks is still an open problem and corresponds to the last\nquestion mark in the zero-density phase diagram of QCD. We argue that\nestablishing the nature of the transition in this case is also a crucial test\nfor numerical simulations of lattice QCD, allowing precise estimates of\npossible systematic errors related e.g. to the choice of fermion-simulation\nalgorithm or of discretized formulation for fermions.", "category": "hep-lat" }, { "text": "The strong-coupling limit of minimal lattice Landau gauge: We study the gluon and ghost propagators of lattice Landau gauge in the\nstrong coupling limit $\\beta = 0$ in pure SU(2) lattice gauge theory to find\nevidence of the conformal infrared behaviour of these propagators as predicted\nby a variety of functional continuum methods for asymptotically small momenta\n$q^2 \\ll \\Lambda_\\mathrm{QCD}^2$. In the strong-coupling limit, this same\nbehaviour is obtained for the larger values of $a^2q^2$ (in units of the\nlattice spacing $a$), where it is otherwise swamped by the gauge field\ndynamics. Deviations for $a^2 q^2 < 1 $ are well parametrized by a transverse\ngluon mass $\\propto 1/a$. Perhaps unexpectedly, these deviations are thus no\nfinite-volume effect but persist in the infinite-volume limit. They furthermore\ndepend on the definition of gauge fields on the lattice, while the asymptotic\nconformal behaviour does not.", "category": "hep-lat" }, { "text": "Lattice investigation of the phase diagram of the 1+1 dimensional\n Gross-Neveu model at finite number of fermion flavors: We explore the phase structure of the 1+1 dimensional Gross-Neveu model at\nfinite number of fermion flavors using lattice field theory. Besides a chirally\nsymmetric phase and a homogeneously broken phase we find evidence for the\nexistence of an inhomogeneous phase, where the condensate is a spatially\noscillating function. Our numerical results include a crude $\\mu$-$T$ phase\ndiagram.", "category": "hep-lat" }, { "text": "Dynamics of Phase Transitions: The 3D 3-state Potts model: In studies of the QCD deconfining phase transition or cross-over by means of\nheavy ion experiments, one ought to be concerned about non-equilibrium effects\ndue to heating and cooling of the system. In this paper we extend our previous\nstudy of Glauber dynamics of 2D Potts models to the 3D 3-state Potts model,\nwhich serves as an effective model for some QCD properties. We investigate the\nlinear theory of spinodal decomposition in some detail. It describes the early\ntime evolution of the 3D model under a quench from the disordered into the\nordered phase well, but fails in 2D. Further, the quench leads to competing\nvacuum domains, which are difficult to equilibrate, even in the presence of a\nsmall external magnetic field. From our hysteresis study we find, as before, a\ndynamics dominated by spinodal decomposition. There is evidence that some\neffects survive in the case of a cross-over. But the infinite volume\nextrapolation is difficult to control, even with lattices as large as $120^3$.", "category": "hep-lat" }, { "text": "A Study of Charmonium Systems across the Deconfinement Transition: We present results from lattice studies of charmonium systems near the\ndeconfinement transition temperature. On quenched isotropic lattices with\nlattice spacings between 0.02 and 0.05 fm, bar{q} q systems with quark masses\nclose to the charm mass and with different spin-parity quantum numbers are\nstudied in the temperature range 0.9 Tc - 3 Tc. Results for temporal\ncorrelators of local operators, and the spectral functions constructed from\nthem, are discussed. For the pseudoscalar and vector channels, the correlators\nare observed to change very little across the deconfinement transition, unlike\nin the case of the light quarks.", "category": "hep-lat" }, { "text": "Two-Dimensional Dynamical Triangulation using the Grand-canonical\n Ensemble: The string susceptibility exponents of dynamically triangulated two\ndimensional surfaces with sphere and torus topology were calculated using the\ngrand-canonical Monte Carlo method. We also simulated the model coupled to\nd-Ising spins (d=1,2,3,5).", "category": "hep-lat" }, { "text": "Tests of the lattice index theorem: We investigate the lattice index theorem and the localization of the\nzero-modes for thick classical center vortices. For non-orientable spherical\nvortices, the index of the overlap Dirac operator differs from the topological\ncharge although the traces of the plaquettes deviate only by a maximum of 1.5%\nfrom trivial plaquettes. This may be related to the fact that even in Landau\ngauge some links of these configuration are close to the non-trivial center\nelements.", "category": "hep-lat" }, { "text": "The Charm Quark on the Lattice: We formulate lattice fermions in a way that encompasses Wilson fermions as\nwell as the static and non-relativistic approximations. In particular, we treat\n$m_qa$ systematically ($m_q$ is the fermion mass) showing how to understand the\nWilson action as an effective action for systems with $\\vek{p}\\ll m_q$. The\nresults show how to extract matrix elements and the spectrum from simulations\nwith $m_qa\\approx1$, which is relevant for the charm quark.", "category": "hep-lat" }, { "text": "The finite temperature QCD using 2+1 flavors of domain wall fermions at\n N_t = 8: We study the region of the QCD phase transition using 2+1 flavors of domain\nwall fermions (DWF) and a $16^3 \\times 8$ lattice volume with a fifth dimension\nof $L_s = 32$. The disconnected light quark chiral susceptibility, quark number\nsusceptibility and the Polyakov loop suggest a chiral and deconfining crossover\ntransition lying between 155 and 185 MeV for our choice of quark mass and\nlattice spacing. In this region the lattice scale deduced from the Sommer\nparameter $r_0$ is $a^{-1} \\approx 1.3$ GeV, the pion mass is $\\approx 300$ MeV\nand the kaon mass is approximately physical. The peak in the chiral\nsusceptibility implies a pseudo critical temperature $T_c = 171(10)(17)$ MeV\nwhere the first error is associated with determining the peak location and the\nsecond with our unphysical light quark mass and non-zero lattice spacing. The\neffects of residual chiral symmetry breaking on the chiral condensate and\ndisconnected chiral susceptibility are studied using several values of the\nvalence $L_s$.", "category": "hep-lat" }, { "text": "Light meson decay constants beyond the quenched approximation: We calculate the effects of including dynamical fermion loops in the lattice\nQCD estimates of meson decay constants, by extrapolating the results from\nnegative flavour numbers after a suitable matching of the pion and rho mass.\nFor moderately light quarks, the values of the decay constants not corrected\nfor the renormalization constants increase with respect to their quenched\nvalues.", "category": "hep-lat" }, { "text": "Properties of U(1) lattice gauge theory with monopole term: In 4D compact U(1) lattice gauge theory with a monopole term added to the\nWilson action we first reveal some properties of a third phase region at\nnegative $\\beta$. Then at some larger values of the monopole coupling $\\lambda$\nby a finite-size analysis we find values of the critical exponent $\\nu$ close\nto, however, different from the Gaussian value.", "category": "hep-lat" }, { "text": "Dirac Spectra of 2-dimensional QCD-like theories: We analyze Dirac spectra of two-dimensional QCD like theories both in the\ncontinuum and on the lattice and classify them according to random matrix\ntheories sharing the same global symmetries. The classification is different\nfrom QCD in four dimensions because the anti-unitary symmetries do not commute\nwith $\\gamma_5$. Therefore in a chiral basis, the number of degrees of freedom\nper matrix element are not given by the Dyson index. Our predictions are\nconfirmed by Dirac spectra from quenched lattice simulations for QCD with two\nor three colors with quarks in the fundamental representation as well as in the\nadjoint representation. The universality class of the spectra depends on the\nparity of the number of lattice points in each direction. Our results show an\nagreement with random matrix theory that is qualitatively similar to the\nagreement found for QCD in four dimensions. We discuss the implications for the\nMermin-Wagner-Coleman theorem and put our results in the context of\ntwo-dimensional disordered systems.", "category": "hep-lat" }, { "text": "Propagators in lattice Coulomb gauge and confinement mechanisms: We discuss the gluon propagator in 3- and 4-dimensional Yang-Mills theories\nin Coulomb gauge and compare it with the corresponding Landau gauge propagator,\nshowing that for both the relevant IR mass scale coincides. We also report\npreliminary results on Coulomb gauge ghost form factor and quark propagators\nand give a comment on the gluon propagator's strong coupling limit.", "category": "hep-lat" }, { "text": "Simulations of Discrete Random Geometries: Simplicial Quantum Gravity\n and Quantum String Theory: I investigate two discrete models of random geometries, namely simplicial\nquantum gravity and quantum string theory. In four-dimensional simplicial\nquantum gravity, I show that the addition of matter gauge fields to the model\nis capable of changing its phase structure by replacing the branched polymers\nof the pure gravity model with a new phase that has a negative string\nsusceptibility exponent and a fractal dimension of four. Some of the results\nare derived from a strong coupling expansion of the model, a technique which is\nused here for the first time in this context. In quantum string theory, I study\na discrete version of the IIB superstring. I show that the divergences\nencountered in the discretization of the bosonic string are eliminated in the\nsupersymmetric case. I give theoretical arguments for the appearance of\none-dimensional structures in the region of large system extents that manifest\nas a power-law tail in the link length distribution; this is confirmed by\nnumerical simulations of the model. I also examine a lower-dimensional version\nof the IKKT matrix model, in which a similar effect can be observed.", "category": "hep-lat" }, { "text": "Employing the perturbative definition of the Higgs mass in a\n non-perturbative calculation: In perturbative calculations the masses of the Higgs, the Ws and the Z are\nusually determined from the pole position of the corresponding gauge-dependent\npropagators. In full non-perturbative lattice calculations it is much more\ndirect to instead investigate the bound state spectrum with its\ngauge-independent meaning, which then contains bound states of Higgses and/or\nWs and Zs. It is possible to extend the perturbative definition of the Higgs\nmass also to such a full non-perturbative setting by determining the respective\nfull non-perturbative propagators of the Higgs, the Ws, and the Z, and analyze\ntheir analytic structure. This helps connecting the Higgs properties indirectly\nwith gauge-invariant physics. This is here studied, using lattice gauge theory,\nfor the case of a W-Z-Higgs system.", "category": "hep-lat" }, { "text": "Strange quark contribution to nucleon form factors: We discuss methods for the calculation of disconnected diagrams and their\napplication to various form factors of the nucleon. In particular, we present\npreliminary results for the strange contribution to the scalar and axial form\nfactors, calculated with N_f=2 dynamical flavors of Wilson fermions on an\nanisotropic lattice.", "category": "hep-lat" }, { "text": "Moving NRQCD for B Form Factors at High Recoil: We derive the continuum and lattice tree-level moving NRQCD (mNRQCD) through\norder 1/m^2. mNRQCD is a generalization of NRQCD for dealing with hadrons with\nnonzero velocity u_mu. The quark's total momentum is written as P^mu=Mu^mu+k^mu\nwhere k^mu << Mu^mu is discretized and Mu^mu is treated exactly. Radiative\ncorrections to couplings on the lattice are discussed. mNRQCD is particularly\nuseful for calculating B->pi and B->D form factors since errors are similar at\nlow and high recoil.", "category": "hep-lat" }, { "text": "Worm Algorithm for CP(N-1) Model: The CP(N-1) model in 2D is an interesting toy model for 4D QCD as it\npossesses confinement, asymptotic freedom and a non-trivial vacuum structure.\nDue to the lower dimensionality and the absence of fermions, the computational\ncost for simulating 2D CP(N-1) on the lattice is much lower than that for\nsimulating 4D QCD. However, to our knowledge, no efficient algorithm for\nsimulating the lattice CP(N-1) model has been tested so far, which also works\nat finite density. To this end we propose a new type of worm algorithm which is\nappropriate to simulate the lattice CP(N-1) model in a dual, flux-variables\nbased representation, in which the introduction of a chemical potential does\nnot give rise to any complications. In addition to the usual worm moves where a\ndefect is just moved from one lattice site to the next, our algorithm\nadditionally allows for worm-type moves in the internal variable space of\nsingle links, which accelerates the Monte Carlo evolution. We use our algorithm\nto compare the two popular CP(N-1) lattice actions and exhibit marked\ndifferences in their approach to the continuum limit.", "category": "hep-lat" }, { "text": "Non-renormalization theorem in a lattice supersymmetric theory and the\n cyclic Leibniz rule: N=4 supersymmetric quantum mechanical model is formulated on the lattice. Two\nsupercharges, among four, are exactly conserved with the help of the cyclic\nLeibniz rule without spoiling the locality. In use of the cohomological\nargument, any possible local terms of the effective action are classified into\ntwo categories which we call type-I and type-II, analogous to the D- and\nF-terms in the supersymmetric field theories. We prove non-renormalization\ntheorem on the type-II terms which include mass and interaction terms with\nkeeping a lattice constant finite, while type-I terms such as the kinetic terms\nhave nontrivial quantum corrections.", "category": "hep-lat" }, { "text": "Symmetries of mesons after unbreaking of chiral symmetry and their\n string interpretation: Using the chirally invariant overlap Dirac operator we remove its\nlowest-lying quasizero modes from the valence quark propagators and study\nevolution of isovector mesons with J=1. At the truncation level about 50 MeV\nSU(2)_L \\times SU(2)_R and U(1)_A symmetries get restored. However, we observe\na degeneracy not only within the chiral and U(1)_A multiplets, but also a\ndegeneracy of all possible chiral multiplets, i.e., the observed quantum levels\nhave a symmetry larger than U(2)_L \\times U(2)_R and their energy does not\ndepend on the spin orientation of quarks and their parities. We offer a\npossible interpretation of these energy levels as the quantum levels of the\ndynamical QCD string. The structure of the radial J=1 spectrum is compatible\nwith E =(n_r +1)\\hbar\\omega with \\hbar\\omega = 900 \\pm 70 MeV.", "category": "hep-lat" }, { "text": "Can lattice data for two heavy-light mesons be understood in terms of\n simply two-quark potentials?: By comparing lattice data for the two heavy-light meson system (Q^2 qbar^2)\nwith a standard many-body approach employing only interquark potentials, it is\nshown that the use of unmodified two-quark potentials leads to a gross\noverestimate of the binding energy.", "category": "hep-lat" }, { "text": "Genetic Algorithm for SU(2) Gauge Theory on a 2-dimensional Lattice: An algorithm is proposed for the simulation of pure SU(N) lattice gauge\ntheories based on Genetic Algorithms(GAs). We apply GAs to SU(2) pure gauge\ntheory on a 2 dimensional lattice and show the results, the action per\nplaquette and Wilson loops, are consistent with those by Metropolis method(MP)s\nand Heatbath method(HB)s. Thermalization speed of GAs is especially faster than\nthe simple MPs.", "category": "hep-lat" }, { "text": "QCD-like technicolor on the lattice: This talk gives an overview, aimed at non-experts, of the recent progress on\nthe studies of technicolor models on the lattice. Phenomenologically successful\ntechnicolor models require walking coupling; thus, an emphasis is put on the\ndetermination of the beta-function of various models. As a case study we\nconsider SU(2) gauge field theory with two adjoint representation fermions,\nso-called minimal walking technicolor theory.", "category": "hep-lat" }, { "text": "Screening masses in quenched (2+1)d Yang-Mills theory: universality from\n dynamics?: We compute the spectrum of gluonic screening-masses in the $0^{++}$ channel\nof quenched 3d Yang-Mills theory near the phase-transition. Our\nfinite-temperature lattice simulations are performed at scaling region, using\nstate-of-art techniques for thermalization and spectroscopy, which allows for\nthorough data extrapolations to thermodynamic limit. Ratios among\nmass-excitations with the same quantum numbers on the gauge theory, 2d Ising\nand $\\lambda\\phi^{4}$ models are compared, resulting in a nice agreement with\npredictions from universality. In addition, a gauge-to-scalar mapping,\npreviously employed to fit QCD Green's functions at deep IR, is verified to\ndynamically describe these universal spectroscopic patterns", "category": "hep-lat" }, { "text": "The kaon B-parameter from unquenched mixed action lattice QCD: We present a preliminary calculation of B_K using domain-wall valence quarks\nand 2+1 flavors of improved staggered sea quarks. Both the size of the residual\nquark mass, which measures the amount of chiral symmetry breaking, and of the\nmixed meson splitting Delta_mix, a measure of taste-symmetry breaking, show\nthat discretization effects are under control in our mixed action lattice\nsimulations. We show preliminary data for pseudoscalar meson masses, decay\nconstants and B_K. We discuss general issues associated with the chiral\nextrapolation of lattice data, and, as an example, present a preliminary chiral\nand continuum extrapolation of f_pi. The quality of our data shows that the\ngood chiral properties of domain-wall quarks, in combination with the light sea\nquark masses and multiple lattice spacings available with the MILC staggered\nconfigurations, will allow for a precise determination of B_K.", "category": "hep-lat" }, { "text": "Meson masses in electromagnetic fields with Wilson fermions: We determine the light meson spectrum in QCD in the presence of background\nmagnetic fields using quenched Wilson fermions. Our continuum extrapolated\nresults indicate a monotonous reduction of the connected neutral pion mass as\nthe magnetic field grows. The vector meson mass is found to remain nonzero, a\nfinding relevant for the conjectured $\\rho$-meson condensation at strong\nmagnetic fields. The continuum extrapolation was facilitated by adding a novel\nmagnetic field-dependent improvement term to the additive quark mass\nrenormalization. Without this term, sizable lattice artifacts that would\ndeceptively indicate an unphysical rise of the connected neutral pion mass for\nstrong magnetic fields are present. We also investigate the impact of these\nlattice artifacts on further observables like magnetic polarizabilities and\ndiscuss the magnetic field-induced mixing between $\\rho$-mesons and pions. We\nalso derive Ward-Takashi identities for QCD+QED both in the continuum\nformulation and for (order $a$-improved) Wilson fermions.", "category": "hep-lat" }, { "text": "Continuum Limit of Scalar Masses and Mixing Energies: We evaluate the continuum limit of the valence approximation to the mass of\nscalar quarkonium and to the scalar quarkonium-glueball mixing energy for a\nrange of different quark masses. Our results answer several questions raised by\nthe proposed identification of $f_0(1710)$ as composed primarily of the\nlightest scalar glueball.", "category": "hep-lat" }, { "text": "Deflated GMRES with Multigrid for Lattice QCD: Lattice QCD solvers encounter critical slowing down for fine lattice spacings\nand small quark mass. Traditional matrix eigenvalue deflation is one approach\nto mitigating this problem. However, to improve scaling we study the effects of\ndeflating on the coarse grid in a hierarchy of three grids for adaptive\nmutigrid applications of the two dimensional Schwinger model. We compare\ndeflation at the fine and coarse levels with other non deflated methods. We\nfind the inclusion of a partial solve on the intermediate grid allows for a low\ntolerance deflated solve on the coarse grid. We find very good scaling in\nlattice size near critical mass when we deflate at the coarse level using the\nGMRES-DR and GMRES-Proj algorithms.", "category": "hep-lat" }, { "text": "Confinement in non-Abelian lattice gauge theory via persistent homology: We investigate the structure of confining and deconfining phases in SU(2)\nlattice gauge theory via persistent homology, which gives us access to the\ntopology of a hierarchy of combinatorial objects constructed from given data.\nSpecifically, we use filtrations by traced Polyakov loops, topological\ndensities, holonomy Lie algebra fields, as well as electric and magnetic\nfields. This allows for a comprehensive picture of confinement. In particular,\ntopological densities form spatial lumps which show signatures of the classical\nprobability distribution of instanton-dyons. Signatures of well-separated dyons\nlocated at random positions are encoded in holonomy Lie algebra fields,\nfollowing the semi-classical temperature dependence of the instanton appearance\nprobability. Debye screening discriminating between electric and magnetic\nfields is visible in persistent homology and pronounced at large gauge\ncoupling. All employed constructions are gauge-invariant without a priori\nassumptions on the configurations under study. This work showcases the\nversatility of persistent homology for statistical and quantum physics studies,\nbarely explored to date.", "category": "hep-lat" }, { "text": "Anisotropic Improved Gauge Actions; --Perturbative and Numerical Studies\n --: The $\\Lambda$ parameter on the anisotropic lattice, the spatial and\ntemperature coupling constant $g_{\\sigma}$, $g_{\\tau}$ and their derivative\nwith respaect to the the anisotropy parameter $\\xi$ are studied perturbatively\nfor the class of improved actions, which cover tree level Symanzik's, Iwasaki's\nand QCDTARO's improved actions. The $\\eta(=g_{\\tau}/g_{\\sigma})$ becomes less\nthan 1 for Iwasaki's and QCDTARO's action, which is confirmed nonperturbatively\nby numerical simulations. Derivatives of the coupling constants with respect to\nthe anisotropy parameter, $\\partial g_{\\tau}/\\partial \\xi$ and $\\partial\ng_{\\sigma}/\\partial \\xi$, change sign for those improved actions.", "category": "hep-lat" }, { "text": "Flavour blindness and patterns of flavour symmetry breaking in lattice\n simulations of up, down and strange quarks: QCD lattice simulations with 2+1 flavours (when two quark flavours are mass\ndegenerate) typically start at rather large up-down and strange quark masses\nand extrapolate first the strange quark mass and then the up-down quark mass to\nits respective physical value. Here we discuss an alternative method of tuning\nthe quark masses, in which the singlet quark mass is kept fixed. Using group\ntheory the possible quark mass polynomials for a Taylor expansion about the\nflavour symmetric line are found, first for the general 1+1+1 flavour case and\nthen for the 2+1 flavour case. This ensures that the kaon always has mass less\nthan the physical kaon mass. This method of tuning quark masses then enables\nhighly constrained polynomial fits to be used in the extrapolation of hadron\nmasses to their physical values. Numerical results for the 2+1 flavour case\nconfirm the usefulness of this expansion and an extrapolation to the physical\npion mass gives hadron mass values to within a few percent of their\nexperimental values. Singlet quantities remain constant which allows the\nlattice spacing to be determined from hadron masses (without necessarily being\nat the physical point). Furthermore an extension of this programme to include\npartially quenched results is given.", "category": "hep-lat" }, { "text": "Two-Dimensional Compact N=(2,2) Lattice Super Yang-Mills Theory with\n Exact Supersymmetry: We construct two-dimensional N=(2,2) lattice super Yang-Mills theory, where\nthe gauge and Higgs fields are all represented by U(N) compact variables, with\nkeeping one exact supercharge along the line of the papers [1,2,3].\nInterestingly, requirements of the exact supersymmetry as well as of the\ncompact gauge and Higgs fields lead to the gauge group U(N) rather than SU(N).\nAs a result of the perturbative renormalization argument, the model is shown to\nflow to the target continuum theory without any fine-tuning. Different from the\ncase of noncompact Higgs fields, the path integral along the flat directions is\nwell-defined in this model.", "category": "hep-lat" }, { "text": "Lattice calculations of the spectroscopy of baryons with broken flavor\n SU(3) symmetry and 3, 5, or 7 colors: Lattice Monte Carlo calculations of baryon spectroscopy in gauge groups\nSU(N), N=3, 5, 7, are presented. The quenched valence fermions come in three\nflavors, two degenerate mass ones and a third heavier flavor. The data shows\nstriking regularities reminiscent of the real-world case of N=3: higher angular\nmomentum states lie higher in mass, and Sigma-like states lie higher than\nLambda-like ones. These simple regularities are reasonably well described by\n1/N expansions.", "category": "hep-lat" }, { "text": "Lattice Results for Heavy Light Matrix Elements: Lattice results for heavy light matrix elements are reviewed and some of\ntheir implications are very briefly discussed. Despite the fact that in most\ncases the lattice results for weak matrix elements at the moment have only a\nmodest accuracy of about 20--30\\% they already have important phenomenological\nrepercussions; e.g.\\ for $V_{td}/V_{ts}$, $x_s/x_d$ and $B\\to K^\\ast\\gamma$.\nPresented at the XXVII International Conference on High Energy Physics,\nGlasgow, July 1994.", "category": "hep-lat" }, { "text": "Infrared Gluon and Ghost Propagators from Lattice QCD. Results from\n large asymmetric lattices: We report on the infrared limit of the quenched lattice Landau gauge gluon\nand ghost propagators as well as the strong coupling constant computed from\nlarge asymmetric lattices. The infrared lattice propagators are compared with\nthe pure power law solutions from Dyson-Schwinger equations (DSE). For the\ngluon propagator, the lattice data is compatible with the DSE solution. The\npreferred measured gluon exponent being $\\sim 0.52$, favouring a null zero\nmomentum propagator. The lattice ghost propagator shows finite volume effects\nand, for the volumes considered, the propagator does not follow a pure power\nlaw. Furthermore, the strong coupling constant is computed and its infrared\nbehaviour investigated.", "category": "hep-lat" }, { "text": "Two loop lattice expansion of the Schroedinger functional coupling in\n improved QCD: The contributions of the improved fermion action of Sheikholeslami and\nWohlert to the two loop coefficient of the expansion of the Schroedinger\nfunctional coupling in terms of the lattice coupling are calculated for the\ngauge group SU(3). These coefficients are required for the second order\nrelation of lattice data to the MSbar-coupling. By taking into account all\nimprovement coefficients we are able to improve the Schroedinger functional to\ntwo loop order.", "category": "hep-lat" }, { "text": "Meron-Cluster Simulation of a Chiral Phase Transition with Staggered\n Fermions: We examine a (3+1)-dimensional model of staggered lattice fermions with a\nfour-fermion interaction and Z(2) chiral symmetry using the Hamiltonian\nformulation. This model cannot be simulated with standard fermion algorithms\nbecause those suffer from a very severe sign problem. We use a new fermion\nsimulation technique - the meron-cluster algorithm - which solves the sign\nproblem and leads to high-precision numerical data. We investigate the finite\ntemperature chiral phase transition and verify that it is in the universality\nclass of the 3-d Ising model using finite-size scaling.", "category": "hep-lat" }, { "text": "An Experimenter's View of Lattice QCD: Lattice QCD has the potential this decade to maximize the sensitivity of the\nentire flavor physics program to new physics and pave the way for understanding\nphysics beyond the Standard Model at the LHC in the coming decade. However, the\nchallenge for the Lattice is to demonstrate reliability at the level of a few\nper cent given a past history of 10-20% errors. The CLEO-c program at the\nCornell Electron Storage Ring is providing the data that will make the\ndemonstration possible.", "category": "hep-lat" }, { "text": "Non-Perturbative Renormalization for Staggered Fermions (Self-energy\n Analysis): We present preliminary results of data analysis for the non-perturbative\nrenormalization (NPR) on the self-energy of the quark propagators calculated\nusing HYP improved staggered fermions on the MILC asqtad lattices. We use the\nmomentum source to generate the quark propagators. In principle, using the\nvector projection operator of $(\\bar{\\bar{\\gamma_\\mu \\otimes 1}})$ and the\nscalar projection operator $(\\bar{\\bar{1 \\otimes 1}})$, we should be able to\nobtain the wave function renormalization factor $Z_q'$ and the mass\nrenormalization factor $Z_q \\cdot Z_m$. Using the MILC coarse lattice, we\nobtain a preliminary but reasonable estimate of $Z_q'$ and $Z_q \\cdot Z_m$ from\nthe data analysis on the self-energy.", "category": "hep-lat" }, { "text": "Screening at finite temperature and density: We present lattice QCD results on heavy quark free energies, extract from its\ntemperature dependence entropy and internal energy contributions, and discuss\nthe onset of medium effects that lead to screening of static quark-antiquark\nsources in a thermal medium. Most results are obtained in (2+1)-flavour QCD on\na line of constant physics with almost realistic quark masses and compared to\nprevious results from 2-flavor QCD as well as pure gauge theory. Furthermore,\nwe discuss results on the density dependence of screening masses that have been\nobtained using a leading order Taylor expansion in the baryon chemical\npotential.", "category": "hep-lat" }, { "text": "Polymer-Chain Adsorption Transition at a Cylindrical Boundary: In a recent letter, a simple method was proposed to generate solvable models\nthat predict the critical properties of statistical systems in hyperspherical\ngeometries. To that end, it was shown how to reduce a random walk in $D$\ndimensions to an anisotropic one-dimensional random walk on concentric\nhyperspheres. Here, I construct such a random walk to model the\nadsorption-desorption transition of polymer chains growing near an attractive\ncylindrical boundary such as that of a cell membrane. I find that the fraction\nof adsorbed monomers on the boundary vanishes exponentially when the adsorption\nenergy decreases towards its critical value. When the adsorption energy rises\nbeyond a certain value above the critical point whose scale is set by the\nradius of the cell, the adsorption fraction exhibits a crossover to a linear\nincrease characteristic to polymers growing near planar boundaries.", "category": "hep-lat" }, { "text": "Hunting the static energy renormalon: We employ Numerical Stochastic Perturbation Theory (NSPT) together with\ntwisted boundary conditions (TBC) to search for the leading renormalon in the\nperturbative expansion of the static energy. This renormalon is expected to\nemerge four times faster than the one for the gluon conden- sate in the\nplaquette. We extract the static energy from Polyakov loop calculations up to\n12 loops and present preliminary results, indicating a significant step towards\nconfirming the theoretical expectation.", "category": "hep-lat" }, { "text": "Form factor ratios for $B_s \\rightarrow K \\, \\ell \\, \u03bd$ and $B_s\n \\rightarrow D_s \\, \\ell \\, \u03bd$ semileptonic decays and $|V_{ub}/V_{cb}|$: We present a lattice quantum chromodynamics determination of the ratio of the\nscalar and vector form factors for two semileptonic decays of the $B_s$ meson:\n$B_s \\rightarrow K \\ell \\nu$ and $B_s \\rightarrow D_s \\ell \\nu$. In conjunction\nwith future experimental data, our results for these correlated form factors\nwill provide a new method to extract $|V_{ub}/V_{cb}|$, which may elucidate the\ncurrent tension between exclusive and inclusive determinations of these\nCabibbo-Kobayashi-Maskawa mixing matrix parameters. In addition to the form\nfactor results, we determine the ratio of the differential decay rates, and\nforward-backward and polarization asymmetries, for the two decays.", "category": "hep-lat" }, { "text": "Behavior near $\u03b8=\u03c0$ of the mass gap in the 2D O(3) non-linear\n sigma model: The validity of the Haldane's conjecture entails that the mass gap of the\n2-dimensional O(3) non-linear sigma model with a $\\theta$-term must tend to\nzero as $\\theta$ approaches the value $\\pi$ by following a precise law. In the\npresent paper we extract the related critical exponents by simulating the model\nat imaginary $\\theta$.", "category": "hep-lat" }, { "text": "Lattice QCD Determination of $g_A$: The nucleon axial coupling, $g_A$, is a fundamental property of protons and\nneutrons, dictating the strength with which the weak axial current of the\nStandard Model couples to nucleons, and hence, the lifetime of a free neutron.\nThe prominence of $g_A$ in nuclear physics has made it a benchmark quantity\nwith which to calibrate lattice QCD calculations of nucleon structure and more\ncomplex calculations of electroweak matrix elements in one and few nucleon\nsystems. There were a number of significant challenges in determining $g_A$,\nnotably the notorious exponentially-bad signal-to-noise problem and the\nrequirement for hundreds of thousands of stochastic samples, that rendered this\ngoal more difficult to obtain than originally thought.\n I will describe the use of an unconventional computation method, coupled with\n\"ludicrously'\" fast GPU code, access to publicly available lattice QCD\nconfigurations from MILC and access to leadership computing that have allowed\nthese challenges to be overcome resulting in a determination of $g_A$ with 1%\nprecision and all sources of systematic uncertainty controlled. I will discuss\nthe implications of these results for the convergence of $SU(2)$ Chiral\nPerturbation theory for nucleons, as well as prospects for further improvements\nto $g_A$ (sub-percent precision, for which we have preliminary results) which\nis part of a more comprehensive application of lattice QCD to nuclear physics.\nThis is particularly exciting in light of the new CORAL supercomputers coming\nonline, Sierra and Summit, for which our lattice QCD codes achieve a\nmachine-to-machine speed up over Titan of an order of magnitude.", "category": "hep-lat" }, { "text": "The QCD Equation of State: Results for the equation of state in 2+1 flavor QCD at zero net baryon\ndensity using the Highly Improved Staggered Quark (HISQ) action by the HotQCD\ncollaboration are presented. The strange quark mass was tuned to its physical\nvalue and the light (up/down) quark masses fixed to $m_l = 0.05m_s$\ncorresponding to a pion mass of 160 MeV in the continuum limit. Lattices with\ntemporal extent $N_t=6$, 8, 10 and 12 were used. Since the cutoff effects for\n$N_t>6$ were observed to be small, reliable continuum extrapolations of the\nlattice data for the phenomenologically interesting temperatures range $130\n\\mathord{\\rm MeV} < T < 400 \\mathord{\\rm MeV}$ could be performed. We discuss\nstatistical and systematic errors and compare our results with other published\nworks.", "category": "hep-lat" }, { "text": "The scalar, vector and tensor form factors for the pion and kaon from\n lattice QCD: We present a calculation of the scalar, vector, and tensor form factors for\nthe pion and kaon in lattice QCD. We use an ensemble of two degenerate light, a\nstrange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with\nclover improvement. The corresponding pion and kaon masses are about 265 MeV\nand 530 MeV, respectively. The calculation is done in both rest and boosted\nframes obtaining data for four-vector momentum transfer squared up to\n$-q^2=2.5$ GeV$^2$ for the pion and 3 GeV$^2$ for the kaon. The excited-states\neffects are studied by analyzing six values of the source-sink time separation\nfor the rest frame ($1.12-2.23$ fm) and for four values for the boosted frame\n($1.12-1.67$ fm). The lattice data are renormalized non-perturbatively and the\nresults for the scheme- and scale-dependent scalar and tensor form factors are\npresented in the $\\overline{\\rm MS}$ scheme at a scale of 2 GeV. We apply\ndifferent parametrizations to describe $q^2$-dependence of the form factors to\nextract the scalar, vector, and tensor radii, as well as the tensor anomalous\nmagnetic moment. We compare the pion and kaon form factors to study SU(3)\nflavor symmetry breaking effects. By combining the data for the vector and\ntensor form factors we also obtain the lowest moment of the densities of\ntransversely polarized quarks in the impact parameter space. Finally, we give\nan estimate for the average transverse shift in the $y$ direction for polarized\nquarks in the $x$ direction.", "category": "hep-lat" }, { "text": "Signal/noise enhancement strategies for stochastically estimated\n correlation functions: We develop strategies for enhancing the signal/noise ratio for stochastically\nsampled correlation functions. The techniques are general and offer a wide\nrange of applicability. We demonstrate the potential of the approach with a\ngeneric two-state system, and then explore the practical applicability of the\nmethod for single hadron correlators in lattice quantum chromodynamics. In the\nlatter case, we determine the ground state energies of the pion, proton, and\ndelta baryon, as well as the ground and first excited state energy of the rho\nmeson using matrices of correlators computed on an exemplary ensemble of\nanisotropic gauge configurations. In the majority of cases, we find a modest\nreduction in the statistical uncertainties on extracted energies compared to\nconventional variational techniques. However, in the case of the delta baryon,\nwe achieve a factor of three reduction in statistical uncertainties. The\nvariety of outcomes achieved for single hadron correlators illustrates an\ninherent dependence of the method on the properties of the system under\nconsideration and the operator basis from which the correlators are\nconstructed.", "category": "hep-lat" }, { "text": "Infinite volume and continuum limits for gluon propagator in 3d SU(2)\n lattice gauge theory: We study the Landau gauge gluon propagator D(p) in the 3d SU(2) lattice gauge\ntheory. We show that in the infinite-volume limit the expectation values over\nthe Gribov region \\Omega, are different (in the infrared) from that calculated\nin the fundamental modular region \\Gamma. Also we show that this conclusion\ndoes not change when spacing $a$ tends to zero.", "category": "hep-lat" }, { "text": "Measure dependence of 2D simplicial quantum gravity: We study pure 2D Euclidean quantum gravity with $R^2$ interaction on\nspherical lattices, employing Regge's formulation. We attempt to measure the\nstring susceptibility exponent $\\gamma_{\\rm str}$ by using a finite-size\nscaling Ansatz in the expectation value of $R^2$. To check on effects of the\npath integral measure we investigate two scale invariant measures, the\n\"computer\" measure $dl/l$ and the Misner measure $dl/\\sqrt A$.", "category": "hep-lat" }, { "text": "Lattice Background Effective Action: a Proposal: We propose a method based on the Schr\\\"odinger functional for computing on\nthe lattice the gauge invariant effective action for external background\nfields. We check this method by studying the U(1) lattice gauge theory in\npresence of a constant magnetic background field.", "category": "hep-lat" }, { "text": "A precise determination of T_c in QCD from scaling: Existing lattice data on the QCD phase transition are analyzed in\nrenormalized perturbation theory. In quenched QCD it is found that T_c scales\nfor lattices with only 3 time slices, and that T_c/Lambda_msbar=1.15 \\pm 0.05.\nA preliminary estimate in QCD with two flavours of dynamical quarks shows that\nthis ratio depends on the quark mass. For realistic quark masses we estimate\nT_c/Lambda_msbar=0.49 \\pm 0.02. We also investigate the equation of state in\nquenched QCD at 1-loop order in renormalised perturbation theory.", "category": "hep-lat" }, { "text": "Strange quark momentum fraction from overlap fermion: We present a calculation of $< x >_s$ for the strange quark in the nucleon.\nWe also report the ratio of the strange $< x >$ to that of $u/d$ in the\ndisconnected insertion which will be useful in constraining the global fit of\nparton distribution functions at small $x$. We adopt overlap fermion action on\n$2 + 1$ flavor domain-wall fermion configurations on the $24^3 \\times 64$\nlattice with a light sea quark mass which corresponds to $m_{\\pi}=330$ MeV.\nSmeared grid $Z_3$ sources are deployed to calculate the nucleon propagator\nwith low-mode substitution. Even-odd grid sources and time-dilution technique\nwith stochastic noises are used to calculate the high mode contribution to the\nquark loop. Low mode averaging (LMA) for the quark loop is applied to reduce\nthe statistical error of the disconnected insertion calculation. We find the\nratio $< x >_s/< x >_{u/d}^{\\mathrm{DI}}= 0.78(3)$ in this study.", "category": "hep-lat" }, { "text": "A lattice potential investigation of quark mass and volume dependence of\n the $\u03a5$ spectrum: We investigate bottomonia splittings by solving a Schrodinger-Pauli-type\nequation with parametrisations of QCD potentials around those that have been\ndetermined previously in lattice simulations. This is done both, in the\ncontinuum and on finite lattices with resolutions ranging from a=0.2 fm down to\na=0.025 fm and extent of up to 12 fm or 144^3 lattice points. We find a strong\ndependence of some splittings, in particular the 2S-1S and 1P-1S splittings, on\nboth the quark mass and the short range form of the static potential in the\nneighbourhood of the bottom quark mass, while splittings such as 3S-2S and\n2P-2S show reduced dependence on the short distance potential. We conclude that\nthe quenched quarkonium spectrum cannot be matched to experiment with a simple\nredefinition of the lattice spacing. We investigate the size of relativistic\ncorrections as a function of the quark mass. Finite size effects are shown to\ndie out rather rapidly as the volume is increased, and we demonstrate the\nrestoration of rotational symmetry as the continuum limit is taken.", "category": "hep-lat" }, { "text": "Confinement and Topological Charge in the Abelian Gauge of QCD: We study the relation between instantons and monopoles in the abelian gauge.\nFirst, we investigate the monopole in the multi-instanton solution in the\ncontinuum Yang-Mills theory using the Polyakov gauge. At a large instanton\ndensity, the monopole trajectory becomes highly complicated, which can be\nregarded as a signal of monopole condensation. Second, we study instantons and\nmonopoles in the SU(2) lattice gauge theory both in the maximally abelian (MA)\ngauge and in the Polyakov gauge. Using the $16^3 \\times 4$ lattice, we find\nmonopole dominance for instantons in the confinement phase even at finite\ntemperatures. A linear-type correlation is found between the total\nmonopole-loop length and the integral of the absolute value of the topological\ndensity (the total number of instantons and anti-instantons) in the MA gauge.\nWe conjecture that instantons enhance the monopole-loop length and promote\nmonopole condensation.", "category": "hep-lat" }, { "text": "$1^{-+}$ Hybrid in $J/\u03c8$ Radiative Decays from Lattice QCD: We present the first theoretical prediction of the production rate of\n$1^{-+}$ light hybrid meson $\\eta_1$ in $J/\\psi$ radiative decays. In the\n$N_f=2$ lattice QCD formalism with the pion mass $m_\\pi\\approx 350$ MeV, the\nrelated electromagnetic multipole form factors are extracted from the\nthree-point functions that involve necessarily quark annihilation diagrams,\nwhich are calculated through the distillation method. The partial width of\n$J/\\psi\\to \\gamma \\eta_1$ is determined to be $2.29(77)~\\mathrm{eV}$ at the\n$\\eta_1$ mass $m_{\\eta_1}=2.23(4)$ GeV. If $\\eta_1$ corresponds to the recently\nobserved $\\eta_1(1855)$ in the process $J/\\psi\\to \\gamma\\eta_1(1855)\\to \\gamma\n\\eta\\eta'$ by BESIII, then the branching fraction $\\mathrm{Br}(J/\\psi\\to\n\\gamma\\eta_1(1855))$ is estimated to be $6.2(2.2)\\times 10^{-5}$, which implies\n$\\mathrm{Br}(\\eta_1(1855)\\to \\eta\\eta')\\sim 4.3\\%$.", "category": "hep-lat" }, { "text": "Improved Hamiltonians for Quantum Simulations: Quantum simulations of lattice gauge theories for the foreseeable future will\nbe hampered by limited resources. The historical success of improved lattice\nactions in classical simulations strongly suggests that Hamiltonians with\nimproved discretization errors will reduce quantum resources, i.e. require\n$\\gtrsim 2^d$ fewer qubits in quantum simulations for lattices with $d$ spatial\ndimensions. In this work, we consider $\\mathcal{O}(a^2)$-improved Hamiltonians\nfor pure gauge theories and design the corresponding quantum circuits for its\nreal-time evolution in terms of primitive gates. An explicit demonstration for\n$\\mathbb{Z}_2$ gauge theory is presented including exploratory tests using the\nibm_perth device.", "category": "hep-lat" }, { "text": "Moving from continuous to discrete symmetry in the 2D XY model: We study the effects of discretization on the U(1) symmetric XY model in two\ndimensions using the Higher Order Tensor Renormalization Group (HOTRG)\napproach. Regarding the $Z_N$ symmetric clock models as specific\ndiscretizations of the XY model, we compare those discretizations to ones from\ntruncations of the tensor network formulation of the XY model based on a\ncharacter expansion, and focus on the differences in their phase structure at\nlow temperatures. We also divide the tensor network formulations into core and\ninteraction tensors and show that the core tensor has the dominant influence on\nthe phase structure. Lastly, we examine a perturbed form of the XY model that\ncontinuously interpolates between the XY and clock models. We examine the\nbehavior of the additional phase transition caused by the perturbation as the\nmagnitude of perturbation is taken to zero. We find that this additional\ntransition has a non-zero critical temperature as the perturbation vanishes,\nsuggesting that even small perturbations can have a significant effect on the\nphase structure of the theory.", "category": "hep-lat" }, { "text": "The Quantized $O(1,2)/O(2)\\times Z_2$ Sigma Model Has No Continuum Limit\n in Four Dimensions. II. Lattice Simulation: A lattice formulation of the $O(1,2)/O(2)\\times Z_2$ sigma model is\ndeveloped, based on the continuum theory presented in the preceding paper.\nSpecial attention is given to choosing a lattice action (the ``geodesic''\naction) that is appropriate for fields having noncompact curved configuration\nspaces. A consistent continuum limit of the model exists only if the\nrenormalized scale constant $\\beta_R$ vanishes for some value of the bare scale\nconstant~$\\beta$. The geodesic action has a special form that allows direct\naccess to the small-$\\beta$ limit. In this limit half of the degrees of freedom\ncan be integrated out exactly. The remaining degrees of freedom are those of a\ncompact model having a $\\beta$-independent action which is noteworthy in being\nunbounded from below yet yielding integrable averages. Both the exact action\nand the $\\beta$-independent action are used to obtain $\\beta_R$ from Monte\nCarlo computations of field-field averages (2-point functions) and\ncurrent-current averages. Many consistency cross-checks are performed. It is\nfound that there is no value of $\\beta$ for which $\\beta_R$ vanishes. This\nmeans that as the lattice cutoff is removed the theory becomes that of a pair\nof massless free fields. Because these fields have neither the geometry nor the\nsymmetries of the original model we conclude that the $O(1,2)/O(2)\\times Z_2$\nmodel has no continuum limit.", "category": "hep-lat" }, { "text": "Curvature of the QCD critical line with 2+1 HISQ fermions: We present results on the curvature of the critical line of QCD with 2+1 HISQ\nfermions at nonzero temperature and quark density obtained by analytic\ncontinuation from imaginary chemical potentials. Monte Carlo simulations are\nperformed by means of the MILC code, suitably modified to include a nonzero\nimaginary baryon chemical potential. We set the chemical potential at the same\nvalue for the three quark species and work on the line of constant physics with\na light to strange mass ratio of 1/20 as determined in\nRef.~\\cite{Bazavov:2011nk}.", "category": "hep-lat" }, { "text": "A class of chiral fermion models: We study the relation between the Roma and Zaragoza proposals for chiral\nfermions on the lattice. The fermion action in the Roma approach is shown to be\nequivalent to one of the Zaragoza type. This result is used to perform a\nmean-field study of the phase diagram for chiral Yukawa models based on the\nRoma action. The phase diagram is compared with the one based on the Zaragoza\nmodel with the most local choice for the fermion interactions.", "category": "hep-lat" }, { "text": "Scaling in SU(3) Pure Gauge Theory with a Renormalization Group Improved\n Action: We study the scaling properties of the static quark potential and the ratio\nof the critical temperature $T_c$ to the square root of the string tension\n$\\sigma$ in the SU(3) pure gauge theory using a renormalization group improved\naction. We first determine the critical coupling $\\beta_c$ on lattices with\ntemporal extension $N_t=3$, 4, and 6, and then calculate the static quark\npotential at the critical couplings on lattices at zero temperature. We note\nthat the static quark potentials obtained are rotationally invariant with\nerrors of at most 1 - 2 % in all the three cases, and that the potential $V(R)$\nin physical units scales in the whole region of $R$ investigated. The values of\n$T_{c}/\\sqrt{\\sigma}$ for the three cases in the infinite volume limit are\nidentical within errors. We estimate the value in the continuum limit to be\n$T_{c}/\\sqrt{\\sigma} = 0.656(4)$, which is slightly larger than the value in\nthe continuum limit from the one-plaquette action, 0.629(3).", "category": "hep-lat" }, { "text": "Bound states for Overlap and Fixed Point Actions close to the chiral\n limit: We study the overlap and the fixed point Dirac operators for massive fermions\nin the two-flavor lattice Schwinger model. The masses of the triplet (pion) and\nsinglet (eta) bound states are determined down to small fermion masses and the\nmass dependence is compared with various continuum model approximations. Near\nthe chiral limit, at very small fermion masses the fixed point operator has\nstability problems, which in this study are dominated by finite size effects,", "category": "hep-lat" }, { "text": "The spin structure of the Lambda hyperon in quenched lattice QCD: It has been suggested to use the production of Lambda hyperons for\ninvestigating the nucleon spin structure. The viability of this idea depends\ncrucially on the spin structure of the Lambda. Using nonperturbatively O(a)\nimproved Wilson fermions in the quenched approximation we have studied matrix\nelements of two-quark operators in the Lambda. We present results for the axial\nvector current, which give us the contributions of the u, d, and s quarks to\nthe Lambda spin.", "category": "hep-lat" }, { "text": "Polyakov loop in 2+1 flavor QCD: We study the temperature dependence of the renormalized Polyakov loop in 2+1\nflavor QCD for temperatures T<210 MeV. We extend previous calculations by the\nHotQCD collaboration using the highly improved staggered quark action and\nperform a continuum extrapolation of the renormalized Polyakov loop. We compare\nthe lattice results with the prediction of non-interacting static-light hadron\nresonance gas, which describes the temperature dependence of the renormalized\nPolyakov loop up to T<140 MeV but fails above that temperature. Furthermore, we\ndiscuss the temperature dependence of the light and strange quark condensates.", "category": "hep-lat" }, { "text": "Implicit schemes for real-time lattice gauge theory: We develop new gauge-covariant implicit numerical schemes for classical\nreal-time lattice gauge theory. A new semi-implicit scheme is used to cure a\nnumerical instability encountered in three-dimensional classical Yang-Mills\nsimulations of heavy-ion collisions by allowing for wave propagation along one\nlattice direction free of numerical dispersion. We show that the scheme is\ngauge covariant and that the Gauss constraint is conserved even for large time\nsteps.", "category": "hep-lat" }, { "text": "How far can you go ? Surprises and pitfalls in three-flavour chiral\n extrapolations: The presence of strange sea quark pairs may have a significant impact of the\npattern of chiral symmetry breaking : in particular large differences can occur\nbetween the chiral limits of two and three massless flavours (i.e., whether\n$m_s$ is kept at its physical value or sent to zero). We recall some\nindications of such a scenario in QCD, in relation with the peculiar dynamics\nof the scalar sector. We explain how this could affect the convergence of\nthree-flavour chiral series, commonly used to extrapolate the results of\nlattice simulations. Finally, we indicate how lattice simulations with three\ndynamical flavours could unveil such an effect through the quark-mass\ndependence of light meson masses and decay constants.", "category": "hep-lat" }, { "text": "The derivative expansion of the renormalization group: By writing the flow equations for the continuum Legendre effective action\n(a.k.a. Helmholtz free energy) with respect to a particular form of smooth\ncutoff, and performing a derivative expansion up to some maximum order, a set\nof differential equations are obtained which at FPs (Fixed Points) reduce to\nnon-linear eigenvalue equations for the anomalous scaling dimension $\\eta$.\nIllustrating this by expanding (single component) scalar field theory, in two,\nthree and four dimensions, up to second order in derivatives, we show that the\nmethod is a powerful and robust means of discovering and quantifying\nnon-perturbative continuum limits (continuous phase transitions).", "category": "hep-lat" }, { "text": "Electromagnetic Corrections in Staggered Chiral Perturbation Theory: To reduce errors in light-quark mass determinations, it is now necessary to\nconsider electromagnetic contributions to light-meson masses. Calculations\nusing staggered quarks and quenched photons are currently underway.\nSuitably-extended chiral perturbation theory is necessary to extrapolate the\nlattice data to the physical limit. Here we give (preliminary) results for\nlight-meson masses using staggered chiral perturbation theory including\nelectromagnetism, and discuss the extent to which quenched-photon simulations\ncan improve quark-mass calculations.", "category": "hep-lat" }, { "text": "Towards continuum limit of screening lengths with chiral Fermions: We investigate mesonic screening correlators at T=2T_c using the overlap\nFermions in the quenched approximation, where T_c is the QCD phase transition\ntemperature. Using lattices with temporal extent up to 8, we found that both\npseudoscalar and vector correlators exhibit a nice $cosh$ behaviour, leading to\na plateau behaviour in the local screening masses as a function of distance.\nThe rho and pi masses so determined show very little variation with the lattice\nspacing a. This augurs well for the use of chiral Fermions, and further\nsuggests the small deviations of these masses from the ideal gas values are\ngenuine effects of interactions.", "category": "hep-lat" }, { "text": "The rate of photon production in the quark-gluon plasma from lattice QCD: We calculate the thermal rate of real-photon production in the quark-gluon\nplasma at a temperature of $T=254$ MeV using lattice QCD. The calculation is\nbased on the difference between the spatially transverse and longitudinal parts\nof the polarization tensor, which has the advantage of falling off rapidly at\nlarge frequencies. We obtain this linear combination in the time-momentum\nrepresentation from lattice QCD with two flavors of quarks in the continuum\nlimit with a precision of about two parts per mille. Applying a theoretically\nmotivated fit ansatz for the associated spectral function, we obtain values for\nthe photon rate that are in line with QCD weak-coupling calculations; for\nphoton momenta $ 1.0\\leq k[{\\rm GeV}]\\leq 1.4$, our non-perturbative results\nconstrain the rate to be no larger than twice the weak-coupling prediction. We\nalso provide a physics interpretation of the electromagnetic spectral functions\nvalid for all frequencies and momenta.", "category": "hep-lat" }, { "text": "Localised Dirac eigenmodes and Goldstone's theorem at finite temperature: I show that a finite density of near-zero localised Dirac modes can lead to\nthe disappearance of the massless excitations predicted by the\nfinite-temperature version of Goldstone's theorem in the chirally broken phase\nof a gauge theory.", "category": "hep-lat" }, { "text": "Vacuum energy of two-dimensional N=(2,2) super Yang-Mills theory: We measure the vacuum energy of two-dimensional N=(2,2) super Yang-Mills\ntheory using lattice simulation. The obtained vacuum energy density is\nE_0=0.09(9)(+10-8) g^2, where the first error is the systematic and the second\nis the statistical one, measured in the dimensionful gauge coupling g which\ngoverns the scale of the system. The result is consistent with unbroken\nsupersymmetry, although we cannot exclude a possible very small non-zero vacuum\nenergy.", "category": "hep-lat" }, { "text": "Machine-learning physics from unphysics: Finding deconfinement\n temperature in lattice Yang-Mills theories from outside the scaling window: We study the machine learning techniques applied to the lattice gauge\ntheory's critical behavior, particularly to the confinement/deconfinement phase\ntransition in the SU(2) and SU(3) gauge theories. We find that the neural\nnetwork, trained on lattice configurations of gauge fields at an unphysical\nvalue of the lattice parameters as an input, builds up a gauge-invariant\nfunction, and finds correlations with the target observable that is valid in\nthe physical region of the parameter space. In particular, if the algorithm\naimed to predict the Polyakov loop as the deconfining order parameter, it\nbuilds a trace of the gauge group matrices along a closed loop in the time\ndirection. As a result, the neural network, trained at one unphysical value of\nthe lattice coupling $\\beta$ predicts the order parameter in the whole region\nof the $\\beta$ values with good precision. We thus demonstrate that the machine\nlearning techniques may be used as a numerical analog of the analytical\ncontinuation from easily accessible but physically uninteresting regions of the\ncoupling space to the interesting but potentially not accessible regions.", "category": "hep-lat" }, { "text": "Energy--momentum tensor on the lattice: recent developments: It is conceivable that the construction of the energy--momentum tensor (EMT)\nin lattice field theory enlarges our ability in lattice field theory and also\ndeepens our understanding on EMT at the non-pertubative level. In this talk, I\nwill review recent developments in this enterprise.", "category": "hep-lat" }, { "text": "A Critical Surface of Chiral-invariant System with Gauge Boson and\n Fermions: In the chirally-invariant context of the $U_{em}(1)$ gauge interaction and\nfour-fermion interactions for ordinary and mirror fermions, the Schwinger-Dyson\nequation for the fermion self-energy function is studied on a lattice. We find\nthat a sensible infrared limit can be defined on a critical surface, which is\nconsistent with the critical line found in the continuum theory.", "category": "hep-lat" }, { "text": "End-to-end distribution function for dilute polymers: We study the end-to-end distribution function for dilute polymers. We present\na computation to order $O(\\epsilon^2)$, $\\epsilon = 4 - d$, and discuss in\ndetail its asymptotic behaviour for small and large distances. The theoretical\npredictions are compared with Monte Carlo results, finding good agreement.", "category": "hep-lat" }, { "text": "Imaginary chemical potential and finite fermion density on the lattice: Standard lattice fermion algorithms run into the well-known sign problem at\nreal chemical potential. In this paper we investigate the possibility of using\nimaginary chemical potential, and argue that it has advantages over other\nmethods, particularly for probing the physics at finite temperature as well as\ndensity. As a feasibility study, we present numerical results for the partition\nfunction of the two-dimensional Hubbard model with imaginary chemical\npotential.\n We also note that systems with a net imbalance of isospin may be simulated\nusing a real chemical potential that couples to I_3 without suffering from the\nsign problem.", "category": "hep-lat" }, { "text": "Calculation of Moments of Structure Functions: The progress on the lattice computation of low moments of both the\nunpolarised and polarised nucleon structure functions is reviewed with\nparticular emphasis on continuum and chiral extrapolations and comparison\nbetween quenched and unquenched fermions.", "category": "hep-lat" }, { "text": "Near-Physical Point Lattice Calculation of Isospin-Breaking Corrections\n to $K_{\\ell2}/\u03c0_{\\ell2}$: In recent years, lattice determinations of non-perturbative quantities such\nas $f_K$ and $f_\\pi$, which are relevant for $V_{us}$ and $V_{ud}$, have\nreached an impressive precision of $\\mathcal{O}(1\\%)$ or better. To make\nfurther progress, electromagnetic and strong isospin breaking effects must be\nincluded in lattice QCD simulations.\n We present the status of the RBC/UKQCD lattice calculation of\nisospin-breaking corrections to light meson leptonic decays. This computation\nis performed in a (2+1)-flavor QCD simulation using Domain Wall Fermions with\nnear-physical quark masses. The isospin-breaking effects are implemented via a\nperturbative expansion of the action in $\\alpha$ and $(m_u-m_d)$. In this\ncalculation, we work in the electro-quenched approximation and the photons are\nimplemented in the Feynman gauge and $\\text{QED}_\\text{L}$ formulation.", "category": "hep-lat" }, { "text": "Kaon decays and other hadronic processes in lattice QCD: This thesis deals with the study of properties and interactions of light\nmesons. Specifically, we focus on hadronic decay and scattering processes,\nwhich are dominated by effects of the strong interaction in the low-energy\nregime. A peculiarity of the strong interaction is that perturbative expansions\nfail at hadronic energy scales. Thus, genuine nonperturbative tools are\nessential to obtain first-principles predictions. Here we use Lattice Field\nTheory, and Effective Field Theories. The mathematical formulation of Quantum\nChromodynamics (QCD) and the methods to resolve its dynamics will be addressed\nin Chapter 1. The research of this dissertation is divided in two parts.\nChapter 2 describes our study of the 't Hooft limit of QCD using lattice\nsimulations, while in Chapter 3 we consider processes that involve\nmultiparticle states. The 't Hooft limit provides a simplification of\nnonabelian gauge theories that leads to nonperturbative predictions. We will\nanalyze the scaling with the number of colours of various observables, such as\nmeson masses, decay constants and weak matrix elements. A question we address\nis the origin of the long-standing puzzle of the $\\Delta I=1/2$ rule, that is,\nthe large hierarchy in the isospin amplitudes of the $K \\to \\pi\\pi$ weak decay.\nRegarding multiparticle processes, we will discuss generalizations of the\nL\\\"uscher formalism to explore three-particle processes from lattice\nsimulations. The focus will be on our contributions, such as our implementation\nof the finite-volume formalism that includes higher partial waves, and the\nfirst application of the formalism to a full lattice QCD spectrum. We will also\ncomment on the extension of the approach to generic three-pion systems. A\nsummary in Spanish will be given in Chapter 4. The final part of the thesis\n(Part II) includes the peer-reviewed publications in their original published\nform.", "category": "hep-lat" }, { "text": "A non-perturbative mechanism for elementary particle mass generation: Taking inspiration from lattice QCD data, we argue that a finite\nnon-perturbative contribution to the quark mass is generated as a consequence\nof the dynamical phenomenon of spontaneous chiral symmetry breaking, in turn\ntriggered by the explicitly breaking of chiral symmetry induced by the critical\nWilson term in the action. In pure lattice QCD this mass term cannot be\nseparated from the unavoidably associated linearly divergent contribution.\nHowever, if QCD is enlarged to a theory where also a scalar field is present,\ncoupled to an SU(2) doublet of fermions via a Yukawa and a Wilson-like term,\nthen in the phase where the scalar field takes a non-vanishing expectation\nvalue, a dynamically generated and \"naturally\" light fermion mass (numerically\nunrelated to the expectation value of the scalar field) is conjectured to\nemerge at a critical value of the Yukawa coupling where the symmetry of the\nmodel is maximally enhanced. Masses dynamically generated in this way display a\nnatural hierarchy according to which the stronger is the strongest of the\ninteractions the fermion is subjected to the larger is its mass.", "category": "hep-lat" }, { "text": "Quark chiral condensate from the overlap quark propagator: From the overlap lattice quark propagator calculated in the Landau gauge, we\ndetermine the quark chiral condensate by fitting operator product expansion\nformulas to the lattice data. The quark propagators are computed on domain wall\nfermion configurations generated by the RBC-UKQCD Collaborations with $N_f=2+1$\nflavors. Three ensembles with different light sea quark masses are used at one\nlattice spacing $1/a=1.75(4)$ GeV. We obtain\n$\\langle\\bar\\psi\\psi\\rangle^{\\overline{\\rm MS}}(2\\mbox{\nGeV})=(-305(15)(21)\\mbox{ MeV})^3$ in the SU(2) chiral limit.", "category": "hep-lat" }, { "text": "The QCD phase diagram for small chemical potentials: We compute derivatives of thermodynamic quantities with respect to $\\mu$, at\n$\\mu=0$ for 2 and 3 flavors of degenerate quark masses. This allows us to\nestimate the phase transition line in the $T,\\mu$ plane and quantify the\ninfluence of a non vanishing chemical potential on the equation of state by\ncomputing lines of constant energy, pressure and density. Moreover we evaluate\nthe order of the QCD phase transition by measuring the Binder Cumulant of the\nchiral condensate. This gives access to the chiral critical point on the phase\ntransition line.", "category": "hep-lat" }, { "text": "Lattice QCD with Classical and Quantum Electrodynamics: We are doubtlessly familiar with some edition of Jackson's tome on\nelectrodynamics, and Schwinger's calculation of the anomalous magnetic moment\nof the electron in QED. From the perspective of strong interactions, however,\nelectromagnetic effects usually amount to negligible contributions. Despite\nthis fact, electromagnetic probes have always been a fundamental source for our\nknowledge of QCD experimentally. Elastic scattering of electrons off nucleons\nprovides us a window to their distributions of charge and magnetism. To account\nfor the spectrum of QCD at the percent level, moreover, we need isospin\nbreaking introduced from both quark masses and electric charges. This overview\nconcerns some of the prospects and progress of studying electromagnetic effects\nin QCD. Our focus is divided between classical and quantum effects. In\nclassical electromagnetic fields, the dynamical response of QCD to external\nconditions can be investigated. The vacuum and hadrons alike should be viewed\nas media which respond to external fields: both magnetize and polarize in\nmagnetic fields, for example. At the quantum level, electromagnetism and QCD\nrenormalize each other. In the era of high precision lattice computations, both\nstrong and electromagnetic contributions must be accounted for to make\npredictions at the percent level.", "category": "hep-lat" }, { "text": "Hadron Spectrum from Dynamical Lattice QCD Simulations: Recent progress in unquenched lattice QCD simulations is reviewed with\nemphasis on understanding of chiral behavior for light quark masses.", "category": "hep-lat" }, { "text": "Higher representations on the lattice: perturbative studies: We present analytical results to guide numerical simulations with Wilson\nfermions in higher representations of the colour group. The ratio of $\\Lambda$\nparameters, the additive renormalization of the fermion mass, and the\nrenormalization of fermion bilinears are computed in perturbation theory,\nincluding cactus resummation. We recall the chiral Lagrangian for the different\npatterns of symmetry breaking that can take place with fermions in higher\nrepresentations, and discuss the possibility of an Aoki phase as the fermion\nmass is reduced at finite lattice spacing.", "category": "hep-lat" }, { "text": "A guide to light-cone PDFs from Lattice QCD: an overview of approaches,\n techniques and results: Within the theory of Quantum Chromodynamics (QCD), the rich structure of\nhadrons can be quantitatively characterized, among others, using a basis of\nuniversal non-perturbative functions: parton distribution functions (PDFs),\ngeneralized parton distributions (GPDs), transverse-momentum dependent\ndistributions (TMDs) and distribution amplitudes (DAs). For more than half a\ncentury, there has been a joint experimental and theoretical effort to obtain\nthese partonic functions. However, the complexity of the strong interactions\nhas placed severe limitations, and first-principle results on the distributions\nwas extracted mostly from their moments computed in Lattice QCD. Recently,\nbreakthrough ideas changed the landscape and several approaches were proposed\nto access the distributions themselves on the lattice.\n In this paper, we review in considerable detail approaches directly related\nto partonic distributions. We highlight a recent idea proposed by X. Ji on\nextracting quasi-distributions that spawned renewed interest in the whole field\nand sparked the largest amount of numerical studies of Lattice QCD. We discuss\ntheoretical and practical developments, including challenges that had to be\novercome, with some yet to be handled. We also review numerical results,\nincluding a discussion based on evolving understanding of the underlying\nconcepts and theoretical and practical progress. Particular attention is given\nto important aspects that validated the quasi-distribution approach, such as\nrenormalization, matching to light-cone distributions and lattice techniques.\n In addition to a thorough discussion of quasi-distributions, we consider\nother approaches: hadronic tensor, auxiliary quark methods, pseudo-PDFs, OPE\nwithout OPE and good lattice cross sections. In closing, we provide prospects\nof the field, with emphasis on the necessary conditions to obtain results with\ncontrolled uncertainties.", "category": "hep-lat" }, { "text": "Localized eigenmodes of covariant Laplacians in the Yang-Mills vacuum: As a probe of the Yang-Mills vacuum, we study numerically the eigenmode\nspectrum of the covariant lattice Laplacian operator. We find that the\neigenmodes at the low and high ends of the spectrum are localized in finite\nregions whose volume is insensitive to the lattice volume. We also find that\nthe vacuum is seen very differently by localized modes of the covariant\nLaplacian in different representations of the gauge group. In the fundamental\nrepresentation, the data suggests that the localization volume is finite in\nphysical units set by the string tension, and localization disappears when\ncenter vortices are removed. In the adjoint and j=3/2 representations the low\nand high-lying modes are far more localized, and the localization volume\nappears to scale to zero, in physical units, in the continuum limit. The\nadjoint Laplacian is insensitive to vortex removal, but we find that\nexponential localization is absent for adjoint eigenmodes in the Higgs phase of\na gauge-Higgs theory. Localization is also absent in the spectrum of the\nCoulomb gauge Faddeev-Popov operator, as required in Coulomb gauge confinement\nscenarios.", "category": "hep-lat" }, { "text": "Extraction of $|V_{cd}|$ and $|V_{cs}|$ from experimental decay rates\n using lattice QCD $D \\to \u03c0(K) \\ell \u03bd$ form factors: We present a determination of the Cabibbo-Kobayashi-Maskawa matrix elements\n$|V_{cd}|$ and $|V_{cs}|$ obtained by combining the momentum dependence of the\nsemileptonic vector form factors $f_+^{D \\to \\pi}(q^2)$ and $f_+^{D \\to\nK}(q^2)$, recently determined from lattice QCD simulations, with the\ndifferential rates measured for the semileptonic $D \\to \\pi \\ell \\nu$ and $D\n\\to K \\ell \\nu$ decays. Our analysis is based on the results for the\nsemileptonic form factors produced by the European Twisted Mass Collaboration\nwith $N_f = 2 + 1 + 1$ flavors of dynamical quarks in the whole range of values\nof the squared 4-momentum transfer accessible in the experiments. The\nstatistical and systematic correlations between the lattice data as well as\nthose present in the experimental data are properly taken into account. With\nrespect to the standard procedure based on the use of only the vector form\nfactor at zero 4-momentum transfer, we obtain more precise and consistent\nresults: $|V_{cd} |= 0.2341 ~ (74)$ and $|V_{cs} |= 0.970 ~ (33)$. The\nsecond-row CKM unitarity is fulfilled within the current uncertainties:\n$|V_{cd}|^2 + |V_{cs}|^2 + |V_{cb}|^2 = 0.996 ~ (64)$. Moreover, using for the\nfirst time hadronic inputs determined from first principles, we have calculated\nthe ratio of the semileptonic $D \\to \\pi(K)$ decay rates into muons and\nelectrons, which represent a test of lepton universality within the SM,\nobtaining in the isospin-symmetric limit of QCD: ${\\cal{R}}_{LU}^{D\\pi} =\n0.985~(2)$ and ${\\cal{R}}_{LU}^{DK} = 0.975~(1)$.", "category": "hep-lat" }, { "text": "Memory efficient finite volume schemes with twisted boundary conditions: In this paper we explore a finite volume renormalization scheme that combines\nthree main ingredients: a coupling based on the gradient flow, the use of\ntwisted boundary conditions and a particular asymmetric geometry, that for\n$SU(N)$ gauge theories consists on a hypercubic box of size $l^2 \\times\n(Nl)^2$, a choice motivated by the study of volume independence in large $N$\ngauge theories. We argue that this scheme has several advantages that make it\nparticularly suited for precision determinations of the strong coupling, among\nthem translational invariance, an analytic expansion in the coupling and a\nreduced memory footprint with respect to standard simulations on symmetric\nlattices, allowing for a more efficient use of current GPU clusters. We test\nthis scheme numerically with a determination of the $\\Lambda$ parameter in the\n$SU(3)$ pure gauge theory. We show that the use of an asymmetric geometry has\nno significant impact in the size of scaling violations, obtaining a value\n$\\Lambda_{\\overline{MS}} \\sqrt{8 t_0} =0.603(17)$ in good agreement with the\nexisting literature. The role of topology freezing, that is relevant for the\ndetermination of the coupling in this particular scheme and for large $N$\napplications, is discussed in detail.", "category": "hep-lat" }, { "text": "Quenched hadron spectroscopy with improved staggered quark action: We investigate light hadron spectroscopy with an improved quenched staggered\nquark action. We compare the results obtained with an improved gauge plus an\nimproved quark action, an improved gauge plus standard quark action, and the\nstandard gauge plus standard quark action. Most of the improvement in the\nspectroscopy results is due to the improved gauge sector. However, the improved\nquark action substantially reduces violations of Lorentz invariance, as\nevidenced by the meson dispersion relations.", "category": "hep-lat" }, { "text": "Hadron Spectrum in QCD with Valence Wilson Fermions and Dynamical\n Staggered Fermions at $6/g^2=5.6: We present an analysis of hadronic spectroscopy for Wilson valence quarks\nwith dynamical staggered fermions at lattice coupling $6/g^2 = \\beta=5.6$ at\nsea quark mass $am_q=0.01$ and 0.025, and of Wilson valence quarks in quenched\napproximation at $\\beta=5.85$ and 5.95, both on $16^3 \\times 32$ lattices. We\nmake comparisons with our previous results with dynamical staggered fermions at\nthe same parameter values but on $16^4$ lattices doubled in the temporal\ndirection.", "category": "hep-lat" }, { "text": "Wave functions of $SU(3)$ pure gauge glueballs on the lattice: The Bethe-Salpeter wave functions of $SU(3)$ pure gauge glueballs are\nrevisited in this study. The ground and the first excited states of scalar and\ntensor glueballs are identified unambiguously by using the variational method\non the basis of large operator sets. We calculate their wave functions in the\nCoulomb gauge and use two lattices with different lattice spacings to check the\ndiscretization artifacts. For ground states, the radial wave functions are\napproximately Gaussian and the size of the tensor is twice as large as that of\nthe scalar. For the first excited states, the radial nodes are clearly observed\nfor both the scalar and the tensor glueballs, such that they can be interpreted\nas the first radial excitations. These observations may shed light on the\ntheoretical understanding of the inner structure of glueballs.", "category": "hep-lat" }, { "text": "Is there any gender/race bias in hep-lat primary publication?\n Machine-Learning Evaluation of Author Ethnicity and Gender: In this work, we analyze papers that are classified as primary hep-lat to\nstudy whether there is any race or gender bias in the journal-publication\nprocess. We implement machine learning to predict the race and gender of\nauthors based on their names and look for measurable differences between\npublication outcomes based on author classification. We would like to invite\ndiscussion on how journals can make improvements in their editorial process and\nhow institutions or grant offices should account for these publication\ndifferences in gender and race.", "category": "hep-lat" }, { "text": "Euclidean partons?: In this talk we reexamine the possibility of evaluating parton distribution\nfunctions from lattice simulations. We show that, while in principle individual\nmoments can be extracted from lattice data, in all cases the process of\nrenormalization, hindered by lattice momenta limitation, represents an\nobstruction to a direct calculation of the full parton distribution function\nfrom QCD simulations. We discuss the case of the Ji quasi-parton distribution\nfunctions, the possibility of using the reduced Ioffe-time distributions and\nthe more recent proposal of directly subtracting power divergent mixings in\nperturbation theory.", "category": "hep-lat" }, { "text": "$|V_{ub}|$ determination in lattice QCD: The 2012 PDG reports a tension at the level of $3 \\sigma$ between two\nexclusive determinations of $|V_{ub}|$. They are obtained by combining the\nexperimental branching ratios of $B \\to \\tau \\nu$ and $B \\to \\pi l \\nu$\n(respectively) with a theoretical computation of the hadronic matrix elements\n$\\fB$ and the $B \\to \\pi$ form factor $f_+(q^2)$. To understand the tension,\nimproved precision and a careful analysis of the systematics involved are\nnecessary. We report the results of the ALPHA collaboration for $\\fB$ from the\nlattice with 2 flavors of $O(a)$ improved Wilson fermions. We employ HQET,\nincluding $1/m_b$ corrections, with pion masses ranging down to $\\approx$ 190\nMeV. Renormalization and matching were performed non-perturbatively, and three\nlattice spacings reaching $a^{-1}\\approx 4.1$ GeV are used in the continuum\nextrapolation. We also present progress towards a computation of $f_+(q^2)$, to\ndirectly compare two independent exclusive determinations of $|V_{ub}|$ with\neach other and with inclusive determinations. Additionally, we report on\npreliminary results for $\\fBq{s}$, needed for the analysis of $B_s \\to\n\\mu^+\\mu^-$.}", "category": "hep-lat" }, { "text": "Gauge Invariant Effective Action in Abelian Chiral Gauge Theory on the\n Lattice: L\\\"uscher's recent formulation of Abelian chiral gauge theories on the\nlattice, in the vacuum (or perturbative) sector in infinite volume, is\nreinterpreted in terms of the lattice covariant regularization. The gauge\ninvariance of the effective action and the integrability of the gauge current\nin anomaly-free cases become transparent. The real part of the effective action\nis simply one-half that of the Dirac fermion and, when the Dirac operator\nbehaves properly in the continuum limit, the imaginary part in this limit\nreproduces the $\\eta$-invariant.", "category": "hep-lat" }, { "text": "Comment on Implications of new physics in the decays $B_c \\to\n (J/\u03c8,\u03b7_c)\u03c4\u03bd$: As part of a study BSM corrections to leptonic decays of the $B_c$ meson,\nTran et al. (arXiv:1801.06927) use the covariant confining quark model (CCQM)\nto estimate the matrix element of the pseudo-scalar curent between the vacuum\nand the $B_c$ meson. We note that this matrix element can be determined using\nexisting lattice QCD results.", "category": "hep-lat" }, { "text": "Gauge-invariant nonlocal quark condensates in QCD: We study, by numerical simulations on a lattice, the behaviour of the\ngauge-invariant nonlocal quark condensates in the QCD vacuum both in the\nquenched approximation and with four flavours of dynamical staggered fermions.\nThe correlation length of the condensate is determined to be roughly twice as\nbig as in the case of the gluon field strength correlators.", "category": "hep-lat" }, { "text": "Electromagnetic structure of charmed baryons in Lattice QCD: As a continuation of our recent work on the electromagnetic properties of the\ndoubly charmed $\\Xi_{cc}$ baryon, we compute the charge radii and the magnetic\nmoments of the singly charmed $\\Sigma_c$, $\\Omega_c$ and the doubly charmed\n$\\Omega_{cc}$ baryons in 2+1 flavor Lattice QCD. In general, the charmed\nbaryons are found to be compact as compared to the proton. The charm quark acts\nto decrease the size of the baryons to smaller values. We discuss the mechanism\nbehind the dependence of the charge radii on the light valence- and sea-quark\nmasses. The magnetic moments are found to be almost stable with respect to\nchanging quark mass. We investigate the individual quark sector contributions\nto the charge radii and the magnetic moments. The magnetic moments of the\nsingly charmed baryons are found to be dominantly determined by the light quark\nand the role of the charm quark is significantly enhanced for the doubly\ncharmed baryons.", "category": "hep-lat" }, { "text": "Nonperturbative Collins-Soper Kernel from Chiral Quarks with Physical\n Masses: We present a lattice QCD calculation of the rapidity anomalous dimension of\nquark transverse-momentum-dependent distributions, i.e., the Collins-Soper (CS)\nkernel, up to transverse separations of about 1 fm. This unitary lattice\ncalculation is conducted, for the first time, employing the\nchiral-symmetry-preserving domain wall fermion discretization and physical\nvalues of light and strange quark masses. The CS kernel is extracted from the\nratios of pion quasi-transverse-momentum-dependent wave functions\n(quasi-TMDWFs) at next-to-leading logarithmic perturbative accuracy. Also for\nthe first time, we utilize the recently proposed Coulomb-gauge-fixed\nquasi-TMDWF correlator without a Wilson line. We observe significantly slower\nsignal decay with increasing quark separations compared to the established\ngauge-invariant method with a staple-shaped Wilson line. This enables us to\ndetermine the CS kernel at large nonperturbative transverse separations and\nfind its near-linear dependence on the latter. Our result is consistent with\nthe recent lattice calculation using gauge-invariant quasi-TMDWFs, and agrees\nwith various recent phenomenological parametrizations of experimental data.", "category": "hep-lat" }, { "text": "Hadron Structure and Form Factors: We review recent results on hadron form factors and nucleon generalized\nparton distibutions obtained with dynamical lattice QCD simulations. We discuss\nlattice artifacts and open questions, and present the connection of lattice\nresults to hadron structure and to the corresponding quantities measured in\nexperiment.", "category": "hep-lat" }, { "text": "Fast Partitioning of Pauli Strings into Commuting Families for\n Expectation Value Measurements of Dense Operators: The cost of measuring quantum expectation values of an operator can be\nreduced by grouping the Pauli string ($SU(2)$ tensor product) decomposition of\nthe operator into maximally commuting sets. We detail an algorithm, presented\nin [1], to partition the full set of $m$-qubit Pauli strings into the minimal\nnumber of commuting families, and benchmark the performance with dense\nHamiltonians on IBM hardware. Here we also compare how our method scales\ncompared to graph-theoretic techniques for the generally commuting case.", "category": "hep-lat" }, { "text": "Is SU(3) gauge theory with 13 massless flavors conformal?: We use lattice simulations to study SU(3) gauge theory with 13 massless\nfermions in the fundamental representation. We present evidence that the theory\nis conformal with a non-zero infrared fixed point in the gauge coupling. We use\na newly-developed technique to calculate the mass anomalous dimension at the\nfixed point via step-scaling of the mode number, allowing us to take the\ncontinuum limit and compare to perturbative predictions. We comment on the\nrelevance of these findings to the extended search for the conformal window in\nthe fundamental representation and in particular 12 massless flavors.", "category": "hep-lat" }, { "text": "Automatic differentiation for error analysis: We present ADerrors.jl, a software for linear error propagation and analysis\nof Monte Carlo data. Although the focus is in data analysis in Lattice QCD,\nwhere estimates of the observables have to be computed from Monte Carlo\nsamples, the software also deals with variables with uncertainties, either\ncorrelated or uncorrelated. Thanks to automatic differentiation techniques\nlinear error propagation is performed exactly, even in iterative algorithms\n(i.e. errors in parameters of non-linear fits). In this contribution we present\nan overview of the capabilities of the software, including access to\nuncertainties in fit parameters and dealing with correlated data. The software,\nwritten in julia, is available for download and use in\nhttps://gitlab.ift.uam-csic.es/alberto/aderrors.jl", "category": "hep-lat" }, { "text": "Lattice QCD Determination of $g_A$: The nucleon axial coupling, $g_A$, is a fundamental property of protons and\nneutrons, dictating the strength with which the weak axial current of the\nStandard Model couples to nucleons, and hence, the lifetime of a free neutron.\nThe prominence of $g_A$ in nuclear physics has made it a benchmark quantity\nwith which to calibrate lattice QCD calculations of nucleon structure and more\ncomplex calculations of electroweak matrix elements in one and few nucleon\nsystems. There were a number of significant challenges in determining $g_A$,\nnotably the notorious exponentially-bad signal-to-noise problem and the\nrequirement for hundreds of thousands of stochastic samples, that rendered this\ngoal more difficult to obtain than originally thought.\n I will describe the use of an unconventional computation method, coupled with\n\"ludicrously'\" fast GPU code, access to publicly available lattice QCD\nconfigurations from MILC and access to leadership computing that have allowed\nthese challenges to be overcome resulting in a determination of $g_A$ with 1%\nprecision and all sources of systematic uncertainty controlled. I will discuss\nthe implications of these results for the convergence of $SU(2)$ Chiral\nPerturbation theory for nucleons, as well as prospects for further improvements\nto $g_A$ (sub-percent precision, for which we have preliminary results) which\nis part of a more comprehensive application of lattice QCD to nuclear physics.\nThis is particularly exciting in light of the new CORAL supercomputers coming\nonline, Sierra and Summit, for which our lattice QCD codes achieve a\nmachine-to-machine speed up over Titan of an order of magnitude.", "category": "hep-lat" }, { "text": "SPHERICALLY SYMMETRIC RANDOM WALKS I. REPRESENTATION IN TERMS OF\n ORTHOGONAL POLYNOMIALS: Spherically symmetric random walks in arbitrary dimension $D$ can be\ndescribed in terms of Gegenbauer (ultraspherical) polynomials. For example,\nLegendre polynomials can be used to represent the special case of\ntwo-dimensional spherically symmetric random walks. In general, there is a\nconnection between orthogonal polynomials and semibounded one-dimensional\nrandom walks; such a random walk can be viewed as taking place on the set of\nintegers $n$, $n=0,~1,~2,~\\ldots$, that index the polynomials. This connection\nallows one to express random-walk probabilities as weighted inner products of\nthe polynomials. The correspondence between polynomials and random walks is\nexploited here to construct and analyze spherically symmetric random walks in\n$D$-dimensional space, where $D$ is {\\sl not} restricted to be an integer. The\nweighted inner-product representation is used to calculate exact closed-form\nspatial and temporal moments of the probability distribution associated with\nthe random walk. The polynomial representation of spherically symmetric random\nwalks is also used to calculate the two-point Green's function for a\nrotationally symmetric free scalar quantum field theory.", "category": "hep-lat" }, { "text": "Determinant of a new fermionic action on a lattice - (II): We investigate the fermion determinant of a new action on a\n$(1+D)$-dimensional lattice for SU(2) gauge groups. This action possesses the\ndiscrete chiral symmetry and provides $2^D$-component fermions. We also comment\non the numerical results on fermion determinants in the $(1+D)$-dimensional\nSU(3) gauge fields.", "category": "hep-lat" }, { "text": "Failure of Mean Field Theory at Large N: We study strongly coupled lattice QCD with $N$ colors of staggered fermions\nin 3+1 dimensions. While mean field theory describes the low temperature\nbehavior of this theory at large $N$, it fails in the scaling region close to\nthe finite temperature second order chiral phase transition. The universal\ncritical region close to the phase transition belongs to the 3d XY universality\nclass even when $N$ becomes large. This is in contrast to Gross-Neveu models\nwhere the critical region shrinks as $N$ (the number of flavors) increases and\nmean field theory is expected to describe the phase transition exactly in the\nlimit of infinite $N$. Our work demonstrates that close to second order phase\ntransitions infrared fluctuations can sometimes be important even when $N$ is\nstrictly infinite.", "category": "hep-lat" }, { "text": "Hamiltonian effective field theory study of the $\\mathbf{N^*(1535)}$\n resonance in lattice QCD: Drawing on experimental data for baryon resonances, Hamiltonian effective\nfield theory (HEFT) is used to predict the positions of the finite-volume\nenergy levels to be observed in lattice QCD simulations of the lowest-lying\n$J^P=1/2^-$ nucleon excitation. In the initial analysis, the phenomenological\nparameters of the Hamiltonian model are constrained by experiment and the\nfinite-volume eigenstate energies are a prediction of the model. The agreement\nbetween HEFT predictions and lattice QCD results obtained on volumes with\nspatial lengths of 2 and 3 fm is excellent. These lattice results also admit a\nmore conventional analysis where the low-energy coefficients are constrained by\nlattice QCD results, enabling a determination of resonance properties from\nlattice QCD itself. Finally, the role and importance of various components of\nthe Hamiltonian model are examined.", "category": "hep-lat" }, { "text": "Free energy of an SU(2) monopole-antimonopole pair: We induce an external ${Z}_2$ monopole-antimonopole pair in an SU(2) lattice\ngauge system and measure its free energy as a way to probe the vacuum\nstructure. We discuss the motivation and computational methodology of the\ninvestigation and illustrate our preliminary results.", "category": "hep-lat" }, { "text": "Phase diagram of the three dimensional Thirring model - A Monte Carlo\n study: Certain approximate solutions of the continuum Schwinger-Dyson Equations\n(SDEs) predict chiral symmetry breaking in the 3d Thirring model when the\nnumber of fermion flavors N_f<4.32 whereas others predict symmetry breaking for\nall N_f. Our results from Monte Carlo simulations with N_f=6, predict a second\norder chiral phase transition. The critical coupling in this case corresponds\nto an ultra-violet fixed point of the renormalization group defining a\nnon-trivial continuum limit. Further, our numerical simulations provide an\nestimate for the critical number of fermion flavors, N_fc \\approx 6.5.", "category": "hep-lat" }, { "text": "A physicist-friendly reformulation of the Atiyah-Patodi-Singer index (on\n a lattice): The Atiyah-Singer index theorem on a closed manifold is well understood and\nappreciated in physics. On the other hand, the Atiyah-Patodi-Singer index,\nwhich is an extension to a manifold with boundary, is physicist-unfriendly, in\nthat it is formulated with a nonlocal boundary condition. Recently we proved\nthat the same index as APS is obtained from the domain-wall fermion Dirac\noperator. Our theorem indicates that the index can be expressed without any\nnonlocal conditions, in such a physicist-friendly way that application to the\nlattice gauge theory is straightforward. The domain-wall fermion provides a\nnatural mathematical foundation for understanding the bulk-edge correspondence\nof the anomaly inflow.", "category": "hep-lat" }, { "text": "Measures of critical exponents in the four dimensional site percolation: Using finite-size scaling methods we measure the thermal and magnetic\nexponents of the site percolation in four dimensions, obtaining a value for the\nanomalous dimension very different from the results found in the literature. We\nalso obtain the leading corrections-to-scaling exponent and, with great\naccuracy, the critical density.", "category": "hep-lat" }, { "text": "A Dual Algorithm for Non-abelian Yang-Mills coupled to Dynamical\n Fermions: We extend the dual algorithm recently described for pure, non-abelian\nYang-Mills on the lattice to the case of lattice fermions coupled to\nYang-Mills, by constructing an ergodic Metropolis algorithm for dynamic\nfermions that is local, exact, and built from gauge-invariant boson-fermion\ncoupled configurations. For concreteness, we present in detail the case of\nthree dimensions, for the group SU(2) and staggered fermions, however the\nalgorithm readily generalizes with regard to group and dimension. The treatment\nof the fermion determinant makes use of a polymer expansion; as with previous\nproposals making use of the polymer expansion in higher than two dimensions,\nthe critical question for practical applications is whether the presence of\nnegative amplitudes can be managed in the continuum limit.", "category": "hep-lat" }, { "text": "Chiral perturbation theory in a theta vacuum: We consider chiral perturbation theory (ChPT) with a non-zero theta term. Due\nto the CP violating term, the vacuum of chiral fields is shifted to a\nnon-trivial element on the SU(N_f) group manifold. The CP violation also\nprovides mixing of different CP eigenstates, between scalar and pseudoscalar,\nor vector and axialvector operators. We investigate upto O(theta^2) effects on\nthe mesonic two point correlators of ChPT to the one-loop order. We also\naddress the effects of fixing topology, by using saddle point integration in\nthe Fourier transform with respect to theta.", "category": "hep-lat" }, { "text": "Preliminary Study of B_K on 2+1 flavor DWF lattices from QCDOC: I present some preliminary calculations of B_K on 2+1 flavor domain-wall\nfermion lattices from the QCDOC, including a set of 16^3x32x8 lattices with\na^{-1} near 1.6 GeV. Although a final result awaits the production of a much\nlonger run, I will compare this preliminary value to previous results.", "category": "hep-lat" }, { "text": "Lattice Study of Radiative $J/\u03c8$ Decay to a Tensor Glueball: The radiative decay of $J/\\psi$ into a pure gauge tensor glueball is studied\nin the quenched lattice QCD formalism. With two anisotropic lattices, the\nmutlipole amplitudes E_1(0), M_2(0) and E_3(0) are obtained to be\n0.114(12)(6)GeV, -0.011(5)(1)GeV, and 0.023(8)(1)GeV, respectively. The first\nerror comes from the statistics, the Q^2 interpolation, and the continuum\nextrapolation, while the second is due to the uncertainty of the scale\nparameter r_0^{-1}=410(20) MeV. Thus the partial decay width\n$\\Gamma(J/\\psi\\rightarrow \\gamma G_{2^{++}})$ is estimated to be 1.01(22)(10)\nkeV which corresponds to a large branch ratio 1.1(2)(1)x10^{-2}. The\nphenomenological implication of this result is also discussed.", "category": "hep-lat" }, { "text": "Existence and Non-Existence of Doubly Heavy Tetraquark Bound States: In this work we investigate the existence of bound states for doubly heavy\ntetraquark systems $ \\bar{Q}\\bar{Q}'qq' $ in a full lattice-QCD computation,\nwhere heavy bottom quarks are treated in the framework of non-relativistic QCD.\nWe focus on three systems with quark content $ \\bar{b}\\bar{b}ud $, $\n\\bar{b}\\bar{b}us $ and $ \\bar{b}\\bar{c}ud $. We show evidence for the existence\nof $ \\bar{b}\\bar{b}ud $ and $ \\bar{b}\\bar{b}us $ bound states, while no binding\nappears to be present for $ \\bar{b}\\bar{c}ud $. For the bound four-quark states\nwe also discuss the importance of various creation operators and give an\nestimate of the meson-meson and diquark-antidiquark percentages.", "category": "hep-lat" }, { "text": "First dynamical simulations with minimally doubled fermions: For thermodynamics studies it is desirable to simulate two degenerate flavors\nand retain at least a remnant of the chiral symmetry. Staggered fermions can\nachieve this at the cost of rooting the determinant. Rooting can be avoided\nusing minimally doubled fermions. This discretization describes two degenerate\nquark flavors while explicitly breaking hyper-cubic symmetry, thus, requiring\nadditional counter-terms. We use one particular formulation of minimally\ndoubled fermions called the Kirsten-Wilczek action and mitigate lattice\nartifacts by improving the spatial derivatives in the Dirac operator. In this\npilot study we determine the counter-terms non-perturbatively to facilitate\nproper dynamical simulations.", "category": "hep-lat" }, { "text": "A novel Bayesian approach to spectral function reconstruction: We present a novel approach to the inference of spectral functions from\nEuclidean time correlator data that makes close contact with modern Bayesian\nconcepts. Our method differs significantly from the maximum entropy method\n(MEM). A new set of axioms is postulated for the prior probability, leading to\nan improved expression, which is devoid of the asymptotically flat directions\npresent in the Shanon-Jaynes entropy. Hyperparameters are integrated out\nexplicitly, liberating us from the Gaussian approximations underlying the\nevidence approach of the MEM. We present a realistic test of our method in the\ncontext of the non-perturbative extraction of the heavy quark potential. Based\non hard-thermal-loop correlator mock data, we establish firm requirements in\nthe number of data points and their accuracy for a successful extraction of the\npotential from lattice QCD. An improved potential estimation from previously\ninvestigated quenched lattice QCD correlators is provided.", "category": "hep-lat" }, { "text": "Phase transition in fluctuating branched geometry: We study grand--canonical and canonical properties of the model of branched\npolymers proposed in \\cite{adfo}. We show that the model has a fourth order\nphase transition and calculate critical exponents. At the transition the\nexponent $\\gamma$ of the grand-canonical ensemble, analogous to the string\nsusceptibility exponent of surface models, $\\gamma \\sim 0.3237525...$ is the\nfirst known example of positive $\\gamma$ which is not of the form $1/n,\\,\nn=2,3,\\ldots$. We show that a slight modification of the model produces a\ncontinuos spectrum of $\\gamma$'s in the range $(0,1/2]$ and changes the order\nof the transition.", "category": "hep-lat" }, { "text": "Bound states for Overlap and Fixed Point Actions close to the chiral\n limit: We study the overlap and the fixed point Dirac operators for massive fermions\nin the two-flavor lattice Schwinger model. The masses of the triplet (pion) and\nsinglet (eta) bound states are determined down to small fermion masses and the\nmass dependence is compared with various continuum model approximations. Near\nthe chiral limit, at very small fermion masses the fixed point operator has\nstability problems, which in this study are dominated by finite size effects,", "category": "hep-lat" }, { "text": "Anomalous finite-size scaling at thermal first-order transitions in\n systems with disordered boundary conditions: We investigate the equilibrium and off-equilibrium behaviors of systems at\nthermal first-order transitions (FOTs) when the boundary conditions favor one\nof the two phases. As a theoretical laboratory we consider the two-dimensional\nPotts model. We show that an anomalous finite-size scaling emerges in systems\nwith open boundary conditions favoring the disordered phase, associated with a\nmixed regime where the two phases are spatially separated. Correspondingly, if\nthe system is slowly heated across the transition, the characteristic times of\nthe off-equilibrium dynamics scale with a power of the size. We argue that\nthese features generally apply to systems at FOTs, when boundary conditions\nfavor one of the two phases. In particular, they should be relevant for the\nexperimental search of FOTs of the quark-gluon plasma in heavy-ion collisions.", "category": "hep-lat" }, { "text": "Accurate Scale Determinations for the Wilson Gauge Action: Accurate determinations of the physical scale of a lattice action are\nrequired to check scaling and take the continuum limit. We present a high\nstatistics study of the static potential for the SU(3) Wilson gauge action on\ncoarse lattices ($5.54 \\leq \\beta \\leq 6.0$). Using an improved analysis\nprocedure we determine the string tension and the Sommer scale $r_0$ (and\nrelated quantities) to 1% accuracy, including all systematic errors. Combining\nour results with earlier ones on finer lattices, we present parameterizations\nof these quantities that should be accurate to about 1% for $5.6 \\leq \\beta\n\\leq 6.5$. We estimate the $\\La$-parameter of quenched QCD to be $\\La_\\MSb =\n247(16)$ MeV.", "category": "hep-lat" }, { "text": "Quarkonium correlators at finite temperature and potential models: We discuss the calculations of quarkonium spectral functions in potential\nmodels and their implications for the interpretation of the lattice data on\nquarkonium correlators. In particular, we find that melting of different\nquarkonium states does not lead to significant change in the Euclidean time\ncorrelators. The large change of the quarkonium correlators above deconfinement\nobserved in the scalar and axial-vector channels appears to be due to the zero\nmode contribution.", "category": "hep-lat" }, { "text": "The Infrared Landau Gauge Gluon Propagator from Lattice QCD: The quenched Landau gauge gluon propagator is investigated in lattice QCD\nwith large assimetric lattices, accessing momenta as low as $q \\sim 100$ MeV or\nsmaller. Our investigation focus on the IR limit of the gluon dressing\nfunction, testing the compatibility with recent solutions of the\nDyson-Schwinger equations. In particular, the low energy parameters $\\kappa$\nand $\\alpha (0)$ are measured.", "category": "hep-lat" }, { "text": "Correlations equalities and some upper bounds for the coupling constant\n implying area decay of Wilson loop for $Z_3$ lattice gauge theories: Correlation identities are obtained for $Z_3$ lattice gauge theory where the\nbonds of the plaquettes are decorated by generalized three-state Ising\nvariables. Making use of correlation inequalities we obtain the area decay of\nthe Wilson loop observable in a range of the coupling parameter larger than\nthose obtained from mean field theory considerations.", "category": "hep-lat" }, { "text": "Prepotential formulation of SU(3) lattice gauge theory: The SU(3) lattice gauge theory is reformulated in terms of SU(3) prepotential\nharmonic oscillators. This reformulation has enlarged $SU(3)\\otimes U(1)\n\\otimes U(1)$ gauge invariance under which the prepotential operators transform\nlike matter fields. The Hilbert space of SU(3) lattice gauge theory is shown to\nbe equivalent to the Hilbert space of the prepotential formulation satisfying\ncertain color invariant Sp(2,R) constraints. The SU(3) irreducible prepotential\noperators which solve these Sp(2,R) constraints are used to construct SU(3)\ngauge invariant Hilbert spaces at every lattice site in terms of SU(3) gauge\ninvariant vertex operators. The electric fields and the link operators are\nreconstructed in terms of these SU(3) irreducible prepotential operators. We\nshow that all the SU(3) Mandelstam constraints become local and take very\nsimple form within this approach. We also discuss the construction of all\npossible linearly independent SU(3) loop states which solve the Mandelstam\nconstraints. The techniques can be easily generalized to SU(N).", "category": "hep-lat" }, { "text": "Specific heat and energy for the three-dimensional O(2) model: We investigate the three-dimensional O(2) model on lattices of size 8^3 to\n160^3 close to the critical point at zero magnetic field. We confirm explicitly\nthe value of the critical coupling J_c found by Ballesteros et al. and estimate\nthere the universal values of g_r and xi/L. At the critical point we study the\nfinite size dependencies of the energy density epsilon and the specific heat C.\nWe find that the nonsingular part of the specific heat C_{ns} is linearly\ndependent on 1/alpha. From the critical behaviour of the specific heat for T\nnot T_c on the largest lattices we determine the universal amplitude ratio\nA+/A-. The alpha- dependence of this ratio is close to the phenomenological\nrelation A+/A- = 1-4alpha.", "category": "hep-lat" }, { "text": "Nucleon form factors on a large volume lattice near the physical point\n in 2+1 flavor QCD: We present results for the isovector nucleon form factors measured on a\n$96^4$ lattice at almost the physical pion mass with a lattice spacing of 0.085\nfm in 2+1 flavor QCD. The configurations are generated with the stout-smeared\n$O(a)$-improved Wilson quark action and the Iwasaki gauge action at\n$\\beta$=1.82. The pion mass at the simulation point is about 146 MeV. A large\nspatial volume of $(8.1~{\\rm fm})^3$ allows us to investigate the form factors\nin the small momentum transfer region. We determine the isovector electric\nradius and magnetic moment from nucleon electric ($G_E$) and magnetic ($G_M$)\nform factors as well as the axial-vector coupling $g_A$. We also report on the\nresults of the axial-vector ($F_A$), induced pseudoscalar ($F_P$) and\npseudoscalar ($G_P$) form factors in order to verify the axial Ward-Takahashi\nidentity in terms of the nucleon matrix elements, which may be called the\ngeneralized Goldberger-Treiman relation.", "category": "hep-lat" }, { "text": "On observable particles in theories with a Brout-Englert-Higgs effect: Even at weak coupling the physical, observable spectrum of gauge theories\nwith a Brout-Englert-Higgs effect can deviate from the elementary one of\nperturbation theory. This can be analytically described and treated using the\nFr\\\"ohlich-Morchio-Strocchi mechanism. We confirm this by lattice simulation\nfor an SU(3) gauge theory with a fundamental scalar, a toy model for grand\nunification. We also show that this has experimentally observable consequence,\ne.g., in scattering cross-sections of lepton collisions in this toy model.", "category": "hep-lat" }, { "text": "Moments of meson distribution functions with dynamical twisted mass\n fermions: We present our preliminary results on the lowest moment of quark\ndistribution functions of the pion using two flavor dynamical simulations with\nWilson twisted mass fermions at maximal twist. The calculation is done in a\nrange of pion masses from 300 to 500 MeV. A stochastic source method is used to\nreduce inversions in calculating propagators. Finite volume effects at the\nlowest quark mass are examined by using two different lattice volumes. Our\nresults show that we achieve statistical errors of only a few percent. We plan\nto compute renormalization constants non-perturbatively and extend the\ncalculation to two more lattice spacings and to the nucleons.", "category": "hep-lat" }, { "text": "Strategies for the Determination of the Running Coupling of\n $(2+1)$-dimensional QED with Quantum Computing: We propose to utilize NISQ-era quantum devices to compute short distance\nquantities in $(2+1)$-dimensional QED and to combine them with large volume\nMonte Carlo simulations and perturbation theory. On the quantum computing side,\nwe perform a calculation of the mass gap in the small and intermediate regime,\ndemonstrating, in the latter case, that it can be resolved reliably. The so\nobtained mass gap can be used to match corresponding results from Monte Carlo\nsimulations, which can be used eventually to set the physical scale. In this\npaper we provide the setup for the quantum computation and show results for the\nmass gap and the plaquette expectation value. In addition, we discuss some\nideas that can be applied to the computation of the running coupling. Since the\ntheory is asymptotically free, it would serve as a training ground for future\nstudies of QCD in $(3+1)$-dimensions on quantum computers.", "category": "hep-lat" }, { "text": "The twelve-flavor $\\boldsymbol\u03b2$-function and dilaton tests of the\n sextet scalar: We discuss near-conformal gauge theories beyond the standard model (BSM)\nwhere interesting results on the twelve-flavor $\\beta$-function of massless\nfermions in the fundamental representation of the SU(3) color gauge group and\ndilaton tests of the light scalar with two massless fermions in the two-index\nsymmetric tensor (sextet) representation can be viewed as parts of the same BSM\nparadigm under investigation. We report results from high precision analysis of\nthe twelve-flavor $\\beta$-function \\cite{Fodor:2016zil} refuting its published\nIRFP \\cite{Cheng:2014jba,Hasenfratz:2016dou}. We present our objections to\nrecent claims \\cite{Hasenfratz:2017mdh,Hasenfratz:2017qyr} for non-universal\nbehavior of staggered fermions used in our analysis. We also report our first\nanalysis of dilaton tests of the light $0^{++}$ scalar in the sextet model and\ncomment on related post-conference developments. The dilaton test is the main\nthrust of this conference contribution including presentation #405 on the\n$n_f=12$ $\\beta$-function and presentation #260 on dilaton tests of the sextet\nmodel. They are both selected from the near-conformal BSM paradigm.", "category": "hep-lat" }, { "text": "Fermions as global correction in lattice QCD: The fermion determinant is a highly non-local object and its logarithm is an\nextensive quantity. For these reasons it is widely believed that the\ndeterminant cannot be treated in acceptance steps of gauge link configurations\nthat differ in a large fraction of the links. However, for exact factorisations\nof the determinant that separate the ultraviolet from the infra-red modes of\nthe Dirac operator it is known that the latter show less variation under\nchanges of the gauge field compared to the former. Using a factorisation based\non recursive domain decomposition allows for a hierarchical algorithm that\nstarts with pure gauge updates of the links within the domains and ends after a\nnumber of filters with a global acceptance step. We find that the global\nacceptance rate is high on moderate lattice sizes. Whether this type of\nalgorithm can help in curing the problem of critical slowing down is presently\nunder study.", "category": "hep-lat" }, { "text": "Self-Avoiding Gonihedric Srting and Spin Systems: We classify different theories of self-intersecting random surfaces assigning\nspecial weights to intersections. When self-intersection coupling constant\n$\\kappa$ tends to zero, then the surface can freely inetrsect and it is\ncompletely self-avoiding when $\\kappa$ tends to infinity. Equivalent spin\nsystems for this general case were constructed. In two-dimension the system\nwith $\\kappa = 0$ is in complete disorder as it is in the case of 2D gauge\nIsing system.", "category": "hep-lat" }, { "text": "Induced representations of Poincare group on the lattice: spin 1/2 and 1\n case: Following standard methods we explore the construction of the discrete\nPoincare group, the semidirect product of discrete translations and integral\nLorentz transformations, using the Wigner-Mackey construction restricted to the\nmomentum and position space on the lattice. The orbit condition, irreducibility\nand assimptotic limit are discussed.", "category": "hep-lat" }, { "text": "On ambiguities of sign determination of the S-matrix from energy levels\n in a finite box: In a recent paper the authors make a study on the determination of the\nS-matrix elements for scattering of particles in the infinite volume from the\nenergy levels in the finite box for the case of multiple channels. The study is\ndone with a toy model in 1+1 dimension and the authors find that there is some\nambiguity in the sign of nondiagonal matrix elements, casting doubts on whether\nthe needed observables in the infinite volume can be obtained from the energy\nlevels of the box. In this paper I present an easy derivation, confirming the\nambiguity of the sign and argue that this, however, does not put restrictions\nin the determination of observables.", "category": "hep-lat" }, { "text": "Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation: It is shown that the Ginsparg-Wilson relation implies an exact symmetry of\nthe fermion action, which may be regarded as a lattice form of an infinitesimal\nchiral rotation. Using this result it is straightforward to construct lattice\nYukawa models with unbroken flavour and chiral symmetries and no doubling of\nthe fermion spectrum. A contradiction with the Nielsen-Ninomiya theorem is\navoided, because the chiral symmetry is realized in a different way than has\nbeen assumed when proving the theorem.", "category": "hep-lat" }, { "text": "A precise determination of T_c in QCD from scaling: Existing lattice data on the QCD phase transition are analyzed in\nrenormalized perturbation theory. In quenched QCD it is found that T_c scales\nfor lattices with only 3 time slices, and that T_c/Lambda_msbar=1.15 \\pm 0.05.\nA preliminary estimate in QCD with two flavours of dynamical quarks shows that\nthis ratio depends on the quark mass. For realistic quark masses we estimate\nT_c/Lambda_msbar=0.49 \\pm 0.02. We also investigate the equation of state in\nquenched QCD at 1-loop order in renormalised perturbation theory.", "category": "hep-lat" }, { "text": "Accelerating Staggered Fermion Dynamics with the Rational Hybrid Monte\n Carlo (RHMC) Algorithm: Improved staggered fermion formulations are a popular choice for lattice QCD\ncalculations. Historically, the algorithm used for such calculations has been\nthe inexact R algorithm, which has systematic errors that only vanish as the\nsquare of the integration step-size. We describe how the exact Rational Hybrid\nMonte Carlo (RHMC) algorithm may be used in this context, and show that for\nparameters corresponding to current state-of-the-art computations it leads to a\nfactor of approximately seven decrease in cost as well as having no step-size\nerrors.", "category": "hep-lat" }, { "text": "Preliminary results of $\u0394I=1/2$ and $3/2$, $K$ to $\u03c0\u03c0$ Decay\n Amplitudes from Lattice QCD: We report a direct lattice calculation of the $K$ to $\\pi\\pi$ decay matrix\nelements for both $\\Delta I=1/2$ and $3/2$ channels on 2+1 flavor, domain wall\nfermion, $16^3\\times32$ lattices with zero $\\pi\\pi$ relative momentum and\n$m_\\pi=420$ MeV. All $K^0$ to $\\pi\\pi$ contractions are carefully listed and\ncalculated. The decay into the isospin zero $\\pi\\pi$ final state, which\nreceives contributions from the disconnected graphs, is very difficult to\ncalculate, but a clear signal in the similar disconnected $\\pi\\pi$ correlator\ncan be seen. Preliminary results, some with large errors, will be presented for\nthe various contributions to the renormalized weak matrix elements $A_0$ and\n$A_2$. We obtain Re$(A_0)$ with $25%$ error in the case of zero momentum on\nshell decay, and find a factor of 6 enhancement for the $\\Delta I=1/2$ rule in\nthe $420$ MeV pion system.", "category": "hep-lat" }, { "text": "Large-N reduction with two adjoint Dirac fermions: We study the single site SU(N) lattice gauge theory with N_f=2 adjoint Wilson\nfermions for values of N up to 53. We determine the phase diagram of the theory\nas a function of the hopping parameter kappa and the inverse 't Hooft coupling\nb, searching for the region in which the Z_N^4 center symmetry is unbroken. In\nthis region the theory is equivalent to the infinite volume theory when N goes\nto infinity. We find a region of values of kappa on both sides of kappa_c for\nwhich the symmetry is unbroken, including both light physical quarks and masses\n~O(1/a). This is surrounded by a region with a complicated sequence of\npartially broken phases. We calculate Wilson loop expectation values and find\nthat using N <= 53 it is possible to extract the heavy-quark potential at small\ndistances (1-3 links) but not at longer distances. For this, larger values of\nN, or lattices with more sites, are needed.", "category": "hep-lat" }, { "text": "Physical properties of Polyakov loop geometrical clusters in SU(2)\n gluodynamics: We apply the liquid droplet model to describe the clustering phenomenon in\nSU(2) gluodynamics, especially, in the vicinity of the deconfinement phase\ntransition. In particular, we analyze the size distributions of clusters formed\nby the Polyakov loops of the same sign. Within such an approach this phase\ntransition can be considered as the transition between two types of liquids\nwhere one of the liquids (the largest droplet of a certain Polyakov loop sign)\nexperiences a condensation, while the other one (the next to largest droplet of\nopposite Polyakov loop sign) evaporates. The clusters of smaller sizes form two\naccompanying gases, and their size distributions are described by the liquid\ndroplet parameterization. By fitting the lattice data we have extracted the\nvalue of Fisher exponent $\\tau =$ 1.806 $\\pm$ 0.008. Also we found that the\ntemperature dependences of the surface tension of both gaseous clusters are\nentirely different below and above the phase transition and, hence, they can\nserve as an order parameter. The critical exponents of the surface tension\ncoefficient in the vicinity of the phase transition are found. Our analysis\nshows that the temperature dependence of the surface tension coefficient above\nthe critical temperature has a $T^2$ behavior in one gas of clusters and $T^4$\nin the other one.", "category": "hep-lat" }, { "text": "Lattice study of the chiral magnetic effect in a chirally imbalanced\n matter: We investigate the chiral magnetic effect by lattice QCD with a chiral\nchemical potential. In a chirally imbalanced matter, we obtain a finite induced\ncurrent along an external magnetic field. We analyze the dependence on the\nlattice spacing, the temperature, the spatial volume, and the fermion mass. The\npresent result indicates that the continuum limit is important for the\nquantitative argument of the strength of the induced current.", "category": "hep-lat" }, { "text": "On Dirac Zero Modes in Hyperdiamond Model: Using the SU(5) symmetry of the 4D hyperdiamond and results on the study of\n4D graphene given in \"Four Dimensional Graphene\" (L.B Drissi, E.H Saidi, M.\nBousmina, CPM-11-01, Phys. Rev. D (2011)), we engineer a class of 4D lattice\nQCD fermions whose Dirac operators have two zero modes. We show that generally\nthe zero modes of the Dirac operator in hyperdiamond fermions are captured by a\ntensor {\\Omega}_{{\\mu}}^{l} with 4\\times5 complex components linking the\nEuclidean SO(4) vector {\\mu}; and the 5-dimensional representation of SU(5).\nThe Bori\\c{c}i-Creutz (BC) and the Karsten-Wilzeck (KW) models as well as their\nDirac zero modes are rederived as particular realizations of\n{\\Omega}_{{\\mu}}^{l}. Other features are also given. Keywords: Lattice QCD,\nBori\\c{c}i-Creutz and Karsten-Wilzeck models, 4D hyperdiamond, 4D graphene,\nSU(5) Symmetry.", "category": "hep-lat" }, { "text": "From deep inelastic scattering to heavy-flavor semi-leptonic decays:\n Total rates into multi-hadron final states from lattice QCD: We present a new technique for extracting decay and transition rates into\nfinal states with any number of hadrons. The approach is only sensitive to\ntotal rates, in which all out-states with a given set of QCD quantum numbers\nare included. For processes involving photons or leptons, differential rates\nwith respect to the non-hadronic kinematics may also be extracted. Our method\ninvolves constructing a finite-volume Euclidean four-point function, whose\ncorresponding spectral function measures the decay and transition rates in the\ninfinite-volume limit. This requires solving the inverse problem of extracting\nthe spectral function from the correlator and also necessitates a smoothing\nprocedure so that a well-defined infinite-volume limit exists. Both of these\nsteps are accomplished by the Backus-Gilbert method and, as we show with a\nnumerical example, reasonable precision can be expected in cases with multiple\nopen decay channels. Potential applications include nucleon structure functions\nand the onset of the deep inelastic scattering regime, as well as semi-leptonic\n$D$ and $B$ decay rates.", "category": "hep-lat" }, { "text": "Pion electric polarizability from lattice QCD: Electromagnetic polarizabilities are important parameters for understanding\nthe interaction between photons and hadrons. For pions these quantities are\npoorly constrained experimentally since they can only be measured indirectly.\nNew experiments at CERN and Jefferson Lab are planned that will measure the\npolarizabilities more precisely. Lattice QCD can be used to compute these\nquantities directly in terms of quark and gluons degrees of freedom, using the\nbackground field method. We present results for the electric polarizability for\ntwo different quark masses, light enough to connect to chiral perturbation\ntheory. These are currently the lightest quark masses used in polarizability\nstudies.", "category": "hep-lat" }, { "text": "K->pi form factors with reduced model dependence: Using partially twisted boundary conditions we compute the K->pi\nsemi-leptonic form factors in the range of momentum transfers 0 <~ q^2 <=\nq^2_{max}=(mK-mpi)^2 in lattice QCD with N_f=2+1 dynamical flavours. In this\nway we are able to determine f+(0) without any interpolation in the momentum\ntransfer, thus eliminating one source of systematic error. This study confirms\nour earlier phenomenological ansatz for the strange quark mass dependence of\nthe scalar form factor. We identify and estimate potentially significant NNLO\neffects in the chiral expansion that guides the extrapolation of the data to\nthe physical point. Our main result is f+(0) = 0.9599(34)(^{+31}_{-43})(14)$,\nwhere the first error is statistical, the second error is due to the\nuncertainties in the chiral extrapolation of the lattice data and the last\nerror is an estimate of potential discretisation effects.", "category": "hep-lat" }, { "text": "Distributions of the Phase Angle of the Fermion Determinant in QCD: The distribution of the phase angle and the magnitude of the fermion\ndeterminant as well as its correlations with the baryon number and the chiral\ncondensate are studied for QCD at non zero quark chemical potential. Results\nare derived to one-loop order in chiral perturbation theory. We find that the\ndistribution of the phase angle is Gaussian for small chemical potential and a\nperiodic Lorentzian when the quark mass is inside the support of the Dirac\nspectrum. The baryon number and chiral condensate are computed as a function of\nthe phase of the fermion determinant and we discuss the severe cancellations\nwhich occur upon integration over the angle. We compute the distribution of the\nmagnitude of the fermion determinant as well as the baryon number and chiral\ncondensate at fixed magnitude.\n Finally, we consider QCD in one Euclidean dimension where it is shown\nanalytically, starting from the fundamental QCD partition function, that the\ndistribution of the phase of the fermion determinant is a periodic Lorentzian\nwhen the quark mass is inside the spectral density of the Dirac operator.", "category": "hep-lat" }, { "text": "Numerical tests of the electroweak phase transition and thermodynamics\n of the electroweak plasma: The finite temperature phase transition in the SU(2) Higgs model at a Higgs\nboson mass $M_H \\simeq 34$ GeV is studied in numerical simulations on\nfour-dimensional lattices with time-like extensions up to $L_t=5$. The effects\nof the finite volume and finite lattice spacing on masses and couplings are\nstudied in detail. The errors due to uncertainties in the critical hopping\nparameter are estimated. The thermodynamics of the electroweak plasma near the\nphase transition is investigated by determining the relation between energy\ndensity and pressure.", "category": "hep-lat" }, { "text": "Semileptonic $B$-meson decays to light pseudoscalar mesons on the HISQ\n ensembles: We report the status of an ongoing lattice-QCD calculation of form factors\nfor exclusive semileptonic decays of $B$ mesons with both charged currents\n($B\\to\\pi\\ell\\nu$, $B_s\\to K\\ell\\nu$) and neutral currents\n($B\\to\\pi\\ell^+\\ell^-$, $B\\to K\\ell^+\\ell^-$). The results are important for\nconstraining or revealing physics beyond the Standard Model. This work uses\nMILC's (2+1+1)-flavor ensembles with the HISQ action for the sea and light\nvalence quarks and the clover action in the Fermilab interpretation for the $b$\nquark. Simulations are carried out at three lattice spacings down to $0.088$\nfm, with both physical and unphysical sea-quark masses. We present preliminary\nresults for correlation-function fits.", "category": "hep-lat" }, { "text": "Study of spatial meson correlators at finite temperature in quenched\n anisotropic lattice QCD: We analyze the meson correlator in the spatial direction at finite\ntemperature. To achieve fine resolution in the spatial direction, we use an\nanisotropic lattice with the standard Wilson plaquette gauge action and the\n$O(a)$ improved Wilson quark action. Below and above $T_c$, properties of\ncorrelators are investigated by two methods: fits with ansatz for the spectral\nfunction, and direct reconstruction of the spectral function using the maximum\nentropy method.", "category": "hep-lat" }, { "text": "Chiral behavior of $K \\to \u03c0l \u03bd$ decay form factors in lattice QCD\n with exact chiral symmetry: We calculate the form factors of the $K \\to \\pi l \\nu$ semileptonic decays in\nthree-flavor lattice QCD, and study their chiral behavior as a function of the\nmomentum transfer and the Nambu-Goldstone boson masses. Chiral symmetry is\nexactly preserved by using the overlap quark action, which enables us to\ndirectly compare the lattice data with chiral perturbation theory (ChPT). We\ngenerate gauge ensembles at a lattice spacing of 0.11fm with four pion masses\ncovering 290-540 MeV and a strange quark mass m_s close to its physical value.\nBy using the all-to-all quark propagator, we calculate the vector and scalar\nform factors with high precision. Their dependence on m_s and the momentum\ntransfer is studied by using the reweighting technique and the twisted boundary\nconditions for the quark fields. We compare the results for the semileptonic\nform factors with ChPT at next-to-next-to leading order in detail. While many\nlow-energy constants appear at this order, we make use of our data of the light\nmeson electromagnetic form factors in order to control the chiral\nextrapolation. We determine the normalization of the form factors as f_+(0) =\n0.9636(36)(+57/-35), and observe reasonable agreement of their shape with\nexperiment.", "category": "hep-lat" }, { "text": "K-meson vector and tensor decay constants and BK-parameter from Nf=2\n tmQCD: We present work in progress on the computation of the K-meson vector and\ntensor decay constants, as well as the B-parameter in Kaon oscillations. Our\nsimulations are performed in a partially quenched setup, with two dynamical\n(sea) Wilson quark flavours, having a maximally twisted mass term. Valence\nquarks are either of the standard or the Osterwalder-Seiler maximally twisted\nvariety. These two regularizations can be suitably combined in order to obtain\na BK parameter which is both multiplicatively renormalizable and O(a) improved.", "category": "hep-lat" }, { "text": "Better Domain-Wall Fermions: We discuss two modifications of domain-wall fermions, aimed to reduce the\nchiral-symmetry violations presently encountered in numerical simulations.", "category": "hep-lat" }, { "text": "Effective Polyakov line actions, and their solutions at finite chemical\n potential: I outline recent progress in the relative weights approach to deriving\neffective Polyakov line actions from an underlying lattice gauge theory, and\ncompare mean field and complex Langevin methods for solving such theories at\nfinite chemical potential.", "category": "hep-lat" }, { "text": "Locality and exponential error reduction in numerical lattice gauge\n theory: In non-abelian gauge theories without matter fields, expectation values of\nlarge Wilson loops and loop correlation functions are difficult to compute\nthrough numerical simulation, because the signal-to-noise ratio is very rapidly\ndecaying for increasing loop sizes. Using a multilevel scheme that exploits the\nlocality of the theory, we show that the statistical errors in such\ncalculations can be exponentially reduced. We explicitly demonstrate this in\nthe SU(3) theory, for the case of the Polyakov loop correlation function, where\nthe efficiency of the simulation is improved by many orders of magnitude when\nthe area bounded by the loops exceeds 1 fm^2.", "category": "hep-lat" }, { "text": "A new phase in the Lorentzian type IIB matrix model and the emergence of\n continuous space-time: The Lorentzian type IIB matrix model is a promising candidate for a\nnon-perturbative formulation of superstring theory. In previous studies, Monte\nCarlo calculations provided interesting results indicating the spontaneous\nbreaking of SO(9) to SO(3) and the emergence of (3+1)-dimensional space-time.\nHowever, an approximation was used to avoid the sign problem, which seemed to\nmake the space-time structure singular. In this talk, we report our results\nobtained by using the complex Langevin method to overcome the sign problem\ninstead of using this approximation. In particular, we discuss the emergence of\ncontinuous space-time in a new phase, which we discovered recently.", "category": "hep-lat" }, { "text": "Lattice 2001: Reflections: A few subjects which strongly intertwine our field are discussed: K --> Pi Pi\ndecay, chiral symmetry on the lattice and a few other selected topics. Open\nquestions are touched also on perturbation theory, locality, Gribov copies, CP\nsymmetry in chiral gauge theories and cut-off effects.", "category": "hep-lat" }, { "text": "Properties of light pseudoscalars from lattice QCD with HISQ ensembles: We fit lattice-QCD data for light-pseudoscalar masses and decay constants,\nfrom HISQ configurations generated by MILC, to SU(3) staggered chiral\nperturbation theory. At present such fits have rather high values of\nchi^2/d.o.f., possibly due to the lack of ensembles with lighter-than-physical\nsea strange-quark masses. We propose solutions to this problem for future work.\nWe also perform simple linear interpolations near the physical point on two\nensembles with different lattice spacings, and obtain the preliminary result\n(f_K / f_pi)^phys = 1.1872(41) in the continuum limit.", "category": "hep-lat" }, { "text": "Solutions of the Ginsparg-Wilson relation and improved domain wall\n fermions: We discuss a number of lattice fermion actions solving the Ginsparg-Wilson\nrelation. We also consider short ranged approximate solutions. In particular,\nwe are interested in reducing the lattice artifacts, while avoiding (or\nsuppressing) additive mass renormalization. In this context, we also arrive at\na formulation of improved domain wall fermions.", "category": "hep-lat" }, { "text": "Decomposition of the static potential in the Maximal Abelian gauge: Decomposition of SU(2) gauge field into the monopole and monopoleless\ncomponents is studied in the Maximal Abelian gauge using Monte-Carlo\nsimulations in lattice SU(2) gluodynamics as well as in two-color QCD with both\nzero and nonzero quark chemical potential. The interaction potential between\nstatic charges is calculated for each component and their sum is compared with\nthe non-Abelian static potential. A good agreement is found in the confinement\nphase. Implications of this result are discussed.", "category": "hep-lat" }, { "text": "Large $N$ scaling and factorization in $\\mathrm{SU}(N)$ Yang-Mills\n theory: We present results for Wilson loops smoothed with the Yang-Mills gradient\nflow and matched through the scale $t_0$. They provide renormalized and precise\noperators allowing to test the $1/N^2$ scaling both at finite lattice spacing\nand in the continuum limit. Our results show an excellent scaling up to $1/N =\n1/3$. Additionally, we obtain a very precise non-perturbative confirmation of\nfactorization in the large $N$ limit.", "category": "hep-lat" }, { "text": "The Charge and Matter radial distributions of Heavy-Light mesons\n calculated on a lattice: For a heavy-light meson with a static heavy quark, we can explore the light\nquark distribution. The charge and matter radial distributions of these\nheavy-light mesons are measured on a 16^3 * 24 lattice at beta=5.7 and a\nhopping parameter corresponding to a light quark mass about that of the strange\nquark. Both distributions can be well fitted up to 4 lattice spacings (r approx\n0.7 fm) with the exponential form w_i^2(r), where w_i(r)=A exp(-r/r_i). For the\ncharge(c) and matter(m) distributions r_c approx 0.32(2) fm and r_m approx\n0.24(2) fm. We also discuss the normalisation of the total charge and matter\nintegrated over all space, finding 1.30(5) and 0.4(1) respectively.", "category": "hep-lat" }, { "text": "Probes of nearly conformal behavior in lattice simulations of minimal\n walking technicolor: We present results from high precision, large volume simulations of the\nlattice gauge theory corresponding to minimal walking technicolor. We find\nevidence that the pion decay constant vanishes in the infinite volume limit and\nthat the dependence of the chiral condensate on quark mass m_q is inconsistent\nwith spontaneous symmetry breaking. These findings are consistent with the\nall-orders beta function prediction as well as the Schroedinger functional\nstudies that indicate the existence of a nontrivial infrared fixed point.", "category": "hep-lat" }, { "text": "The compact Q=2 Abelian Higgs model in the London limit: vortex-monopole\n chains and the photon propagator: The confining and topological properties of the compact Abelian Higgs model\nwith doubly-charged Higgs field in three space-time dimensions are studied. We\nconsider the London limit of the model. We show that the monopoles are forming\nchain-like structures (kept together by ANO vortices) the presence of which is\nessential for getting simultaneously permanent confinement of singly-charged\nparticles and breaking of the string spanned between doubly-charged particles.\nIn the confinement phase the chains are forming percolating clusters while in\nthe deconfinement (Higgs) phase the chains are of finite size. The described\npicture is in close analogy with the synthesis of the Abelian monopole and the\ncenter vortex pictures in confining non--Abelian gauge models. The screening\nproperties of the vacuum are studied by means of the photon propagator in the\nLandau gauge.", "category": "hep-lat" }, { "text": "Dual formulations of Polyakov loop lattice models: Dual representations are constructed for non-abelian lattice spin models with\nU(N) and SU(N) symmetry groups, for all N and in any dimension. These models\nare usually related to the effective models describing the interaction between\nPolyakov loops in the strong coupled QCD. The original spin degrees of freedom\nare explicitly integrated out and a dual theory appears to be a local theory\nfor the dual integer-valued variables. The construction is performed for the\npartition function and for the most general correlation function. The latter\ninclude the two-point function corresponding to quark-anti-quark free energy\nand the N-point function related to the free energy of a baryon. We consider\nboth pure gauge models and models with static fermion determinant for both the\nstaggered and Wilson fermions with an arbitrary number of flavours. While the\nBoltzmann weights of such models are complex in the presence of non-zero\nchemical potential the dual Boltzmann weights appear to be strictly positive on\nadmissible configurations. An essential part of this work with respect to\nprevious studies is an extension of the dual representation to the case of 1)\nan arbitrary value of the temporal coupling constant in the Wilson action and\n2) an arbitrary number of flavours of static quark determinants. The\napplications and extensions of the results are discussed in detail. In\nparticular, we outline a possible approach to Monte-Carlo simulations of the\ndual theory, to the large N expansion and to the development of a tensor\nrenormalization group.", "category": "hep-lat" }, { "text": "Universality and Scaling at the chiral transition in two-flavor QCD at\n finite temperature: The order of the phase transition in finite-temperature QCD with two\ndegenerate light quarks is still an open problem and corresponds to the last\nquestion mark in the zero-density phase diagram of QCD. We argue that\nestablishing the nature of the transition in this case is also a crucial test\nfor numerical simulations of lattice QCD, allowing precise estimates of\npossible systematic errors related e.g. to the choice of fermion-simulation\nalgorithm or of discretized formulation for fermions.", "category": "hep-lat" }, { "text": "Lattice QCD study on $K^\\ast(892)$ meson decay width: We deliver an exploratory lattice QCD examination of the $K^\\ast(892)$ meson\ndecay width with the help of the p-wave scattering phase $\\delta_1$ of\npion-kaon ($\\pi K$) system in the isospin $I=1/2$ channel, which are extracted\nby the modified Rummukainen-Gottlieb formula for two-particle system with\narbitrary mass, and it clearly reveals the entity of a resonance at a mass\naround $K^\\ast(892)$ meson mass. The effective range formula is applied to\ndescribe the energy dependence of the scattering phase and we obtain the\neffective $K^\\ast \\to \\pi K$ coupling constant as $g_{K^\\ast \\pi K} =\n6.38(78)$, and subsequently achieve the decay width to be $64.9 \\pm 8.0$ MeV,\nwhich is in reasonable accordance with the current experiment. Our lattice\ninvestigations are conducted on a $20^3\\times48$ MILC full QCD gauge\nconfiguration at $(m_\\pi + m_K) / m_{K^\\ast} \\approx 0.739$ and the lattice\nspacing $a \\approx 0.15$ fm.", "category": "hep-lat" }, { "text": "Matching coefficients for improved staggered bilinears: We calculate one-loop matching factors for bilinear operators composed of\nimproved staggered fermions. We compare the results for different improvement\nschemes used in the recent literature, including the HYP action and an action\nclose to the Asqtad action. We find that all improvement schemes substantially\nreduce the size of the one-loop contributions to matching factors. The\nresulting corrections are comparable to, or smaller than, those found with\nWilson and domain-wall fermions.", "category": "hep-lat" }, { "text": "Covariant gauge on the lattice: a new implementation: We derive a new implementation of linear covariant gauges on the lattice,\nbased on a minimizing functional that can be interpreted as the Hamiltonian of\na spin-glass model in a random external magnetic field. We show that our method\nsolves most problems encountered in earlier implementations, mostly related to\nthe no-go condition formulated by L. Giusti, Nucl. Phys. B 498, 331 (1997). We\ncarry out tests in the SU(2) case in four space-time dimensions. We also\npresent preliminary results for the transverse gluon propagator at different\nvalues of the gauge parameter xi.", "category": "hep-lat" }, { "text": "New insight in the 2-flavor Schwinger model based on lattice simulations: We consider the Schwinger model with two degenerate, light fermion flavors by\nmeans of lattice simulations. At finite temperature, we probe the viability of\na bosonization method by Hosotani et al. Next we explore an analogue to the\npion decay constant, which agrees for independent formulations based on the\nGell-Mann--Oakes--Renner relation, the 2-dimensional Witten--Veneziano formula\nand the $\\delta$-regime. Finally we confront several conjectures about the\nchiral condensate with lattice results.", "category": "hep-lat" }, { "text": "Perfect Lattice Topology: The Quantum Rotor as a Test Case: Lattice actions and topological charges that are classically and quantum\nmechanically perfect (i.e. free of lattice artifacts) are constructed\nanalytically for the quantum rotor. It is demonstrated that the Manton action\nis classically perfect while the Villain action is quantum perfect. The\ngeometric construction for the topological charge is only perfect at the\nclassical level. The quantum perfect lattice topology associates a topological\ncharge distribution, not just a single charge, with each lattice field\nconfiguration. For the quantum rotor with the classically perfect action and\ntopological charge, the remaining cut-off effects are exponentially suppressed.", "category": "hep-lat" }, { "text": "Two-color QCD with staggered fermions at finite temperature under the\n influence of a magnetic field: In this paper we investigate the influence of a constant external magnetic\nfield on the finite-temperature phase structure and the chiral properties of a\nsimplified lattice model for QCD. We assume an SU(2) gauge symmetry and employ\ndynamical staggered fermions of identical mass without rooting, corresponding\nto Nf=4 flavors of identical electric charge. For fixed mass (given in lattice\nunits) the critical temperature is seen to rise with the magnetic field\nstrength. For three fixed beta-values, selected such that we stay (i) within\nthe chirally broken phase, (ii) within the transition region or (iii) within\nthe chirally restored phase, we study the approach to the chiral limit for\nvarious values of the magnetic field. Within the chirally broken (confinement)\nphase the chiral condensate is found to increase monotonically with a growing\nmagnetic field strength. In the chiral limit the increase starts linear in\nagreement with a chiral model studied by Shushpanov and Smilga. Within the\nchirally restored (deconfinement) phase the chiral condensate tends to zero in\nthe chiral limit, irrespective of the strength of the magnetic field.", "category": "hep-lat" }, { "text": "Observing instantons directly on the lattice without cooling: Based on the study of the simple Abelian Higgs model in $1+1$ dimensions we\nwill present a new method to identify and localize extended instantons. The\nidea is to measure the topological charge on regions somewhat larger than the\nextended instantons so as to average out the ultraviolet fluctuations but\nwithout losing the detailed topological information when going to the full\nspace. The instanton size and probability density can be directly extracted\nfrom this analysis. Local dislocations, which can be avoided for fine enough\nlattices, can be reinterpreted as modified boundary conditions producing\nsectors with net topological charge.", "category": "hep-lat" }, { "text": "Staggered Baryon Operators with Flavor SU(3) Quantum Numbers: The construction of the first baryon operators for staggered lattice QCD\nexploited the taste symmetry to emulate physical quark flavor; contemporary 2+1\nflavor simulations explicitly include three physical quark flavors and\nnecessitate interpreting a valence sector with twelve quarks. After discussing\nexpected features of the resulting baryon spectrum, I consider the spectra of\noperators transforming irreducibly under SU(3)xGTS, the direct product of\nflavor SU(3) and the geometrical time-slice group of the 1-flavor staggered\ntheory. I then describe the construction of a set of maximally local baryon\noperators transforming irreducibly under SU(3)xGTS and enumerate this set. In\nprinciple, the operators listed here could be used to extract the masses of all\nthe lightest spin-1/2 and spin-3/2 baryon resonances of staggered QCD. Using\nappropriate operators from this set in partially quenched simulations should\nallow for particularly clean 2+1 flavor calculations of the masses of the\nnucleon and the lightest decuplet.", "category": "hep-lat" }, { "text": "Renormalization of the effective theory for heavy quarks at small\n velocity: The slope of the Isgur-Wise function at the normalization point,\n$\\xi^{(1)}(1)$,is one of the basic parameters for the extraction of the $CKM$\nmatrix element $V_{cb}$ from exclusive semileptonic decay data. A method for\nmeasuring this parameter on the lattice is the effective theory for heavy\nquarks at small velocity $v$. This theory is a variant of the heavy quark\neffective theory in which the motion of the quark is treated as a perturbation.\nIn this work we study the lattice renormalization of the slow heavy quark\neffective theory. We show that the renormalization of $\\xi^{(1)}(1)$ is not\naffected by ultraviolet power divergences, implying no need of difficult\nnon-perturbative subtractions. A lattice computation of $\\xi^{(1)}(1)$ with\nthis method is therefore feasible in principle. The one-loop renormalization\nconstants of the effective theory for slow heavy quarks are computed to order\n$v^2$ together with the lattice-continuum renormalization constant of\n$\\xi^{(1)}(1)$ . We demonstrate that the expansion in the heavy-quark velocity\nreproduces correctly the infrared structure of the original (non-expanded)\ntheory to every order. We compute also the one-loop renormalization constants\nof the slow heavy quark effective theory to higher orders in $v^2$ and the\nlattice-continuum renormalization constants of the higher derivatives of the\n$\\xi$ function. Unfortunately, the renormalization constants of the higher\nderivatives are affected by ultraviolet power divergences, implying the\nnecessity of numerical non-perturbative subtractions. The lattice computation\nof higher derivatives of the Isgur-Wise function seems therefore problematic.", "category": "hep-lat" }, { "text": "Power-counting theorem for staggered fermions: Lattice power-counting is extended to QCD with staggered fermions. As\npreparation, the difficulties encountered by Reisz's original formulation of\nthe lattice power-counting theorem are illustrated. One of the assumptions that\nis used in his proof does not hold for staggered fermions, as was pointed out\nlong ago by Luscher. Finally, I generalize the power-counting theorem, and the\nmethods of Reisz's proof, such that the difficulties posed by staggered\nfermions are overcome.", "category": "hep-lat" }, { "text": "Universal critical behavior and the transition temperature in\n (2+1)-flavor QCD: We discuss the universal critical behavior in (2+1)-flavor QCD by analyzing\nlattice data from improved staggered fermions generated by the HotQCD\nCollaboration. We present recent results from two different lattice\ndiscretizations and various lattice spacings ($N_\\tau=6,8,12$) at fixed\nphysical strange quark mass ($m_s$) but varying light quark mass ($m_l$). We\nfind that the chiral order-parameter, i.e. the chiral condensate, shows the\nexpected universal scaling that is associated with the critical point in the\nchiral limit already for light quark masses $m_l/m_s \\lsim 0.05$. From an\nanalysis of the disconnected chiral susceptibility we estimate a preliminary\nvalue of the QCD transition temperature.", "category": "hep-lat" }, { "text": "Computing the static potential using non-string-like trial states: We present a method for computing the static quark-antiquark potential, which\nis not based on Wilson loops, but where the trial states are formed by\neigenvector components of the covariant lattice Laplace operator. We have\ntested this method in SU(2) Yang-Mills theory and have obtained results with\nstatistical errors of similar magnitude compared to a standard Wilson loop\ncomputation. The runtime of the method is, however, significantly smaller, when\ncomputing the static potential not only for on-axis, but also for many off-axis\nquark-antiquark separations, i.e. when a fine spatial resolution is required.", "category": "hep-lat" }, { "text": "B- and D-meson decay constants from three-flavor lattice QCD: We calculate the leptonic decay constants of B_{(s)} and D_{(s)} mesons in\nlattice QCD using staggered light quarks and Fermilab bottom and charm quarks.\nWe compute the heavy-light meson correlation functions on the MILC\nasqtad-improved staggered gauge configurations which include the effects of\nthree light dynamical sea quarks. We simulate with several values of the light\nvalence- and sea-quark masses (down to ~m_s/10) and at three lattice spacings\n(a ~ 0.15, 0.12, and 0.09 fm) and extrapolate to the physical up and down quark\nmasses and the continuum using expressions derived in heavy-light meson\nstaggered chiral perturbation theory. We renormalize the heavy-light axial\ncurrent using a mostly nonperturbative method such that only a small correction\nto unity must be computed in lattice perturbation theory and higher-order terms\nare expected to be small. We obtain f_{B^+} = 196.9(8.9) MeV, f_{B_s} =\n242.0(9.5) MeV, f_{D^+} = 218.9(11.3) MeV, f_{D_s} = 260.1(10.8) MeV, and the\nSU(3) flavor-breaking ratios f_{B_s}/f_{B} = 1.229(26) and f_{D_s}/f_{D} =\n1.188(25), where the numbers in parentheses are the total statistical and\nsystematic uncertainties added in quadrature.", "category": "hep-lat" }, { "text": "Light hadron spectrum and quark masses: Recent developments in lattice QCD calculations of the light hadron spectrum\nand quark masses are reviewed.", "category": "hep-lat" }, { "text": "Calculating the Two-photon Contribution to $\u03c0^0 \\rightarrow e^+ e^-$\n Decay Amplitude: We develop a new method that allows us to deal with two-photon intermediate\nstates in a lattice QCD calculation. We apply this method to perform a\nfirst-principles calculation of the $\\pi^0 \\rightarrow e^+ e^-$ decay\namplitude. Both the real and imaginary parts of amplitude are calculated. The\nimaginary part is compared with the prediction of optical theorem to\ndemonstrate the effectiveness of this method. Our result for the real part of\ndecay amplitude is $19.68(52)(1.10) \\ \\text{eV}$, where the first error is\nstatistical and the second is systematic.", "category": "hep-lat" }, { "text": "Operator product expansion and the short distance behavior of 3-flavor\n baryon potentials: The short distance behavior of baryon-baryon potentials defined through\nNambu-Bethe-Salpeter wave functions is investigated using the operator product\nexpansion. In a previous analysis of the nucleon-nucleon case, corresponding to\nthe SU(3) channels $27_s$ and $\\overline{10}_a$, we argued that the potentials\nhave a repulsive core. A new feature occurs for the case of baryons made up of\nthree flavors: manifestly asymptotically attractive potentials appear in the\nsinglet and octet channels. Attraction in the singlet channel was first\nindicated by quark model considerations, and recently been found in numerical\nlattice simulations. The latter have however not yet revealed asymptotic\nattraction in the octet channels; we give a speculative explanation for this\napparent discrepancy.", "category": "hep-lat" }, { "text": "Current Status of Indirect CP Violation in Neutral Kaon System: In the standard model (SM), the CP violation is introduced through a single\nphase in the CKM matrix. The neutral kaon system is one of the most precise\nchannels to test how the SM theory describes the experiment data such as\n$\\epsilon_K$ accurately. The indirect CP violation is parametrized into\n$\\epsilon_{K}$, which can be calculated directly using lattice QCD. In this\ncalculation, the largest uncertainty comes from two sources: one is $\\hat{B}_K$\nand the other is $V_{cb}$. We use the lattice results of $\\hat{B}_K$ and\nexclusive $V_{cb}$ to calculate the theoretical estimate of $\\epsilon_K$, which\nturns out to be $3.1\\sigma$ away from its experimental value. Here, the error\nis evaluated using the standard error propagation method.", "category": "hep-lat" }, { "text": "On the entropy bound of three dimensional simplicial gravity: It is proven that the partition function of 3-dimensional simplicial gravity\nhas an exponential upper bound with the following assumption: any three\ndimensional sphere $S^3$ is constructed by repeated identification of\nneighboring links and neighboring triangles in the boundary of a simplicial\n3-ball. This assumption is weaker than the one proposed by other authors.", "category": "hep-lat" }, { "text": "Density of states for gravitational waves: We present ongoing investigations of the first-order confinement transition\nof a composite dark matter model, to predict the resulting spectrum of\ngravitational waves. To avoid long autocorrelations at the first-order\ntransition, we employ the Logarithmic Linear Relaxation (LLR) density of states\nalgorithm. After testing our calculations by reproducing existing results for\ncompact U(1) lattice gauge theory, we focus on the pure-gauge SU(4) theory\nrelated to the Stealth Dark Matter model.", "category": "hep-lat" }, { "text": "Mitigating topological freezing using out-of-equilibrium simulations: Motivated by the recently-established connection between Jarzynski's equality\nand the theoretical framework of Stochastic Normalizing Flows, we investigate a\nprotocol relying on out-of-equilibrium lattice Monte Carlo simulations to\nmitigate the infamous computational problem of topological freezing. We test\nour proposal on $2d$ $\\mathrm{CP}^{N-1}$ models and compare our results with\nthose obtained adopting the Parallel Tempering on Boundary Conditions proposed\nby M. Hasenbusch, obtaining comparable performances. Our work thus sets the\nstage for future applications combining our Monte Carlo setup with machine\nlearning techniques.", "category": "hep-lat" }, { "text": "Higgs boson mass bounds in the presence of a very heavy fourth quark\n generation: We study the effect of a potential fourth quark generation on the upper and\nlower Higgs boson mass bounds. This investigation is based on the numerical\nevaluation of a chirally invariant lattice Higgs-Yukawa model emulating the\nsame Higgs-fermion coupling structure as in the Higgs sector of the electroweak\nStandard Model. In particular, the considered model obeys a Ginsparg-Wilson\nversion of the underlying ${SU}(2)_L\\times {U}(1)_Y$ symmetry, being a global\nsymmetry here due to the neglection of gauge fields in this model. We present\nour results on the modification of the upper and lower Higgs boson mass bounds\ninduced by the presence of a hypothetical very heavy fourth quark doublet.\nFinally, we compare these findings to the standard scenario of three fermion\ngenerations.", "category": "hep-lat" }, { "text": "Using Gradient Flow to Renormalise Matrix Elements for Meson Mixing and\n Lifetimes: Neutral meson mixing and meson lifetimes are theory-side parametrised in\nterms four-quark operators which can be determined by calculating weak decay\nmatrix elements using lattice Quantum Chromodynamics. While calculations of\nmeson mixing matrix elements are standard, determinations of lifetimes\ntypically suffer from complications in renormalisation procedures because\ndimension-6 four-quark operators can mix with operators of lower mass dimension\nand, moreover, quark-line disconnected diagrams contribute.\n We present work detailing the idea to use fermionic gradient flow to\nnon-perturbatively renormalise matrix elements describing meson mixing or\nlifetimes, and combining it with a perturbative calculation to match to the\n$\\overline{\\rm MS}$ scheme using the shoft-flow-time expansion.", "category": "hep-lat" }, { "text": "CP invariance of chiral gauge theories and Majorana-Yukawa couplings on\n the lattice: The construction of CP-invariant lattice chiral gauge theories and the\nconstruction of lattice Majorana fermions with chiral Yukawa couplings is\nsubject to topological obstructions. In the present work we suggest lattice\nextensions of charge and parity transformation for Weyl fermions. This enables\nus to construct lattice chiral gauge theories that are CP invariant. For the\nconstruction of Majorana-Yukawa couplings, we discuss two models with\nsymplectic Majorana fermions: a model with two symplectic doublets, and one\nwith an auxiliary doublet.", "category": "hep-lat" }, { "text": "Lattice Gauge Fixing, Gribov Copies and BRST Symmetry: We show that a modification of the BRST lattice quantization allows to\ncircumvent an old paradox, formulated by Neuberger, related to lattice Gribov\ncopies and non-perturbative BRST invariance. In the continuum limit the usual\nBRST formulation is recovered.", "category": "hep-lat" }, { "text": "Lattice field theory results for hybrid static potentials at short\n quark-antiquark separations and their parametrization: We present SU(3) lattice Yang-Mills data for hybrid static potentials from\nfive ensembles with different small lattice spacings and the corresponding\nparametrizations for quark-antiquark separations $0.08\\,\\text{fm} \\le r \\le\n1.12\\,\\text{fm}$. We remove lattice discretization errors at tree level of\nperturbation theory and partly at order $a^2$ as well as the $a$-dependent self\nenergy. In particular the tree-level improvement of static potentials is\ndiscussed in detail and two methods are compared. The resulting\nparametrizations are expected to represent continuum limit results for hybrid\nstatic potentials within statistical errors.", "category": "hep-lat" }, { "text": "Can axial U(1) anomaly disappear at high temperature?: In our recent study of two-flavor lattice QCD using chiral fermions, we find\nstrong suppression of axial U(1) anomaly above the critical temperature of\nchiral phase transition. Our simulation data also indicate suppression of\ntopological susceptibility. In this talk, we present both of our theoretical\nand numerical evidence for disappearance of axial U(1) anomaly, emphasizing the\nimportance of controlling lattice chiral symmetry violation, which is enhanced\nat high temperature.", "category": "hep-lat" }, { "text": "String tensions of SU(N) gauge theories in 2+1 dimensions: We calculate the energy spectrum of closed strings in SU(N) gauge theories\nwith N=2,3,4,6,8 in 2+1 dimensions to a high accuracy. We attempt to control\nall systematic errors, and this allows us to perform a precise comparison with\ndifferent theoretical predictions.\n When we study the dependence of the string mass on its length L we find that\nthe Nambu-Goto prediction is a very good approximation down to relatively short\nlengths, where the Luscher term alone is insufficient. We then isolate the\ncorrections to the Luscher term, and compare them to recent theoretical\npredictions, which indeed seem to be mildly preferred by the data.\n When we take these corrections into account and extract string tensions from\nthe string masses, we find that their continuum limit is lower by 2%-1% from\nthe predictions of Karabli, Kim, and Nair. The discrepancy decreases with N,\nbut when we extrapolate our results to N=oo we still find a discrepancy of\n0.88% which is a 4.5 sigma effect.", "category": "hep-lat" }, { "text": "Level spacings for weakly asymmetric real random matrices and\n application to two-color QCD with chemical potential: We consider antisymmetric perturbations of real symmetric matrices in the\ncontext of random matrix theory and two-color quantum chromodynamics. We\ninvestigate the level spacing distributions of eigenvalues that remain real or\nbecome complex conjugate pairs under the perturbation. We work out analytical\nsurmises from small matrices and show that they describe the level spacings of\nlarge random matrices. As expected from symmetry arguments, these level\nspacings also apply to the overlap Dirac operator for two-color QCD with\nchemical potential.", "category": "hep-lat" }, { "text": "Thermodynamics of free Domain Wall fermions: Studying various thermodynamic quantities for the free domain wall fermions\nfor both finite and infinite fifth dimensional extent N_5, we find that the\nlattice corrections are minimum for $N_T\\geq10$ for both energy density and\nsusceptibility, for its irrelevant parameter M in the range 1.45-1.50. The\ncorrection terms are, however, quite large for small lattice sizes of\n$N_T\\leq8$. We propose modifications of the domain wall operator, as well as\nthe overlap operator, to reduce the finite cut-off effects to within 10% of the\ncontinuum results of the thermodynamic quantities for the currently used\nN_T=6-8 lattices. Incorporating chemical potential, we show that \\mu^2\ndivergences are absent for a large class of such domain wall fermion actions\nalthough the chiral symmetry is broken for $\\mu\\neq0$.", "category": "hep-lat" }, { "text": "Matrix elements of (delta S=2) operators with Wilson fermions: We test the recent proposal of using the Ward identities to compute the\nK0-K0bar mixing amplitude with Wilson fermions, without the problem of spurious\nlattice subtractions. From our simulations, we observe no difference between\nthe results obtained with and without subtractions. In addition, from the\nstandard study of the complete set of (delta S=2) operators, we quote the\nfollowing (preliminary) results (in the MS(NDR) scheme): Bk(2 GeV)=0.70(10), <\nO7^{3/2}>_{K->pi pi} = 0.10(2)(1) GeV^3, < O8^{3/2}>_{K->pi pi} = 0.49(6)(0)\nGeV^3.", "category": "hep-lat" }, { "text": "Searching for continuous phase transitions in 5D SU(2) lattice gauge\n theory: We study the phase diagram of 5-dimensional $SU(2)$ Yang-Mills theory on the\nlattice. We consider two extensions of the fundamental plaquette Wilson action\nin the search for the continuous phase transition suggested by the $4+\\epsilon$\nexpansion. The extensions correspond to new terms in the action: i) a unit size\nplaquette in the adjoint representation or ii) a two-unit sided square\nplaquette in the fundamental representation. We use Monte Carlo to sample the\nfirst and second derivative of the entropy near the confinement phase\ntransition, with lattices up to $12^{5}$. While we exclude the presence of a\nsecond order phase transition in the parameter space we sampled for model i),\nour data is not conclusive in some regions of the parameter space of model ii).", "category": "hep-lat" }, { "text": "What the Gribov copy tells on the confinment and the theory of dynamical\n chiral symmetry breaking: We performed lattice Landau gauge QCD simulation on \\beta=6.0, 16^4, 24^4,\n32^4 and \\beta=6.4, 32^4, 48^4 and 56^4 by adopting the gauge fixing that\nminimizes the norm of the gauge field, and measured the running coupling by\nusing the gluon propagator and the ghost propagator. In view of ambiguity in\nthe vertex renormalization factor \\tilde Z_1 in the lattice, we adjust the\nnormalization of the running coupling by the perturbative QCD results near the\nhighest momentum point. It has a maximum \\alpha_s(q)~ 2.1(3) at around q=0.5\nGeV and decreases as q approaches 0, and the Kugo-Ojima parameter reached\n-0.83(2). The infrared exponent of the ghost propagator at 0.4GeV region is\n\\alpha_G=0.20 but there is an exceptional Gribov copy with \\alpha_G=0.27. The\nfeatures of the exceptional Gribov copy are investigated by measuring four\none-dimensional Fourier transform(1-d FT) of the gluon propagator transverse to\neach lattice axis. We observe, in general, correlation between absolute value\nof the Kugo-Ojima parameter and the degree of reflection positivity violation\nin the 1-d FT of the gluon propagator. The 1-d FT of the exceptional Gribov\ncopy has an axis whose gluon propagator manifestly violates reflection\npositivity, and the average of the Cartan subalgebra components of the\nKugo-Ojima parameter along this axis is consistent to -1. The running coupling\nof the enemble average shows a suppression at 0 momentum, but when the ghost\npropagator of the exceptional Gribov copy is adopted, the suppression\ndisappears and the data implies presence of the infrared fixed point\n\\alpha_s(0)~ 2.5(5) and \\kappa=0.5 suggested by the Dyson-Schwinger approach in\nthe multiplicative renormalizable scheme. Comparison with the SU(2) QCD and\nN_f=2 unquenched SU(3) QCD are also made.", "category": "hep-lat" }, { "text": "Stout-smearing, gradient flow and $c_{\\text{SW}}$ at one loop order: The one-loop determination of the coefficient $c_\\text{SW}$ of the Wilson\nquark action has been useful to push the leading cut-off effects for on-shell\nquantities to $\\mathcal{O}(\\alpha^2 a)$ and, in conjunction with\nnon-perturbative determinations of $c_\\text{SW}$, to $\\mathcal{O}(a^2)$, as\nlong as no link-smearing is employed. These days it is common practice to\ninclude some overall link-smearing into the definition of the fermion action.\nUnfortunately, in this situation only the tree-level value\n$c_\\text{SW}^{(0)}=1$ is known, and cut-off effects start at\n$\\mathcal{O}(\\alpha a)$. We present some general techniques for calculating one\nloop quantities in lattice perturbation theory which continue to be useful for\nsmeared-link fermion actions. Specifically, we discuss the application to the\n1-loop improvement coefficient $c_\\text{SW}^{(1)}$ for overall stout-smeared\nWilson fermions.", "category": "hep-lat" }, { "text": "Gauge Invariance and Lattice Monopoles: The number and the location of monopoles in Lattice configurations depend on\nthe choice of the gauge, in contrast to the obvious requirement that monopoles,\nas physical objects, have a gauge-invariant status.\n It is proved, starting from non-abelian Bianchi identities, that monopoles\nare indeed gauge-invariant: the technique used to detect them has instead an\nefficiency which depends on the choice of the abelian projection, in a known\nand well understood way.", "category": "hep-lat" }, { "text": "Lyapunov Spectra in SU(2) Lattice Gauge Theory: We develop a method for calculating the Lyapunov characteristic exponents of\nlattice gauge theories. The complete Lyapunov spectrum of SU(2) gauge theory is\nobtained and Kolmogorov-Sinai entropy is calculated. Rapid convergence with\nlattice size is found.", "category": "hep-lat" }, { "text": "The pion_0 to gamma gamma decay and the chiral anomaly in the\n quark-composites approach to QCD: We evaluate the pion_0 into two gammas decay amplitude by an effective action\nderived from QCD in the quark composites approach, getting the standard value.\nWe also verify that our effective action correctly reproduces the chiral\nanomaly.", "category": "hep-lat" }, { "text": "Gradient Flow Coupling in the SU(2) gauge theory with two adjoint\n fermions: We study SU(2) gauge theory with two fermion flavors in the adjoint\nrepresentation. Using a clover improved HEX smeared action and the gradient\nflow running coupling allows us to simulate with larger lattice size than\nbefore. We find an infrared fixed point after a continuum extrapolation in the\nrange $4.5 \\lesssim g^{*2} \\lesssim 5$. We also measure the mass anomalous\ndimension and find the value $ 0.25 \\lesssim \\gamma^* \\lesssim 0.28 $ at the\nfixed point.", "category": "hep-lat" }, { "text": "Physical observables from boundary artifacts: scalar glueball in\n Yang-Mills theory: By relating the functional averages of a generic scalar operator in\nsimulations with Open (O) and Periodic (P) boundary conditions (BCs)\nrespectively for $SU(3)$ lattice gauge theory, we show that the scalar glueball\nmass and the glueball to vacuum matrix element can be extracted very\nefficiently from the former. Numerical results are compared with those\nextracted from the two point function of the time slice energy density (both\nPBC and OBC). The scaling properties of the mass and the matrix element are\nstudied with the help of Wilson (gradient) flow.", "category": "hep-lat" }, { "text": "Controlling Residual Chiral Symmetry Breaking in Domain Wall Fermion\n Simulations: At stronger gauge-field couplings, the domain wall fermion (DWF) residual\nmass, a measure of chiral symmetry breaking, grows rapidly. This measure is\nlargely due to near zero fermion eigenmodes of logarithm of the 4D transfer\nmatrix along the fifth dimension, and these eigenmodes increase rapidly at\nstrong coupling. To suppress these eigenmodes, we have added to the DWF path\nintegral a multiplicative weighting factor consisting of a ratio of\ndeterminants of Wilson-Dirac fermions having a chirally twisted mass with a\nlarge negative real component and a small imaginary chiral component. Numerical\nresults show that this weighting factor with an appropriate choice of twisted\nmasses significantly suppresses the residual mass while allowing adequate\ntopological tunneling.", "category": "hep-lat" }, { "text": "Developing and testing the density of states FFA method in the SU(3)\n spin model: The Density of States Functional Fit Approach (DoS FFA) is a recently\nproposed modern density of states technique suitable for calculations in\nlattice field theories with a complex action problem. In this article we\npresent an exploratory implementation of DoS FFA for the SU(3) spin system at\nfinite chemical potential $\\mu$ - an effective theory for the Polyakov loop.\nThis model has a complex action problem similar to the one of QCD but also\nallows for a dual simulation in terms of worldlines where the complex action\nproblem is solved. Thus we can compare the DoS FFA results to the reference\ndata from the dual simulation and assess the performance of the new approach.\nWe find that the method reproduces the observables from the dual simulation for\na large range of $\\mu$ values, including also phase transitions, illustrating\nthat DoS FFA is an interesting approach for exploring phase diagrams of lattice\nfield theories with a complex action problem.", "category": "hep-lat" }, { "text": "Non-perturbative improvement of nHYP smeared Wilson fermions: Using Schroedinger functional techniques, we determine the coefficient of the\nclover term necessary for non-perturbative O(a) improvement of hypercubic\nsmeared Wilson fermions on a quenched plaquette action background. Unlike for\nunsmeared Wilson fermions, the resulting clover coefficients are close to the\ntree-level value even at coarse lattice spacings, indicating the absence of\nlarge cutoff effects. A number of exploratory tests are also performed with the\nimproved action.", "category": "hep-lat" }, { "text": "Excited states of massive fermions in a chiral gauge theory: It is shown numerically, in a chiral U(1) gauge Higgs theory in which the\nleft and right-handed fermion components have opposite U(1) charges, that the\nspectrum of gauge and Higgs fields surrounding a static fermion contains both a\nground state and at least one stable excited state. To bypass the difficulties\nassociated with dynamical fermions in a lattice chiral gauge theory we consider\nonly static fermion sources in a quenched approximation, at fixed lattice\nspacing and couplings, and with a lattice action along the lines suggested long\nago by Smit and Swift.", "category": "hep-lat" }, { "text": "Type of dual superconductivity for the $SU(2)$ Yang--Mills theory: We investigate the type of dual superconductivity responsible for quark\nconfinement. For this purpose, we solve the field equations of the $U(1)$\ngauge-scalar model to obtain the static vortex solution in the whole range\nwithout restricting to the long-distance region. Then we use the resulting\nmagnetic field of the vortex to fit the gauge-invariant chromoelectric field\nconnecting a pair of quark and antiquark which was measured by numerical\nsimulations for $SU(2)$ Yang--Mills theory on a lattice. This result improves\nthe accuracy of the fitted value for the Ginzburg--Landau parameter to\nreconfirm the type I dual superconductivity for quark confinement which was\nclaimed by preceding works based on a fitting using the Clem ansatz. Moreover,\nwe calculate the Maxwell stress tensor to obtain the distribution of the force\naround the flux tube. This result suggests that the attractive force acts among\nchromoelectric flux tubes, in agreement with the type I dual superconductivity.", "category": "hep-lat" }, { "text": "Critical Behavior of the Schwinger Model with Wilson Fermions: We present a detailed analysis, in the framework of the MFA approach, of the\ncritical behaviour of the lattice Schwinger model with Wilson fermions on\nlattices up to $24^2$, through the study of the Lee-Yang zeros and the specific\nheat. We find compelling evidence for a critical line ending at $\\kappa = 0.25$\nat large $\\beta$. Finite size scaling analysis on lattices $8^2,12^2,16^2,\n20^2$ and $24^2$ indicates a continuous transition. The hyperscaling relation\nis verified in the explored $\\beta$ region.", "category": "hep-lat" }, { "text": "Aharonov--Bohm Effect in 3D Abelian Higgs Theory: We study a field--theoretical analogue of the Aharonov--Bohm effect in the 3D\nAbelian Higgs Model: the corresponding topological interaction is proportional\nto the linking number of the vortex and the particle world trajectories. We\nshow that the Aharonov--Bohm effect gives rise to a nontrivial interaction of\ntested charged particles.", "category": "hep-lat" }, { "text": "Multicanonical simulation of 3D dynamical triangulation model and a new\n phase structure: We apply the multicanonical technique to the three dimensional dynamical\ntriangulation model, which is known to exhibit a first order phase transition\nwith the Einstein-Hilbert action. We first clarify the first order nature of\nthe phase transition with the Einstein-Hilbert action in several ways including\na high precision finite size scaling analysis. We then add a new local term to\nthe action and confirm the conjecture made through the MCRG technique that the\nline of the first order phase transition extends to the expanded phase diagram,\nending at a point. Fractal dimension at the end point is measured to be around\nthree up to the present size.", "category": "hep-lat" }, { "text": "Clock model interpolation and symmetry breaking in O(2) models: Motivated by recent attempts to quantum simulate lattice models with\ncontinuous Abelian symmetries using discrete approximations, we define an\nextended-O(2) model by adding a $\\gamma \\cos(q\\varphi)$ term to the ordinary\nO(2) model with angular values restricted to a $2\\pi$ interval. In the $\\gamma\n\\rightarrow \\infty$ limit, the model becomes an extended $q$-state clock model\nthat reduces to the ordinary $q$-state clock model when $q$ is an integer and\notherwise is a continuation of the clock model for noninteger $q$. By shifting\nthe $2\\pi$ integration interval, the number of angles selected can change\ndiscontinuously and two cases need to be considered. What we call case $1$ has\none more angle than what we call case $2$. We investigate this class of clock\nmodels in two space-time dimensions using Monte Carlo and tensor\nrenormalization group methods. Both the specific heat and the magnetic\nsusceptibility show a double-peak structure for fractional $q$. In case $1$,\nthe small-$\\beta$ peak is associated with a crossover, and the large-$\\beta$\npeak is associated with an Ising critical point, while both peaks are\ncrossovers in case $2$. When $q$ is close to an integer by an amount $\\Delta q$\nand the system is close to the small-$\\beta$ Berezinskii-Kosterlitz-Thouless\ntransition, the system has a magnetic susceptibility that scales as $\\sim 1 /\n(\\Delta q)^{1 - 1/\\delta'}$ with $\\delta'$ estimates consistent with the\nmagnetic critical exponent $\\delta = 15$. The crossover peak and the Ising\ncritical point move to Berezinskii-Kosterlitz-Thouless transition points with\nthe same power-law scaling. A phase diagram for this model in the $(\\beta, q)$\nplane is sketched. These results are possibly relevant for configurable\nRydberg-atom arrays where the interpolations among phases with discrete\nsymmetries can be achieved by varying continuously the distances among atoms\nand the detuning frequency.", "category": "hep-lat" }, { "text": "Measurement of hadron masses in 2-color finite density QCD: We investigate hadron spectra in 2-color QCD using lattice simulation with\n$N_{f}=2$ at low temperature and finite density in which there appears not only\nthe hadronic phase but also the superfluid phase. We first calculate the pion\nand rho meson spectrum, which is well-known from previous works. The spectral\nordering of these mesons flips around the quark chemical potential\n$\\mu=m^{0}_{\\pi}/2$ ($m^{0}_{\\pi}$: the pion mass at $\\mu=0$), where the phase\ntransition between the hadronic and superfluid phases occurs. For $\\mu \\gtrsim\nm^{0}_{\\pi}/2$, the effective mass for the pion linearly increases while the\none for the rho meson monotonically decreases. Furthermore, we measure hadron\nspectra with the isospin $I=0$ and the angular momentum $J^{P}=0^{\\pm}$. The\neffective masses for the meson, diquark, and antidiquark with the same quantum\nnumber become degenerate just below $\\mu = m^{0}_{\\pi}/2$, and the three\nhadrons have the same mass in the superfluid phase. It suggests that mixing\noccurs between spectra associating with mesons and baryons due to the\n$U(1)_{B}$ symmetry breaking. This phenomenon can be explained in the linear\nsigma model with the approximate $SU(4)$ Pauli-Gursey symmetry.", "category": "hep-lat" }, { "text": "Lambda(1405) and Negative-Parity Baryons in Lattice QCD: We review briefly recent studies of the Lambda(1405) spectrum in Lattice QCD.\nOrdinary three-quark pictures of the Lambda(1405) in quenched Lattice QCD fail\nto reproduce the mass of the experimental value, which seems to support the\npenta-quark picture for the Lambda(1405) such as a Kbar-N molecule-like state.\nIt is also noted that the present results suffer from relatively large\nsystematic uncertainties coming from the finite volume effect, the chiral\nextrapolation and the quenching effect.", "category": "hep-lat" }, { "text": "A Noisy Monte Carlo Algorithm: We propose a Monte Carlo algorithm to promote Kennedy and Kuti's linear\naccept/reject algorithm which accommodates unbiased stochastic estimates of the\nprobability to an exact one. This is achieved by adopting the Metropolis\naccept/reject steps for both the dynamical and noise configurations. We test it\non the five state model and obtain desirable results even for the case with\nlarge noise. We also discuss its application to lattice QCD with stochastically\nestimated fermion determinants.", "category": "hep-lat" }, { "text": "Non-perturbative results for the coefficients b_m and b_a-b_p in O(a)\n improved lattice QCD: We determine the improvement coefficients b_m and b_a-bp in quenched lattice\nQCD for a range of beta-values, which is relevant for current large scale\nsimulations. At fixed beta, the results are rather sensitive to the precise\nchoices of parameters. We therefore impose improvement conditions at constant\nrenormalized parameters, and the coefficients are then obtained as smooth\nfunctions of g_0^2. Other improvement conditions yield a different functional\ndependence, but the difference between the coefficients vanishes with a rate\nproportional to the lattice spacing. We verify this theoretical expectation in\na few examples and are therefore confident that O(a) improvement is achieved\nfor physical quantities. As a byproduct of our analysis we also obtain the\nfinite renormalization constant which relates the subtracted bare quark mass to\nthe bare PCAC mass.", "category": "hep-lat" }, { "text": "Calculation of the pion charge radius from an improved model-independent\n method: We propose a new improved model-independent method for calculating the pion\ncharge radius. In a recently-proposed model-independent method for the pion\ncharge radius, we find it difficult to compute the pion charge radius for small\npole mass $M_{\\rm{pole}}^2$ and volume due to systematic errors coming from\nfinite volume effect and higher-order contamination of the Taylor expansion of\nthe form factor. We circumvent this difficulty by introducing a new appropriate\nfunction and propose a modified method that can calculate the pion charge\nradius with less systematic errors in the small $M_{\\rm{pole}}^2$ and volume\ncases. As preliminary results, we check that our improved model-independent\nmethod works well on a mockup data and also an actual lattice QCD data at the\npion mass of 0.51 GeV.", "category": "hep-lat" }, { "text": "Inclusion of isospin breaking effects in lattice simulations: Isospin symmetry is explicitly broken in the Standard Model by the mass and\nelectric charge of the up and down quarks. These effects represent a\nperturbation of hadronic amplitudes at the percent level. Although these\ncontributions are small, they play a crucial role in hadronic and nuclear\nphysics. Moreover, as lattice computations are becoming increasingly precise,\nit is becoming more and more important to include these effects in numerical\nsimulations. We summarize here how to properly define QCD and QED on a finite\nand discrete space-time so that isospin corrections to hadronic observables can\nbe computed ab-initio and we review the main results on the isospin corrections\nto the hadron spectrum. We mainly focus on the recent work going beyond the\nelectro-quenched approximation.", "category": "hep-lat" }, { "text": "2+1 flavour Domain Wall Fermion simulations by the RBC and UKQCD\n collaborations: We review simulations of dynamical domain wall fermions at a fixed inverse\nlattice spacing of 1.73GeV and with pion masses as light as 330MeV and spatial\ndimensions as large as 2.7fm performed by the RBC and UKQCD collaborations.\nThese results include pseudoscalar masses and decay constants and low energy\nconstants of the chiral effective lagrangian. We also review results for the\nneutral kaon mixing amplitude $B_K$, the Kl3 form factor, pseudoscalar meson\nstructure, and vector meson decay constants. In the baryon sector we review\nresults for the spectrum, and nucleon form factors and structure functions.\nHighlights of our programme include preliminary quark masses, and\ndeterminations of $V_{us}$ from both $f_K/f_\\pi$ and from Kl3, and an updated\nresult for $B_K$. We find significant finite volume effects in the nucleon\naxial charge $g_A$ for our $m_\\pi=330$ MeV ensemble on a $(2.7 {\\rm fm})^3$\nlattice, and highlight the importance of large physical volumes for non-trivial\nnucleon physics.", "category": "hep-lat" }, { "text": "Upper Higgs boson mass bounds from a chirally invariant lattice\n Higgs-Yukawa model: We establish the cutoff-dependent upper Higgs boson mass bound by means of\ndirect lattice computations in the framework of a chirally invariant lattice\nHiggs-Yukawa model emulating the same chiral Yukawa coupling structure as in\nthe Higgs-fermion sector of the Standard Model. As expected from the triviality\npicture of the Higgs sector, we observe the upper mass bound to decrease with\nrising cutoff parameter $\\Lambda$. Moreover, the strength of the fermionic\ncontribution to the upper mass bound is explored by comparing to the\ncorresponding analysis in the pure $\\Phi^4$-theory.", "category": "hep-lat" }, { "text": "On the type of the temperature phase transition in phi-4 model: The temperature induced phase transition is investigated in the one-component\nscalar field \\phi^4 model on a lattice by using Monte Carlo simulations. Using\nthe GPGPU technology a huge amount of data is collected that gives a\npossibility to determine the Linde-Weinberg low bound on the coupling constant\n\\lambda_0 and investigate the type of the phase transition for a wide interval\nof coupling values. It is found that for the values of \\lambda close to this\nbound a weak-first-order phase transition happens. It converts into a second\norder phase transition with the increase of \\lambda. A comparison with analytic\ncalculations in continuum field theory and lattice simulations obtained by\nother authors is given.", "category": "hep-lat" }, { "text": "Chiral symmetry restoration in QCD with many flavours: We discuss the phases of QCD in the parameter space spanned by the number of\nlight flavours and the temperature with respect to the realisation of chiral\nand conformal symmetries. The intriguing interplay of these symmetries is best\nstudied by means of lattice simulations, and some selected results from our\nrecent work are presented here.", "category": "hep-lat" }, { "text": "Distributing the chiral and flavour components of Dirac-Kahler fermions\n across multiple lattices: We use a specific implementation of discrete differential geometry to\ndescribe Dirac-Kahler fermions in such a way that we can separate their chiral\nand flavour components. The formulation introduces additional lattices so that\non each lattice there is a single field of definate chirality. Within this\nframework, we define an non-compact Abelian gauge theory.", "category": "hep-lat" }, { "text": "Exotic phases of finite temperature SU(N) gauge theories with massive\n fermions: F, Adj, A/S: The phase diagrams at high temperature of SU(N) gauge theories with massive\nfermions are calculated by numerically minimizing the one-loop effective\npotential. We consider fermions in the Fundamental (F), Adjoint (Adj),\nAntisymmetric (AS), and Symmetric (S) representations, for N from 3 to 9, with\nperiodic and antiperiodic boundary conditions applied. For one flavour of AS/S\n(Dirac) fermion with periodic boundary conditions the C-breaking phase is\nfavoured perturbatively for all values of the fermion mass. In the case of one\nflavour of adjoint Majorana fermion, and periodic boundary conditons, the\ndeconfined phase is favoured for any fermion mass. For one or more adjoint\nDirac fermion (two or more Majorana fermions) we find partially-confining\nphases as well as new phases with unusual properties. Our results for SU(3) and\nSU(4) are consistent with our lattice simulations of a related model.", "category": "hep-lat" }, { "text": "From C to Parton Sea: Bjorken-x Dependence of the PDFs: Studying the structure of nucleons is not only important to understanding the\nstrong interactions of quarks and gluons, but also to improving the precision\nof new-physics searches. Since a broad class of experiments, including the LHC\nand dark-matter detection, require Standard-Model backgrounds with parton\ndistribution functions (PDFs) as inputs for disentangling SM contributions from\npotential new physics. For a long time, lattice calculations of the PDFs (as\nwell as many hadron structures) has been limited to the first few moments. In\nthis talk, we present a first direct calculation of the Bjorken-x dependence of\nthe PDFs using Large-Momentum Effective Theory (LaMET). An exploratory study of\nthe antiquark/sea flavor asymmetry of these distributions will be discussed.\nThis breakthrough opens an exciting new frontier calculating more complicated\nquantities, such as gluon structure and transverse-momentum dependence, which\nwill complement existing theoretical programs for the upcoming Electron-Ion\nCollider (EIC) or Large Hadron-Electron Collider (LHeC).", "category": "hep-lat" }, { "text": "Axial Nucleon form factors from lattice QCD: We present results on the nucleon axial form factors within lattice QCD using\ntwo flavors of degenerate twisted mass fermions. Volume effects are examined\nusing simulations at two volumes of spatial length $L=2.1$ fm and $L=2.8$ fm.\nCut-off effects are investigated using three different values of the lattice\nspacings, namely $a=0.089$ fm, $a=0.070$ fm and $a=0.056$ fm. The nucleon axial\ncharge is obtained in the continuum limit and chirally extrapolated to the\nphysical pion mass enabling comparison with experiment.", "category": "hep-lat" }, { "text": "Lattice calculation of matrix elements relevant for Delta I=1/2 rule and\n epsilon-prime: We have gained enough statistical precision to distinguish signal from noise\nin matrix elements of all operators relevant for the Delta I=1/2 rule in kaon\ndecays and for the direct CP violation parameter epsilon-prime. We confirm\nsignificant enhancement of Delta I=1/2 transitions observed in experiments,\nalthough a few large systematic uncertainties remain in our predictions:\nhigher-order chiral corrections and lattice spacing dependence. The estimate of\nepsilon-prime parameter is further complicated by the problem of matching\nlattice and continuum operators.", "category": "hep-lat" }, { "text": "Acceleration of the Arnoldi method and real eigenvalues of the\n non-Hermitian Wilson-Dirac operator: In this paper, we present a method for the computation of the low-lying real\neigenvalues of the Wilson-Dirac operator based on the Arnoldi algorithm. These\neigenvalues contain information about several observables. We used them to\ncalculate the sign of the fermion determinant in one-flavor QCD and the sign of\nthe Pfaffian in N=1 super Yang-Mills theory. The method is based on polynomial\ntransformations of the Wilson-Dirac operator, leading to considerable\nimprovements of the computation of eigenvalues. We introduce an iterative\nprocedure for the construction of the polynomials and demonstrate the\nimprovement in the efficiency of the computation. In general, the method can be\napplied to operators with a symmetric and bounded eigenspectrum.", "category": "hep-lat" }, { "text": "How the Quark Number fluctuates in QCD at small chemical potential: We discuss the distribution of the quark number over the gauge fields for QCD\nat nonzero quark chemical potential. As the quark number operator is\nnon-hermitian, the distribution is over the complex plane. Moreover, because of\nthe fermion determinant, the distribution is not real and positive. The\ncomputation is carried out within leading order chiral perturbation theory and\ngives direct insight into the delicate cancellations that take place in\ncontributions to the total baryon number.", "category": "hep-lat" }, { "text": "A calculation of the $B_{B}$ parameter in the static limit: We calculate the $B_{B}$ parameter, relevant for $\\overline{B}^0$ -- $B^0$\nmixing, from a lattice gauge theory simulation at $\\beta = 6.0$. The bottom\nquarks are simulated in the static theory, the light quarks with Wilson\nfermions. Improved smearing functions produced by a variational technique,\nMOST, are used to reduce statistical errors and minimize excited-state\ncontamination of the ground-state signal. We obtain $B_B(4.33 GeV) =\n0.98^{+4}_{-4}$ (statistical) $^{+3}_{-18}$ (systematic) which corresponds to\n$\\widehat{B}_B = 1.40^{+6}_{-6}$ (statistical) $^{+4}_{-26}$ (systematic) for\nthe one-loop renormalization-scheme-independent parameter. The systematic\nerrors include the uncertainty due to alternative (less favored) treatments of\nthe perturbatively-calculated mixing coefficients; this uncertainty is at least\nas large as residual differences between Wilson-static and clover-static\nresults. Our result agrees with extrapolations of results from relativistic\n(Wilson) heavy quark simulations.", "category": "hep-lat" }, { "text": "UV divergence of the quasi-PDF operator under the lattice regularization: Even since the \"quasi\" parton distribution function (PDF) was proposed under\nthe large-momentum effective theory (LaMET) framework, its renormalization\nunder the lattice regularization has been a central challenge to be solved due\nto the linear divergence. Thus, we investigate several possible ways to\nrenormalize the quasi-PDF operators in high accuracy with non-perturbative\ncalculation using the quench configurations at several lattice spacings. We\nfind that the ratio of the UV divergences obtained from the Wilson loop and\noff-shell quasi-PDF operator is not a constant of the Wilson link length $z$.\nAlthough the linear divergence in them may be consistent to each other\nnumerically, there is some additional UV divergence in the quasi-PDF operator.", "category": "hep-lat" }, { "text": "Partially Quenched QCD with Non-Degenerate Dynamical Quarks: We discuss the importance of using partially quenched theories with three\ndegenerate quarks for extrapolating to QCD, and present some relevant results\nfrom chiral perturbation theory.", "category": "hep-lat" }, { "text": "The Weak-Coupling Limit of Simplicial Quantum Gravity: In the weak-coupling limit, kappa_0 going to infinity, the partition function\nof simplicial quantum gravity is dominated by an ensemble of triangulations\nwith the ratio N_0/N_D close to the upper kinematic limit. For a combinatorial\ntriangulation of the D--sphere this limit is 1/D. Defining an ensemble of\nmaximal triangulations, i.e. triangulations that have the maximal possible\nnumber of vertices for a given volume, we investigate the properties of this\nensemble in three dimensions using both Monte Carlo simulations and a\nstrong-coupling expansion of the partition function, both for pure simplicial\ngravity and a with a suitable modified measure. For the latter we observe a\ncontinuous phase transition to a crinkled phase and we investigate the fractal\nproperties of this phase.", "category": "hep-lat" }, { "text": "Perturbative renormalization functions of local operators for staggered\n fermions with stout improvement: In this paper we present the perturbative computation of the renormalization\nfunctions for the quark field and for a complete set of ultra-local fermion\nbilinears. The computation of the relevant Green's functions was carried out at\n1-loop level for the staggered action using massive fermions. The gluon links\nwhich appear both in the fermion action and in the definition of the bilinears\nhave been improved by applying a stout smearing procedure up to 2 times,\niteratively. In the gluon sector we employed the Symanzik improved gauge action\nfor different sets of values of the Symanzik coefficients. The renormalization\nfunctions are presented in (two variants of) the RI' and in the MSbar\nrenormalization scheme; the dependence on all stout parameters, as well as on\nthe fermion mass, the gauge fixing parameter and the renormalization scale, is\nshown explicitly. This work is related to our recent paper [Phys. Rev. D86\n(2012) 094512, arXiv:1209.6015]. To make our results easily accessible to the\nreader, we include them in the distribution package of this paper, as a\nMathematica input file, Staggered.m.", "category": "hep-lat" }, { "text": "Light-quark connected intermediate-window contributions to the muon\n $g-2$ hadronic vacuum polarization from lattice QCD: We present a lattice-QCD calculation of the light-quark connected\ncontribution to window observables associated with the leading-order hadronic\nvacuum polarization contribution to the anomalous magnetic moment of the muon,\n$a_\\mu^{\\mathrm{HVP,LO}}$. We employ the MILC Collaboration's isospin-symmetric\nQCD gauge-field ensembles, which contain four flavors of dynamical\nhighly-improved-staggered quarks with four lattice spacings between $a\\approx\n0.06$-$0.15$~fm and close-to-physical quark masses. We consider several\neffective-field-theory-based schemes for finite-volume and other lattice\ncorrections and combine the results via Bayesian model averaging to obtain\nrobust estimates of the associated systematic uncertainties. After unblinding,\nour final results for the intermediate and ``W2'' windows are $a^{ll,{\\mathrm\nW}}_{\\mu}(\\mathrm{conn.})=206.6(1.0) \\times 10^{-10}$ and $a^{ll,\\mathrm\n{W2}}_{\\mu}(\\mathrm{conn.}) = 100.7(3.2)\\times 10^{-10}$, respectively.", "category": "hep-lat" }, { "text": "Study of the finite temperature transition in 3-flavor QCD using the R\n and RHMC algorithms: We study the finite temperature transition in QCD with three flavors of equal\nmasses using the R and RHMC algorithm on lattices with temporal extent\nN_{\\tau}=4 and 6. For the transition temperature in the continuum limit we find\nr_0 T_c=0.429(8) for the light pseudo-scalar mass corresponding to the end\npoint of the 1st order transition region. When comparing the results obtained\nwith the R and RHMC algorithms for p4fat3 action we see no significant\nstep-size errors down to a lightest pseudo-scalar mass of m_{ps} r_0=0.4.", "category": "hep-lat" }, { "text": "Fast Partitioning of Pauli Strings into Commuting Families for\n Expectation Value Measurements of Dense Operators: The cost of measuring quantum expectation values of an operator can be\nreduced by grouping the Pauli string ($SU(2)$ tensor product) decomposition of\nthe operator into maximally commuting sets. We detail an algorithm, presented\nin [1], to partition the full set of $m$-qubit Pauli strings into the minimal\nnumber of commuting families, and benchmark the performance with dense\nHamiltonians on IBM hardware. Here we also compare how our method scales\ncompared to graph-theoretic techniques for the generally commuting case.", "category": "hep-lat" }, { "text": "Domain-wall and overlap fermions at nonzero quark chemical potential: We have recently given a construction of the overlap Dirac operator at\nnonzero quark chemical potential. Here, we introduce a quark chemical potential\nin the domain-wall fermion formalism and show that our earlier result is\nreproduced if the extent of the fifth dimension is taken to infinity and its\nlattice spacing is taken to zero. We also extend this result to include a bare\nquark mass, consider its continuum limit, and prove a number of properties of\nthe overlap operator at nonzero quark chemical potential. In particular, we\nshow that the relation between the anomaly and the index of the overlap\noperator remains valid.", "category": "hep-lat" }, { "text": "Vacuum structure of gauge theory on lattice with two parallel plaquette\n action: We perform Monte Carlo simulations of a lattice gauge system with an action\nwhich contains two parallel plaquettes. The action is defined as a product of\ngauge group variables over two parallel plaquettes belonging to a given\nthree-dimensional cube. The peculiar property of this system is that it has\nstrong degeneracy of the vacuum state inherited from corresponding gonihedric\n$Z_2$ gauge spin system. These vacuua are well separated and can not be\nconnected by a gauge transformation. We measure different observables in these\nvacuua and compare their properties.", "category": "hep-lat" }, { "text": "$\u039b(1405)$ from lattice QCD: Low-lying $\\Lambda$ baryons with spin 1/2 are analyzed in two-flavor lattice\nQCD. In order to extract two low-lying states for each parity, we construct $2\n\\times 2$ cross correlators from flavor SU(3) ``octet'' and ``singlet'' baryon\noperators, and diagonalize them. Two-flavor CP-PACS gauge configurations are\nemployed, which are generated with the renormalization-group improved gauge\naction and the ${\\mathcal O}(a)$-improved quark action. Simulation are\nperformed at three different $\\beta$'s, $\\beta = 1.80$, 1.95 and 2.10, whose\ncorresponding lattice spacings are $a = 0.2150$, 0.1555 and 0.1076 fm. For each\ncutoff, we adopt four different hopping parameters, ($\\kappa_{\\rm val},\n\\kappa_{\\rm sea}$). The corresponding pion masses range from about 500 MeV to\n1.1 GeV. The results are extrapolated to the physical quark-mass point. Our\nresults indicate that there are two negative-parity $\\Lambda$ states nearly\ndegenerate at around 1.6 GeV, whereas no state as low as $\\Lambda (1405)$ is\nobserved. By extracting the flavor components of each state, we find that the\nlowest (1st-excited) negative-parity state is dominated by flavor-singlet\n(flavor-octet) component.", "category": "hep-lat" }, { "text": "Applying Integrability to Gauge Theories: Lattice Yang-Mills theories in any dimension may be regarded as coupled\n1+1-dimensional integrable field theories. These integrable systems decouple at\nlarge center-of-mass energies, where the action becomes effectively\nanisotropic. This effective action is the high-energy center-of-mass limit of\nthe gauge theory. In 2+1 dimensions, the quark-antiquark potential and the mass\nspectrum can be calculated, using the exact 1+1-dimensional S-matrix and form\nfactors. The methods are quite similar to those applying integrability in\nstatistical and condensed-matter physics. The high-energy anisotropic action at\none loop in 3+1 dimensions has been found using a Wilsonian renormalization\nmethod. We briefly discuss the isotropic theory in 2+1 dimensions and the\nconnection with soft scattering in 3+1 dimensions.", "category": "hep-lat" }, { "text": "Flavor Twisted Boundary Conditions in the Breit Frame: We use a generalization of chiral perturbation theory to account for the\neffects of flavor twisted boundary conditions in the Breit frame. The relevant\nframework for two light flavors is an SU(6|4) partially quenched theory, where\nthe extra valence quarks differ only by their boundary conditions. Focusing on\nthe pion electromagnetic form factor, finite volume corrections are calculated\nat next-to-leading order in the chiral expansion and are estimated to be small\non current lattices.", "category": "hep-lat" }, { "text": "Formal Developments for Lattice QCD with Applications to Hadronic\n Systems: Lattice quantum chromodynamics (QCD) will soon become the primary theoretical\ntool in rigorous studies of single- and multi-hadron sectors of QCD. It is\ntruly ab initio meaning that its only parameters are those of standard model.\nThe result of a lattice QCD calculation corresponds to that of nature only in\nthe limit when the volume of spacetime is taken to infinity and the spacing\nbetween discretized points on the lattice is taken to zero. A better\nunderstanding of these discretization and volume effects not only provides the\nconnection to the infinite-volume continuum observables, but also leads to\noptimized calculations that can be performed with available computational\nresources. This thesis includes various formal developments in this direction,\nalong with proposals for improvements, to be applied to the upcoming lattice\nQCD studies of nuclear and hadronic systems. Among these developments are i) an\nanalytical investigation of the recovery of rotational symmetry with the use of\nsuitably-formed smeared operators toward the continuum limit, ii) an extension\nof the Luscher finite-volume method to two-nucleon systems with arbitrary\nangular momentum, spin, parity and center of mass momentum, iii) the\napplication of such formalism in extracting the scattering parameters of the\n3S1-3D1 coupled channels, iv) an investigation of twisted boundary conditions\nin the single- and two-hadron sectors, with proposals for improving the\nvolume-dependence of the deuteron binding energy upon proper choices of\nboundary conditions, and v) exploring the volume dependence of the masses of\nhadrons and light-nuclei due to quantum electrodynamic interactions, including\nthe effects arising from particles' compositeness. The required background as\nwell as a brief status report of the field pertinent to the discussions in this\nthesis are presented.", "category": "hep-lat" }, { "text": "A Study of PCAC for the Nonperturbative Improvement of the Wilson Action: We present an exploratory study for the nonperturbative determination of the\ncoefficient of the ${\\cal O}(a)$ improvement term to the Wilson action,\n$c_{SW}$. Following the work by L\\\"{u}scher et al., we impose the PCAC relation\nas a nonperturbative improvement condition on $c_{SW}$, without, however, using\nthe Schr\\\"{o}dinger functional in our calculation.", "category": "hep-lat" }, { "text": "Spectrum of the Hermitian Wilson Dirac operator: Recent results on the spectral properties of the Hermitian Wilson-Dirac\noperator are presented.", "category": "hep-lat" }, { "text": "QCD Thermodynamics with an almost realistic quark mass spectrum: We will report on the status of a new large scale calculation of\nthermodynamic quantities in QCD with light up and down quarks corresponding to\nan almost physical light quark mass value and a heavier strange quark mass.\nThese calculations are currently being performed on the QCDOC Teraflops\ncomputers at BNL. We will present new lattice calculations of the transition\ntemperature and various susceptibilities reflecting properties of the chiral\ntransition. All these quantities are of immediate interest for heavy ion\nphenomenology.", "category": "hep-lat" }, { "text": "Moments of Ioffe time parton distribution functions from non-local\n matrix elements: We examine the relation of moments of parton distribution functions to matrix\nelements of non-local operators computed in lattice quantum chromodynamics. We\nargue that after the continuum limit is taken, these non-local matrix elements\ngive access to moments that are finite and can be matched to those defined in\nthe $\\overline{MS}$ scheme. We demonstrate this fact with a numerical\ncomputation of moments through non-local matrix elements in the quenched\napproximation and we find that these moments are in excellent agreement with\nthe moments obtained from direct computations of local twist-2 matrix elements\nin the quenched approximation.", "category": "hep-lat" }, { "text": "B-Bbar Mixing and Matching with Fermilab Heavy Quarks: We discuss the matching procedure for heavy-light 4-quark operators using the\nFermilab method for heavy quarks and staggered fermions for light quarks. These\ningredients enable us to construct the continuum-limit operator needed to\ndetermine the oscillation frequency of neutral B mesons. The matching is then\ncarried out at the one-loop level. We also present an updated preliminary\nresult for the SU(3)-breaking ratio \\xi, based on calculations using the MILC\nCollaboration's ensembles of lattice gauge fields.", "category": "hep-lat" }, { "text": "A Numerical Test of KPZ Scaling: Potts Models Coupled to Two-Dimensional\n Quantum Gravity: We perform Monte Carlo simulations using the Wolff cluster algorithm of the\nq=2 (Ising), 3, 4 and q=10 Potts models on dynamical phi-cubed graphs of\nspherical topology with up to 5000 nodes. We find that the measured critical\nexponents are in reasonable agreement with those from the exact solution of the\nIsing model and with those calculated from KPZ scaling for q=3,4 where no exact\nsolution is available. Using Binder's cumulant we find that the q=10 Potts\nmodel displays a first order phase transition on a dynamical graph, as it does\non a fixed lattice. We also examine the internal geometry of the graphs\ngenerated in the simulation, finding a linear relationship between ring length\nprobabilities and the central charge of the Potts model", "category": "hep-lat" }, { "text": "Relativistic Lattice Boltzmann Methods: Theory and Applications: We present a systematic account of recent developments of the relativistic\nLattice Boltzmann method (RLBM) for dissipative hydrodynamics. We describe in\nfull detail a unified, compact and dimension-independent procedure to design\nrelativistic LB schemes capable of bridging the gap between the\nultra-relativistic regime, $k_{\\rm B} T \\gg mc^2$, and the non-relativistic\none, $k_{\\rm B} T \\ll mc^2$. We further develop a systematic derivation of the\ntransport coefficients as a function of the kinetic relaxation time in\n$d=1,2,3$ spatial dimensions. The latter step allows to establish a\nquantitative bridge between the parameters of the kinetic model and the\nmacroscopic transport coefficients. This leads to accurate calibrations of\nsimulation parameters and is also relevant at the theoretical level, as it\nprovides neat numerical evidence of the correctness of the Chapman-Enskog\nprocedure. We present an extended set of validation tests, in which simulation\nresults based on the RLBMs are compared with existing analytic or semi-analytic\nresults in the mildly-relativistic ($k_{\\rm B} T \\sim mc^2$) regime for the\ncase of shock propagations in quark-gluon plasmas and laminar electronic flows\nin ultra-clean graphene samples. It is hoped and expected that the material\ncollected in this paper may allow the interested readers to reproduce the\npresent results and generate new applications of the RLBM scheme.", "category": "hep-lat" }, { "text": "Improved thermodynamics of SU(2) gauge theory: In this work we present the results of our investigation about the\nthermodynamics of SU(2) gauge theory. We employ a Symanzik improved action to\nreduce strongly the discretisations effects, and we use the scaling relations\nto take into account the finite volume effects close to the critical\ntemperature. We determine the beta-function for this particular theory and we\nuse it in the determination of different thermodynamic observables. Finally we\ncompare our results with previous works where only the standard Wilson action\nwas considered. We confirm the relevance of using the improved action to access\neasily the correct continuum thermodynamics of the theory.", "category": "hep-lat" }, { "text": "Three dimensional vacuum domains in four dimensional SU(2) gluodynamics: Performing lattice simulations of the four dimensional SU(2)gluodynamics we\nfind evidence for existence of three-dimensional domains whose total volume\nscales in physical units. Technically, the domains are defined in terms of the\nminimal density of negative links in Z(2) projection of gauge fields. The\nvolume can be viewed also as the minimal volume bound by the center vortices.\nWe argue that the three-dimensional domains are closely related to confinement.", "category": "hep-lat" }, { "text": "$|V_{cb}|$ using lattice QCD: Lattice QCD calculations of hadronic matrix elements allow one to draw\ninferences about quark flavor interactions from measurements of hadron decays.\nWithin the context of the Standard Model, the magnitude of the charm-bottom\nquark coupling $V_{cb}$ can be determined from semileptonic decays such as\n$B\\to D^{(*)}\\ell\\nu$. This brief review summarizes the present status and\nshort-term outlook for determining $|V_{cb}|$ using lattice QCD.", "category": "hep-lat" }, { "text": "A no-go theorem for the Majorana fermion on a lattice: A variant of the Nielsen--Ninomiya no-go theorem is formulated. This theorem\nstates that, under several assumptions, it is impossible to write down a\ndoubler-free Euclidean lattice action of a single Majorana fermion in $8k$ and\n$8k+1$ dimensions.", "category": "hep-lat" }, { "text": "N=1 super Yang-Mills on the lattice: We present results from a numerical study of N=1 supersymmetric Yang-Mills\ntheory using domain wall fermions. A set of dynamical simulations were\nperformed for the gauge group SU(2) using the Wilson gauge action on 8^3x8 and\n16^3x32 lattices. We considered a range of gluino masses (i.e., fifth dimension\nextents L_s=16-28 and input gluino mass values m_f=0.01-0.04) in order to\nperform chiral limit extrapolations of physical quantities. In these\nproceedings, we summarize our findings from a study of the Dirac spectrum and\npresent new results for the topological charge on beta=2.3, 2.353 and 2.4\nensembles.", "category": "hep-lat" }, { "text": "Spectral Functions of Hadrons in Lattice QCD: Using the maximum entropy method, spectral functions of the pseudo-scalar and\nvector mesons are extracted from lattice Monte Carlo data of the imaginary time\nGreen's functions. The resonance and continuum structures as well as the ground\nstate peaks are successfully obtained. Error analysis of the resultant spectral\nfunctions is also given on the basis of the Bayes probability theory.", "category": "hep-lat" }, { "text": "Determination of the renormalized heavy-quark mass in Lattice QCD: We study on the lattice the correlator of heavy-quark currents in the\nvicinity of vanishing momentum. The renormalized charmed quark mass, the\nrenormalized strong coupling constant and gluon condensate can be defined in\nterms of the derivatives of that correlator at zero momentum. We analyze\nquenched Monte-Carlo data on a small lattice $8^3*16$ for $\\beta=6$. We\ngeneralize dispersion relations to the lattice theory in a simple way and use\nthem successfully to fit the correlator at both small and large distances. We\nfit the short-distance part of the correlator with the relevant expressions of\nperturbative QCD on the lattice and obtain the value of the renormalized quark\nmass $m_c^{\\bar{MS}}(m_c)\\,=\\,1.20(4)\\,GeV$.", "category": "hep-lat" }, { "text": "Field Theory Simulations on a Fuzzy Sphere - an Alternative to the\n Lattice: We explore a new way to simulate quantum field theory, without introducing a\nspatial lattice. As a pilot study we apply this method to the 3d \\lambda \\phi^4\nmodel. The regularisation consists of a fuzzy sphere with radius R for the two\nspatial directions, plus a discrete Euclidean time. The fuzzy sphere\napproximates the algebra of functions of the sphere with a matrix algebra, and\nthe scalar field is represented by a Hermitian N x N matrix at each time site.\nWe evaluate the phase diagram, where we find a disordered phase and an ordered\nregime, which splits into phases of uniform and non-uniform order. We discuss\nthe behaviour of the model in different limits of large N and R, which lead to\na commutative or to a non-commutative \\lambda \\phi^4 model in flat space.", "category": "hep-lat" }, { "text": "Lattice QCD calculation of hadronic light-by-light scattering: We perform a lattice QCD calculation of the hadronic light-by-light\nscattering amplitude in a broad kinematical range. At forward kinematics, the\nresults are compared to a phenomenological analysis based on dispersive sum\nrules for light-by-light scattering. The size of the pion pole contribution is\ninvestigated for momenta of typical hadronic size. The presented numerical\nmethods can be used to compute the hadronic light-by-light contribution to the\nanomalous magnetic moment of the muon. Our calculations are carried out in\ntwo-flavor QCD with the pion mass in the range of 270 to 450MeV, and contain so\nfar only the diagrams with fully connected quark lines.", "category": "hep-lat" }, { "text": "Multigrid for Chiral Lattice Fermions: Domain Wall: Critical slowing down for the Krylov Dirac solver presents a major obstacle\nto further advances in lattice field theory as it approaches the continuum\nsolution. We propose a new multi-grid approach for chiral fermions, applicable\nto both the 5-d domain wall or 4-d Overlap operator. The central idea is to\ndirectly coarsen the 4-d Wilson kernel, giving an effective domain wall or\noverlap operator on each level. We provide here an explicit construction for\nthe Shamir domain wall formulation with numerical tests for the 2-d Schwinger\nprototype, demonstrating near ideal multi-grid scaling. The framework is\ndesigned for a natural extension to 4-d lattice QCD chiral fermions, such as\nthe M\\\"obius, Zolotarev or Borici domain wall discretizations or directly to a\nrational expansion of the 4-d Overlap operator. For the Shamir operator, the\neffective overlap operator is isolated by the use of a Pauli-Villars\npreconditioner in the spirit of the K\\\"ahler-Dirac spectral map used in a\nrecent staggered MG algorithm [1].", "category": "hep-lat" }, { "text": "Effective Monopole Potential for SU(2) Lattice Gluodynamics in Spatial\n Maximal Abelian Gauge: We investigate the dual superconductor hypothesis in finite-temperature SU(2)\nlattice gluodynamics in the Spatial Maximal Abelian gauge. This gauge is more\nphysical than the ordinary Maximal Abelian gauge due to absence of\nnon-localities in temporal direction. We show numerically that in the Spatial\nMaximal Abelian gauge the probability distribution of the abelian monopole\nfield is consistent with the dual superconductor mechanism of confinement: the\nabelian condensate vanishes in the deconfinement phase and is not zero in the\nconfinement phase.", "category": "hep-lat" }, { "text": "Finite-volume effects in long-distance processes with massless leptonic\n propagators: In Ref. [1], a method was proposed to calculate QED corrections to hadronic\nself energies from lattice QCD without power-law finite-volume errors. In this\npaper, we extend the method to processes which occur at second-order in the\nweak interaction and in which there is a massless (or almost massless) leptonic\npropagator. We demonstrate that, in spite of the presence of the propagator of\nan almost massless electron, such an infinite-volume reconstruction procedure\ncan be used to obtain the amplitude for the rare kaon decay\n$K^+\\to\\pi^+\\nu\\bar\\nu$ from a lattice quantum chromodynamics computation with\nonly exponentially small finite-volume corrections.", "category": "hep-lat" }, { "text": "Dirac sheets and gauge fixing in $U(1)$ lattice gauge theory: Photon correlators in $~U(1)~$ pure gauge theory for different lattice\nactions are considered under the Lorentz gauge condition. They are shown to\ndepend strongly on the gauge fixing ambiguity and on the corresponding\nexistence of Dirac sheets. For the Coulomb phase a gauge fixing algorithm is\nproposed which avoids Dirac sheets and allows to find the global extremum of\nthe non-local gauge condition. Sorry, figures are not included and can be sent\nby ordinary mail.", "category": "hep-lat" }, { "text": "Non-Perturbative Gauge-Higgs Unification in Five Dimensions: We study the phase diagram and mass spectrum of an $SU(2)$ Gauge-Higgs\nUnification scenario on a five-dimensional orbifold.We observe spontaneous\nsymmetry breaking within the Higgs phase of the theory and, in the vicinity of\na newly discovered phase, we find that the ratio of Higgs to gauge boson masses\ntakes a Standard Model-like value. Precisely in this region of the phase\ndiagram, we observe dimensional reduction via localisation.", "category": "hep-lat" }, { "text": "Models of Walking Technicolor on the Lattice: We study QCD with 2 colour-sextet quarks as a walking-Technicolor candidate.\nAs such it provides a description of the Higgs sector of the standard model, in\nwhich the Higgs field is replaced by the Goldstone `pions' of this QCD-like\ntheory, and the Higgs itself is the $\\sigma$. Such a theory will need to be\nextended if it is to also give masses to the quarks and leptons. What we are\nattempting to determine is whether it is indeed QCD-like and hence walking, or\nif it has an infrared fixed point making it a conformal field theory. We do\nthis by simulating its lattice version at finite temperature and observing the\nrunning of the bare (lattice) coupling at the chiral transition, as the lattice\nspacing is varied, and comparing this running with that predicted by 2-loop\nperturbation theory. Our results on lattices with temporal extents ($N_t$) up\nto 12 indicate that the coupling runs, but not as fast as asymptotic freedom\npredicts. We discuss our program for studying the zero-temperature\nphenomenology of this theory.", "category": "hep-lat" }, { "text": "Lattice study of the simplified model of M-theory for larger gauge\n groups: Lattice discretization of the supersymmetric Yang-Mills quantum mechanics is\ndis cussed. First results of the quenched Monte Carlo simulations, for D=4 and\nwith higher g auge groups (3 <= N <= 8), are presented. We confirm an earlier\n(N=2) evidence tha t the system reveals different behaviours at low and high\ntemperatures separated by a narrow transiti on region. These two regimes may\ncorrespond to a black hole and elementary excitations phases conjectured in the\nM-theory. Dependence of the \"transition temperature\" on N is consistent with 't\nHooft scaling and shows a smooth saturation of lattice results towards the\nlarge N limit. Is not yet resolved if the observed change between the two\nregimes corresponds to a genuine phase transition or to a gentle crossover . A\nnew, noncompact formulation of the lattice model is also proposed and its\nadvantages are briefly discussed.", "category": "hep-lat" }, { "text": "SU(3)-breaking ratios for $D_{(s)}$ and $B_{(s)}$ mesons: We present results for the $SU(3)$ breaking ratios of decay constants\n$f_{D_s}/f_D$ and $f_{B_s}/f_B$ and - for the first time with physical pion\nmasses - the ratio of bag parameters $B_{B_s}/B_{B_d}$, as well as the ratio\n$\\xi$, forming the ratio of the nonpeturbative contributions to neutral\n$B_{(s)}$ meson mixing. Our results are based on Lattice QCD simulations with\nchirally symmetric 2+1 dynamical flavors of domain wall fermions. Eight\nensembles at three different lattice spacing in the range $a = 0.11 -\n0.07\\,\\mathrm{fm}$ enter the analysis two of which feature physical light quark\nmasses. Multiple heavy quark masses are simulated ranging from below the charm\nquark mass to half the bottom quark mass. The $SU(3)$ breaking ratios display a\nvery benign heavy mass behaviour allowing for extrapolation to the physical\nbottom quark mass. The results in the continuum limit including all sources of\nsystematic errors are $f_{D_s}/f_D =\n1.1740(51)_\\mathrm{stat}(^{+68}_{-68})_\\mathrm{sys}$, $f_{B_s}/f_B =\n1.1949(60)_\\mathrm{stat}(^{+\\hphantom{0}95}_{-175})_\\mathrm{sys}$,\n$B_{B_s}/B_{B_d} = 0.9984(45)_\\mathrm{stat}(^{+80}_{-63})_\\mathrm{sys}$ and\n$\\xi = 1.1939(67)_\\mathrm{stat}(^{+\\hphantom{0}95}_{-177})_\\mathrm{sys}$.\nCombining these with experimentally measured values we extract the ratios of\nCKM matrix elements $|V_{cd}/V_{cs}| =\n0.2164(57)_\\mathrm{exp}(^{+12}_{-12})_\\mathrm{lat}$ and $|V_{td}/V_{ts}| =\n0.20329(41)_\\mathrm{exp}(^{+162}_{-301})_\\mathrm{lat}$.", "category": "hep-lat" }, { "text": "Euclidean lattice simulation for the dynamical supersymmetry breaking: The global supersymmetry is spontaneously broken if and only if the\nground-state energy is strictly positive. We propose to use this fact to\nobserve the spontaneous supersymmetry breaking in euclidean lattice\nsimulations. For lattice formulations that possess a manifest fermionic\nsymmetry, there exists a natural choice of a hamiltonian operator that is\nconsistent with a topological property of the Witten index. We confirm validity\nof our idea in models of the supersymmetric quantum mechanics. We then examine\na possibility of a dynamical supersymmetry breaking in the two-dimensional\n$\\mathcal{N}=(2,2)$ super Yang-Mills theory with the gauge group $\\SU(2)$, for\nwhich the Witten index is unknown. Differently from a recent conjectural claim,\nour numerical result tempts us to conclude that supersymmetry is not\nspontaneously broken in this system.", "category": "hep-lat" }, { "text": "Staggered domain wall fermions: Staggered Domain Wall Fermions (SDWF) combine the attractive chiral\nproperties of staggered fermions with those of domain wall fermions. SDWF\ndescribe four flavors with exact U(1)xU(1) flavor chiral symmetry. An extra\nlattice dimension is introduced and the full SU(4)xSU(4) flavor chiral symmetry\nis recovered as its size is increased. Here, the free theory of SDWF is\ndescribed and a preliminary discussion of the interacting case is presented.\nSDWF may be well suited for numerical simulation of lattice QCD thermodynamics.", "category": "hep-lat" }, { "text": "I=2 $\u03c0$-$\u03c0$ scattering length with dynamical overlap fermion: We report on a lattice QCD calculation of the I=2 $\\pi\\pi$ scattering length\nusing the overlap fermion formulation for both sea and valence quarks. We\ninvestigate the consistency of the lattice data with the prediction of the\nnext-to-next-to-leading order chiral perturbation theory after correcting\nfinite volume effects. The calculation is performed on gauge ensembles of\ntwo-flavor QCD generated by the JLQCD collaboration on a $16^3\\times 32$\nlattice at a lattice spacing $\\sim$ 0.12 fm.", "category": "hep-lat" }, { "text": "Role of chiral symmetry in the nucleon excitation spectrum: The origin of the low-lying nature of the $N$*(1440), or Roper resonance, has\nbeen the subject of significant interest for many years, including several\ninvestigations using lattice QCD. The majority of lattice studies have not\nobserved a low-lying excited state energy level in the region of the Roper\nresonance. However, it has been claimed that chiral symmetry could play an\nimportant role in our understanding of this resonance. The purpose of this\nstudy is to systematically examine the role of chiral symmetry in the low-lying\nnucleon spectrum by directly comparing the clover and overlap fermion actions.\nTo ensure any differences in results are attributable to the choice of fermion\naction, simulations are performed on the same set of gauge field configurations\nat matched pion masses. Correlation matrix techniques are employed to determine\nthe excitation energy of the first positive-parity excited state for each\naction. The clover and overlap actions show a remarkable level of agreement. We\ndo not find any evidence that fermion action chiral symmetry plays a\nsignificant role in understanding the Roper resonance on the lattice.", "category": "hep-lat" }, { "text": "Matching effective chiral Lagrangians with dimensional and lattice\n regularization: We compute the free energy in the presence of a chemical potential coupled to\na conserved charge in effective O($n$) scalar field theory (without explicit\nsymmetry breaking terms) to NNL order for asymmetric volumes in general\n$d$--dimensions, using dimensional (DR) and lattice regularizations. This\nyields relations between the 4-derivative couplings appearing in the effective\nactions for the two regularizations, which in turn allows us to translate\nresults, e.g. the mass gap in a finite periodic box in $d=3+1$ dimensions, from\none regularization to the other. Consistency is found with a new direct\ncomputation of the mass gap using DR. For the case $n=4, d=4$ the model is the\nlow-energy effective theory of QCD with $N_{\\rm f}=2$ massless quarks. The\nresults can thus be used to obtain estimates of low energy constants in the\neffective chiral Lagrangian from measurements of the low energy observables,\nincluding the low lying spectrum of $N_{\\rm f}=2$ QCD in the $\\delta$--regime\nusing lattice simulations, as proposed by Peter Hasenfratz, or from the\nsusceptibility corresponding to the chemical potential used.", "category": "hep-lat" }, { "text": "2+1 Flavor QCD simulated in the epsilon-regime in different topological\n sectors: We generated configurations with the parametrized fixed-point Dirac operator\nD_{FP} on a (1.6 fm)^4 box at a lattice spacing a=0.13 fm. We compare the\ndistributions of the three lowest k=1,2,3 eigenvalues in the nu= 0,1,2\ntopological sectors with that of the Random Matrix Theory predictions. The\nratios of expectation values of the lowest eigenvalues and the cumulative\neigenvalue distributions are studied for all combinations of k and nu. After\nincluding the finite size correction from one-loop chiral perturbation theory\nwe obtained for the chiral condensate in the MSbar scheme\nSigma(2GeV)^{1/3}=0.239(11) GeV, where the error is statistical only.", "category": "hep-lat" }, { "text": "Calculation of $\u03c1$ meson decay width from the PACS-CS configurations: We present preliminary results on the $\\rho$ meson decay width from $N_f=2+1$\nfull QCD configurations generated by PACS-CS Collaboration. The decay width is\nestimated from the $P$-wave scattering phase shift for the isospin $I=1$\ntwo-pion system. The finite size formula presented by L\\\"uscher in the center\nof mass frame and its extension to non-zero total momentum frame by Rummukainen\nand Gottlieb are employed for the calculations of the phase shift. Our\ncalculations are carried out at $m_\\pi=410\\ {\\rm MeV}$ ($m_\\pi/m_\\rho=0.46$)\nand $a=0.091\\ {\\rm fm}$ on a $32^3\\times 64$ ($La=2.9 {\\rm fm}$) lattice.", "category": "hep-lat" }, { "text": "Non-perturbative renormalisation of left-left four-fermion operators\n with Neuberger fermions: We outline a general strategy for the non-perturbative renormalisation of\ncomposite operators in discretisations based on Neuberger fermions, via a\nmatching to results obtained with Wilson-type fermions. As an application, we\nconsider the renormalisation of the four-quark operators entering the Delta S=1\nand Delta S=2 effective Hamiltonians. Our results are an essential ingredient\nfor the determination of the low-energy constants governing non-leptonic kaon\ndecays.", "category": "hep-lat" }, { "text": "Transversity PDFs of the proton from lattice QCD with physical quark\n masses: We present a lattice QCD calculation of the transversity isovector- and\nisoscalar-quark parton distribution functions (PDFs) of the proton utilizing a\nperturbative matching at next-to-leading-order (NLO) accuracy. Additionally, we\ndetermine the isovector and isoscalar tensor charges for the proton. In both\ncalculations, the disconnected contributions to the isoscalar matrix elements\nhave been ignored. The calculations are performed using a single ensemble of\n$N_f = 2 +1$ highly-improved staggered quarks simulated with physical-mass\nquarks and a lattice spacing of $a = 0.076$ fm. The Wilson-clover action, with\nphysical quark masses and smeared gauge links obtained from one iteration of\nhypercubic (HYP) smearing, is used in the valence sector. Using the NLO\noperator product expansion, we extract the lowest four to six Mellin moments\nand the PDFs from the matrix elements via a neural network. In addition, we\ncalculate the $x$-dependence of the PDFs with hybrid-scheme renormalization and\nthe recently developed leading-renormalon resummation technique, at NLO with\nthe resummation of leading small-$x$ logarithms.", "category": "hep-lat" }, { "text": "Influence of Fermions on Vortices in SU(2)-QCD: Gauge fields control the dynamics of fermions, also a back reaction of\nfermions on the gauge field is expected. This back reaction is investigated\nwithin the vortex picture of the QCD vacuum. We show that the center vortex\nmodel reproduces the string tension of the full theory also with the presence\nof fermionic fields.", "category": "hep-lat" }, { "text": "Provenance for Lattice QCD workflows: We present a provenance model for the generic workflow of numerical Lattice\nQuantum Chromodynamics (QCD) calculations, which constitute an important\ncomponent of particle physics research. These calculations are carried out on\nthe largest supercomputers worldwide with data in the multi-PetaByte range\nbeing generated and analyzed. In the Lattice QCD community, a custom metadata\nstandard (QCDml) that includes certain provenance information already exists\nfor one part of the workflow, the so-called generation of configurations.\n In this paper, we follow the W3C PROV standard and formulate a provenance\nmodel that includes both the generation part and the so-called measurement part\nof the Lattice QCD workflow. We demonstrate the applicability of this model and\nshow how the model can be used to answer some provenance-related research\nquestions. However, many important provenance questions in the Lattice QCD\ncommunity require extensions of this provenance model. To this end, we propose\na multi-layered provenance approach that combines prospective and retrospective\nelements.", "category": "hep-lat" }, { "text": "Complete Monopole Dominance of the Yang-Mills Confining Potential: We continue our investigation of quark confinement using a particular variant\nof the Cho-Duan-Ge gauge independent Abelian decomposition. The decomposition\nsplits the gauge field into a restricted Abelian part and a coloured part in a\nway that preserves gauge covariance. The restricted part of the gauge field can\nbe divided into a Maxwell term and a topological term. Previously, we showed\nthat by a particular choice of this decomposition we could fully describe the\nconfining potential using only the restricted gauge field. We proposed that\nvarious topological objects (a form of magnetic monopole) could arise in the\nrestricted field which would drive confinement. Our mechanism does not\nexplicitly refer to a dual Meissner effect, nor does it use centre vortices. We\ndid not need to gauge fix or introduce any new dynamical fields.\n We show that if we do gauge fix as well as performing the Abelian\ndecomposition then it is possible to ensure that the topological part of the\nrestricted field fully accounts for the confining potential. Our relationship\nis exact: there is no approximation or model involved. This isolates the\nobjects responsible for confinement from non-confining contributions to the\ngauge field, allowing a direct search for our proposed topological objects.\nUsing numerical studies in SU(2), we confirm that our proposed monopoles are\npresent in the field, and the winding number associated with these monopoles is\na key factor driving quark confinement.\n In SU(2), our monopoles are described by two parameters. We show that it is\npossible to re-parametrise the Yang Mills action and the functional integration\nmeasure in terms of these variables (plus the necessary additional parameters).\nWe can thus treat the monopoles as dynamical variables in the functional\nintegral. This might be the first step in a future analytical computation to\ncomplement our numerical results.", "category": "hep-lat" }, { "text": "Quarkonium mass splittings in three-flavor lattice QCD: We report on calculations of the charmonium and bottomonium spectrum in\nlattice QCD. We use ensembles of gauge fields with three flavors of sea quarks,\nsimulated with the asqtad improved action for staggered fermions. For the heavy\nquarks we employ the Fermilab interpretation of the clover action for Wilson\nfermions. These calculations provide a test of lattice QCD, including the\ntheory of discretization errors for heavy quarks. We provide, therefore, a\ncareful discussion of the results in light of the heavy-quark effective\nLagrangian. By and large, we find that the computed results are in agreement\nwith experiment, once parametric and discretization errors are taken into\naccount.", "category": "hep-lat" }, { "text": "Linear Covariant Gauges on the Lattice: Linear covariant gauges, such as Feynman gauge, are very useful in\nperturbative calculations. Their nonperturbative formulation is, however,\nhighly non-trivial. In particular, it is a challenge to define linear covariant\ngauges on a lattice. We consider a class of gauges in lattice gauge theory that\ncoincides with the perturbative definition of linear covariant gauges in the\nformal continuum limit. The corresponding gauge-fixing procedure is described\nand analyzed in detail, with an application to the pure SU(2) case. In\naddition, results for the gluon propagator in the two-dimensional case are\ngiven.", "category": "hep-lat" }, { "text": "Hyperon sigma terms for 2+1 quark flavours: QCD lattice simulations determine hadron masses as functions of the quark\nmasses. From the gradients of these masses and using the Feynman-Hellmann\ntheorem the hadron sigma terms can then be determined. We use here a novel\napproach of keeping the singlet quark mass constant in our simulations which\nupon using an SU(3) flavour symmetry breaking expansion gives highly\nconstrained (i.e. few parameter) fits for hadron masses in a multiplet. This is\na highly advantageous procedure for determining the hadron mass gradient as it\navoids the use of delicate chiral perturbation theory. We illustrate the\nprocedure here by estimating the light and strange sigma terms for the baryon\noctet.", "category": "hep-lat" }, { "text": "Towards an algebraic approach to the discretisation of fermions: A discretisation scheme for differential geometry is applied to the problem\nof constructing lattice actions, the naive and staggered action are thus\nderived. It is found that after specifying an ansatz for the space of fields,\nthe corresponding lattice action is obtained. The gauging procedure, and the\napplicability of the method to twisted super-symmetry on a lattice is outlined.\nSome comments on the QED axial anomaly are made, for the theory in which the\nlattice projection operator is not inserted.", "category": "hep-lat" }, { "text": "Improved Perturbation Theory for Improved Lattice Actions: We study a systematic improvement of perturbation theory for gauge fields on\nthe lattice; the improvement entails resumming, to all orders in the coupling\nconstant, a dominant subclass of tadpole diagrams.\n This method, originally proposed for the Wilson gluon action, is extended\nhere to encompass all possible gluon actions made of closed Wilson loops; any\nfermion action can be employed as well. The effect of resummation is to replace\nvarious parameters in the action (coupling constant, Symanzik coefficients,\nclover coefficient) by ``dressed'' values; the latter are solutions to certain\ncoupled integral equations, which are easy to solve numerically.\n Some positive features of this method are: a) It is gauge invariant, b) it\ncan be systematically applied to improve (to all orders) results obtained at\nany given order in perturbation theory, c) it does indeed absorb in the dressed\nparameters the bulk of tadpole contributions.\n Two different applications are presented: The additive renormalization of\nfermion masses, and the multiplicative renormalization Z_V (Z_A) of the vector\n(axial) current. In many cases where non-perturbative estimates of\nrenormalization functions are also available for comparison, the agreement with\nimproved perturbative results is significantly better as compared to results\nfrom bare perturbation theory.", "category": "hep-lat" }, { "text": "High-accuracy two-loop computation of the critical mass for Wilson\n fermions: We test an algebraic algorithm based on the coordinate-space method,\nevaluating with high accuracy the critical mass for Wilson fermions in lattice\nQCD at two loops. We test the results by using different types of infrared\nregularization.", "category": "hep-lat" }, { "text": "Duality and scaling in 3-dimensional scalar electrodynamics: Three-dimensional scalar electrodynamics, with a local U(1) gauge symmetry,\nis believed to be dual to a scalar theory with a global U(1) symmetry, near the\nphase transition point. The conjectured duality leads to definite predictions\nfor the scaling exponents of the gauge theory transition in the type II region,\nand allows thus to be scrutinized empirically. We review these predictions, and\ncarry out numerical lattice Monte Carlo measurements to test them: a number of\nexponents, characterising the two phases as well as the transition point, are\nfound to agree with expectations, supporting the conjecture. We explain why\nsome others, like the exponent characterising the photon correlation length,\nappear to disagree with expectations, unless very large system sizes and the\nextreme vicinity of the transition point are considered. Finally, we remark\nthat in the type I region the duality implies an interesting quantitative\nrelationship between a magnetic flux tube and a 2-dimensional non-topological\nsoliton.", "category": "hep-lat" }, { "text": "Neutron Electric Dipole Moment on the Lattice: a Theoretical Reappraisal: We present a strategy for a lattice evaluation of the neutron electric dipole\nmoment induced by the strong CP violating term of the QCD Lagrangian. Our\nstrategy is based on the standard definition of the electric dipole moment,\ninvolving the charge density operator J0, in case of three flavors with\nnon-degenerate masses. We present a complete diagrammatic analysis showing how\nthe axial chiral Ward identities can be used to replace the opological charge\noperator with the flavor-singlet pseudoscalar density PS. Our final result is\ncharacterized only by disconnected diagrams, where the disconnected part can be\neither the single insertion of PS or the separate insertions of both PS and J0.\nThe applicability of our strategy to the case of lattice formulations that\nexplicitly break chiral symmetry, like the Wilson and Clover actions, is\ndiscussed.", "category": "hep-lat" }, { "text": "Matrix elements relevant for Delta I=1/2 rule and epsilon-prime from\n Lattice QCD with staggered fermions: We perform a study of matrix elements relevant for the Delta I=1/2 rule and\nthe direct CP-violation parameter epsilon-prime from first principles by\ncomputer simulation in Lattice QCD. We use staggered (Kogut-Susskind) fermions,\nand employ the chiral perturbation theory method for studying K to 2 Pi decays.\nHaving obtained a reasonable statistical accuracy, we observe an enhancement of\nthe Delta I=1/2 amplitude, consistent with experiment within our large\nsystematic errors. Finite volume and quenching effects have been studied and\nwere found small compared to noise. The estimates of epsilon-prime are hindered\nby large uncertainties associated with operator matching. In this paper we\nexplain the simulation method, present the results and address the systematic\nuncertainties.", "category": "hep-lat" }, { "text": "Neutron electric dipole moment on the lattice: We carry out a feasibility study toward a lattice QCD calculation of the\nneutron electric dipole moment (NEDM) in the presence of the $\\theta$ term\nusing two different approaches. In the first method, we calculate the CP-odd\nelectromagnetic form factor $F_3$, which becomes the NEDM in the zero momentum\ntransfer limit. At the first order in $\\theta$, we derive a formula connecting\nthe lattice three-point function to the CP-odd electromagnetic form factor. In\nthe second method we directly extract the NEDM from the energy difference\nbetween spin-up and spin-down neutron states in the presence of a constant\nelectric field, without expanding a small but non-zero $\\theta$. We test both\napproaches numerically, employing the domain-wall quark action with the RG\nimproved gauge action in quenched QCD at $a^{-1}\\simeq 2$ GeV on a $16^3\\times\n32\\times 16$ lattice, and further applying the second method to the clover\nquark action at a similar lattice spacing and nucleon mass. We obtain good\nsignals from both approaches. In particular the second method works well with\nboth fermion formulations.", "category": "hep-lat" }, { "text": "Determination of $s$- and $p$-wave $I=1/2$ $K\u03c0$ scattering amplitudes\n in $N_{\\mathrm{f}}=2+1$ lattice QCD: The elastic $I=1/2$, $s$- and $p$-wave kaon-pion scattering amplitudes are\ncalculated using a single ensemble of anisotropic lattice QCD gauge field\nconfigurations with $N_{\\mathrm{f}} = 2+1$ flavors of dynamical Wilson-clover\nfermions at $m_{\\pi} = 230\\mathrm{MeV}$. A large spatial extent of $L =\n3.7\\mathrm{fm}$ enables a good energy resolution while partial wave mixing due\nto the reduced symmetries of the finite volume is treated explicitly.The\n$p$-wave amplitude is well described by a Breit-Wigner shape with parameters\n$m_{K^{*}}/m_{\\pi} = 3.808(18)$ and $g^{\\mathrm{BW}}_{K^{*}K\\pi} = 5.33(20)$\nwhich are insensitive to the inclusion of $d$-wave mixing and variation of the\n$s$-wave parametrization. An effective range description of the near-threshold\n$s$-wave amplitude yields $m_{\\pi}a_0 = -0.353(25)$.", "category": "hep-lat" }, { "text": "Correlation functions in lattice formulations of quantum gravity: We compare different models of a quantum theory of four-dimensional lattice\ngravity based on Regge's original proposal. From Monte Carlo simulations we\ncalculate two-point functions between geometrical quantities and estimate the\nmasses of the corresponding interaction particles.", "category": "hep-lat" }, { "text": "The topological susceptibility in finite temperature QCD and axion\n cosmology: We study the topological susceptibility in 2+1 flavor QCD above the chiral\ncrossover transition temperature using Highly Improved Staggered Quark action\nand several lattice spacings, corresponding to temporal extent of the lattice,\n$N_\\tau=6,8,10$ and $12$. We observe very distinct temperature dependences of\nthe topological susceptibility in the ranges above and below $250$ MeV. While\nfor temperatures above $250$ MeV, the dependence is found to be consistent with\ndilute instanton gas approximation, at lower temperatures the fall-off of\ntopological susceptibility is milder. We discuss the consequence of our results\nfor cosmology wherein we estimate the bounds on the axion decay constant and\nthe oscillation temperature if indeed the QCD axion is a possible dark matter\ncandidate.", "category": "hep-lat" }, { "text": "Inclusive hadronic decay rate of the $\u03c4$ lepton from lattice QCD: Inclusive hadronic decays of the $\\tau$ lepton are very interesting from the\nphenomenological point of view since they give access to the CKM matrix\nelements $V_{ud}$ and $V_{us}$. In this paper, for the first time, by employing\nthe HLT method for hadronic smeared spectral densities we compute on the\nlattice the inclusive decay rate of the processes $\\tau \\to X_{ud}\\, \\nu_\\tau$,\nwhere $X_{ud}$ is a generic hadronic state with $\\bar{u} d$ flavor quantum\nnumbers. Our computation, which avoids any recourse to OPE and/or perturbative\napproximations, is carried out in isospin symmetric $N_{f}=2+1+1$ lattice QCD\nat physical quark masses, using ensembles produced by the ETMC at three lattice\nspacings and two volumes. All uncertainties, except for isospin breaking\neffects, are taken into account and a result with a subpercent error is\nobtained for $|V_{ud}|$, which is nicely consistent with the current world\naverage. These findings validate our approach and also motivate the inclusion\nof isospin breaking corrections and its extension to the inclusive decay $\\tau\n\\to X_{us}\\, \\nu_\\tau$, paving the way towards a high-precision first\nprinciples determination of $|V_{us}|$ and $|V_{ud}|$ from inclusive $\\tau$\ndecay.", "category": "hep-lat" }, { "text": "Exploring the HMC trajectory-length dependence of autocorrelation times\n in lattice QCD: We study autocorrelation times of physical observables in lattice QCD as a\nfunction of the molecular dynamics trajectory length in the hybrid Monte-Carlo\nalgorithm. In an interval of trajectory lengths where energy and reversibility\nviolations can be kept under control, we find a variation of the integrated\nautocorrelation times by a factor of about two in the quantities of interest.\nTrajectories longer than conventionally used are found to be superior both in\nthe Nf=0 and Nf=2 examples considered here. We also provide evidence that they\nlead to faster thermalization of systems with light quarks.", "category": "hep-lat" }, { "text": "Strong isospin violation and chiral logarithms in the baryon spectrum: We present a precise lattice QCD calculation of the contribution to the\nneutron-proton mass splitting arising from strong isospin breaking,\n$m_n-m_p|_{QCD}=2.32\\pm0.17$ MeV. We also determine $m_{\\Xi^-} -\nm_{\\Xi^0}|_{QCD} = 5.44\\pm0.31$ MeV. The calculation is performed at three\nvalues of the pion mass, with several values of the quark mass splitting and\nmultiple lattice volumes, but only a single lattice spacing and an estimate of\ndiscretization errors. The calculations are performed on the anisotropic\nclover-Wilson ensembles generated by the Hadron Spectrum Collaboration. The\nomega-baryon mass is used to set the scale $a_t^{-1}=6111\\pm127$ MeV, while the\nkaon masses are used to determine the value of the light-quark mass spitting.\nThe nucleon mass splitting is then determined as a function of the pion mass.\nWe observe, for the first time, conclusive evidence for non-analytic light\nquark mass dependence in lattice QCD calculations of the baryon spectrum. When\nleft as a free parameter, the fits prefer a nucleon axial coupling of\n$g_A=1.24(56)$. To highlight the presence of this chiral logarithm in the\nnucleon mass splitting, we also compute the isospin splitting in the\ncascade-baryon system which is less sensitive to chiral dynamics. Finally, we\nupdate the best lattice QCD determination of the CP-odd pion-nucleon coupling\nthat would arise from a non-zero QCD theta-term, $\\bar{g}_0 / (\\sqrt{2}f_\\pi) =\n(14.7\\pm1.8\\pm1.4) \\cdot 10^{-3} \\bar{\\theta}$.\n The original lattice QCD correlation functions, analysis results and\nextrapolated quantities are packaged in HDF5 files made publicly available\nincluding a simple Python script to access the numerical results, construct\neffective mass plots along with our analysis results, and perform the\nextrapolations of various quantities determined in this work.", "category": "hep-lat" }, { "text": "Disconnected Quark Loop Contributions to Nucleon Structure: We calculate the disconnected contribution to isoscalar nucleon charges for\nscalar, axial and tensor channels of light and strange quarks. The calculation\nhas been done with the Clover valence quarks on the MILC $N_f=2+1+1$ HISQ\nlattices whose light quark masses corresponding to the pion masses of 305 MeV\nand 217 MeV at $a \\approx 0.12$ fm and 312 MeV at $a \\approx 0.09$ fm.\nAll-mode-averaging technique is used for the evaluation two-point functions.\nDisconnected quark loops are estimated by using the truncated solver method\nwith Gaussian random noise sources. Contamination from the excited states is\nremoved by fitting the results of various source-sink separations and operator\ninsertions to the formula including up to the first excited state,\nsimultaneously.", "category": "hep-lat" }, { "text": "Recent progress in applying lattice QCD to kaon physics: Standard lattice calculations in kaon physics are based on the evaluation of\nmatrix elements of local operators between two single-hadron states or a\nsingle-hadron state and the vacuum. Recent progress in lattice QCD has gone\nbeyond these standard observables. I will review the status and prospects of\nlattice kaon physics with an emphasis on non-leptonic $K\\to\\pi\\pi$ decay and\nlong-distance processes including $K^0$-$\\overline{K^0}$ mixing and rare kaon\ndecays.", "category": "hep-lat" }, { "text": "$m_c$ (and $m_b$) from lattice QCD: Quark mass determinations based on lattice QCD simulations have continued to\nmake strides in recent years. Here I review that progress with a focus on\ndevelopments computing the charm (and bottom) quark masses since the 2015\nedition of CHARM. These advances have resulted in groups now quoting\n(sub-)percent-level precision for these quantities, and, importantly, using a\nvariety of techniques subject to differing systematic uncertainties.\nImprovements to quantify the effects of QED are also now being included. I will\nhighlight three of the strategies being used to determine $m_c$ at this level\nof precision.", "category": "hep-lat" }, { "text": "NRQCD and Static Systems -- A General Variational Approach: We present initial results from Monte Carlo simulations of NRQCD-light,\nstatic-light, and NRQCD-NRQCD mesons, using a variational technique (MOST), as\npart of our ongoing calculation of the $f_{B}$ decay constant. The basis states\nfor the variational calculation are quark-antiquark operators separated by all\npossible relative distances not equivalent under the cubic group (for example,\nfor a $20^{3}$ lattice there are 286 operators). The efficacy of the method is\ndemonstrated by the good plateaus obtained for the ground state and the clean\nextraction of the wave functions of the ground and first radially excited\nstate.", "category": "hep-lat" }, { "text": "Chern-Simons term in the 4-dimensional SU(2) Higgs Model: Using Seiberg's definition for the geometric charge in SU(2) lattice gauge\ntheory, we have managed to apply it also to the Chern-Simons term. We checked\nthe periodic structure and determined the Chern-Simons density on small\nlattices $L^4$ and $L^3 \\times 2,\\, 4$ with $L=4,\\, 6,\\mbox{ and }8$ near the\ncritical region in the SU(2) Higgs model. The data indicate that tunneling is\nincreased at high temperature.", "category": "hep-lat" }, { "text": "Meron-Cluster Solution of Fermion and Other Sign Problems: Numerical simulations of numerous quantum systems suffer from the notorious\nsign problem. Important examples include QCD and other field theories at\nnon-zero chemical potential, at non-zero vacuum angle, or with an odd number of\nflavors, as well as the Hubbard model for high-temperature superconductivity\nand quantum antiferromagnets in an external magnetic field. In all these cases\nstandard simulation algorithms require an exponentially large statistics in\nlarge space-time volumes and are thus impossible to use in practice.\nMeron-cluster algorithms realize a general strategy to solve severe sign\nproblems but must be constructed for each individual case. They lead to a\ncomplete solution of the sign problem in several of the above cases.", "category": "hep-lat" }, { "text": "High-Precision c and b Masses, and QCD Coupling from Current-Current\n Correlators in Lattice and Continuum QCD: We extend our earlier lattice-QCD analysis of heavy-quark correlators to\nsmaller lattice spacings and larger masses to obtain new values for the c mass\nand QCD coupling, and, for the first time, values for the b mass:\nm_c(3GeV,n_f=4)=0.986(6)GeV, alpha_msb(M_Z,n_f=5)=0.1183(7), and\nm_b(10GeV,n_f=5)=3.617(25)GeV. These are among the most accurate determinations\nby any method. We check our results using a nonperturbative determination of\nthe mass ratio m_b(mu,n_f)/m_c(mu,n_f); the two methods agree to within our 1%\nerrors and taken together imply m_b/m_c=4.51(4). We also update our previous\nanalysis of alpha_msb from Wilson loops to account for revised values for r_1\nand r_1/a, finding a new value alpha_\\msb(M_Z,n_f=5)=0.1184(6); and we update\nour recent values for light-quark masses from the ratio m_c/m_s. Finally, in\nthe Appendix, we derive a procedure for simplifying and accelerating\ncomplicated least-squares fits.", "category": "hep-lat" }, { "text": "Exploring quark transverse momentum distributions with lattice QCD: We discuss in detail a method to study transverse momentum dependent parton\ndistribution functions (TMDs) using lattice QCD. To develop the formalism and\nto obtain first numerical results, we directly implement a bi-local quark-quark\noperator connected by a straight Wilson line, allowing us to study T-even,\n\"process-independent\" TMDs. Beyond results for x-integrated TMDs and quark\ndensities, we present a study of correlations in x and transverse momentum. Our\ncalculations are based on domain wall valence quark propagators by the LHP\ncollaboration calculated on top of gauge configurations provided by MILC with\n2+1 flavors of asqtad-improved staggered sea quarks.", "category": "hep-lat" }, { "text": "Cutoff effects in the O(N) sigma model at large N: The computation of the step scaling function for the finite size mass-gap in\nthe O(N) sigma model at large N is reviewed. Practically exact nonperturbative\nresults become available for both finite and vanishing lattice spacing. We use\nthem as a testbed to investigate standard procedures of continuum extrapolation\nin lattice field theory.", "category": "hep-lat" }, { "text": "Rare $B$ decays using lattice QCD form factors: In this write-up we review and update our recent lattice QCD calculation of\n$B \\to K^*$, $B_s \\to \\phi$, and $B_s \\to K^*$ form factors [arXiv:1310.3722].\nThese unquenched calculations, performed in the low-recoil kinematic regime,\nprovide a significant improvement over the use of extrapolated light cone sum\nrule results. The fits presented here include further kinematic constraints and\nestimates of additional correlations between the different form factor shape\nparameters. We use these form factors along with Standard Model determinations\nof Wilson coefficients to give Standard Model predictions for several\nobservables [arXiv:1310.3887]. The modest improvements to the form factor fits\nlead to improved determinations of $F_L$, the fraction of longitudinally\npolarized vector mesons, but have little effect on most other observables.", "category": "hep-lat" }, { "text": "Toward dense QCD in quantum computers: Lattice QCD at nonzero baryon density is a big challenge in hadron physics.\nIn this presentation, I discuss the quantum computation of lattice gauge theory\nat nonzero density. I show some benchmark results of the Schwinger model\nobtained by the quantum adiabatic algorithm and the quantum variational\nalgorithm.", "category": "hep-lat" }, { "text": "The lower moments of nucleon structure functions in lattice QCD with\n physical quark masses: We present results for the nucleon structure functions and form factors\nobtained from 2+1 flavor lattice QCD with physical light quark masses\n($m_{\\pi}=135$ MeV) in a large spatial extent of about 10 fm. Our calculations\nare performed with the PACS10 gauge configurations generated by the PACS\nCollaboration with the six stout-smeared ${\\mathscr{O}}(a)$ improved\nWilson-clover quark action and Iwasaki gauge action at $\\beta=1.82$ and $2.00$\ncorresponding to lattice spacings of $0.085$ fm and $0.064$ fm respectively.\nThe lower moments of structure functions, $\\langle x \\rangle_{u-d}$ and\n$\\langle x \\rangle_{\\Delta u - \\Delta d}$ given by the twist-2 operators being\nproperly renormalized, are evaluated in the $\\overline{\\rm MS}$ scheme at the\nrenormalization scale of 2 GeV only at $\\beta=1.82$, since the renormalization\nfactors at $\\beta=2.00$ have not yet determined nonperturbatively in the RI/MOM\nscheme. Instead, at two lattice spacings, we evaluate appropriate ratios of\n$g_{A}/g_{V}$ and $\\langle x \\rangle_{u-d}/\\langle x \\rangle_{\\Delta u -\\Delta\nd}$, which are not renormalized in the continuum limit. These quantities thus\ncan be directly compared with the experimental data without the\nrenormalization.", "category": "hep-lat" }, { "text": "The dual sector of the \u03c6^4 Theory in 4D: The one-component $\\lambda\\phi^4$ theory in four dimensions in the\nspontaneously broken symmetry phase has a non-trivial, non-perturbative sector\nwhich can be studied by means of a duality transformation of its Ising limit.\nDuality maps this theory to a model of interacting membranes. Physical states\ncorrespond to membrane excitations. The way this non-perturbative behaviour can\nbe reconciled with the triviality of the theory in its continuum limit is\ndiscussed.", "category": "hep-lat" }, { "text": "Color Dynamics in External Fields: We investigate the vacuum dynamics of U(1), SU(2), and SU(3) lattice gauge\ntheories in presence of external (chromo)magnetic fields, both in (3+1) and\n(2+1) dimensions. We find that the critical coupling for the phase transition\nin compact U(1) gauge theory is independent of the strength of an external\nmagnetic field. On the other hand we find that, both in (3+1) and (2+1)\ndimensions, the deconfinement temperature for SU(2) and SU(3) gauge systems in\na constant abelian chromomagnetic field decreases when the strength of the\napplied field increases. We conclude that the dependence of the deconfinement\ntemperature on the strength of an external constant chromomagnetic field is a\npeculiar feature of non abelian gauge theories and could be useful to get\ninsight into color confinement.", "category": "hep-lat" }, { "text": "Lattice QCD determination of states with spin 5/2 or higher in the\n spectrum of nucleons: Energies for excited isospin 1/2 states that include the nucleon are computed\nusing quenched, anisotropic lattices. Baryon interpolating field operators that\nare used include nonlocal operators that provide $G_2$ irreducible\nrepresentations of the octahedral group. The decomposition of spin 5/2 or\nhigher states is realized for the first time in a lattice QCD calculation. We\nobserve patterns of degenerate energies in the irreducible representations of\nthe octahedral group that correspond to the subduction of the continuum spin\n5/2 or higher.", "category": "hep-lat" }, { "text": "Machine Learning Trivializing Maps: A First Step Towards Understanding\n How Flow-Based Samplers Scale Up: A trivializing map is a field transformation whose Jacobian determinant\nexactly cancels the interaction terms in the action, providing a representation\nof the theory in terms of a deterministic transformation of a distribution from\nwhich sampling is trivial. Recently, a proof-of-principle study by Albergo,\nKanwar and Shanahan [arXiv:1904.12072] demonstrated that approximations of\ntrivializing maps can be `machine-learned' by a class of invertible,\ndifferentiable neural models called \\textit{normalizing flows}. By ensuring\nthat the Jacobian determinant can be computed efficiently, asymptotically exact\nsampling from the theory of interest can be performed by drawing samples from a\nsimple distribution and passing them through the network. From a theoretical\nperspective, this approach has the potential to become more efficient than\ntraditional Markov Chain Monte Carlo sampling techniques, where\nautocorrelations severely diminish the sampling efficiency as one approaches\nthe continuum limit. A major caveat is that it is not yet understood how the\nsize of models and the cost of training them is expected to scale. As a first\nstep, we have conducted an exploratory scaling study using two-dimensional\n$\\phi^4$ with up to $20^2$ lattice sites. Although the scope of our study is\nlimited to a particular model architecture and training algorithm, initial\nresults paint an interesting picture in which training costs grow very quickly\nindeed. We describe a candidate explanation for the poor scaling, and outline\nour intentions to clarify the situation in future work.", "category": "hep-lat" }, { "text": "Rare decay B -> K ll form factors from lattice QCD: We calculate, for the first time using unquenched lattice QCD, form factors\nfor the rare decay B -> Kll in and beyond the Standard Model. Our lattice QCD\ncalculation utilizes a nonrelativistic QCD formulation for the b valence\nquarks, the highly improved staggered quark formulation for the light valence\nquarks, and employs the MILC 2+1 asqtad ensembles. The form factor results,\nbased on the z expansion, are valid over the full kinematic range of q^2. We\nconstruct the ratios f0/f+ and fT/f+, which are useful in constraining new\nphysics and verifying effective theory form factor symmetry relations. We also\ndiscuss the calculation of Standard Model observables.", "category": "hep-lat" }, { "text": "A complete non-perturbative renormalization prescription for quasi-PDFs: In this work we present, for the first time, the non-perturbative\nrenormalization for the unpolarized, helicity and transversity quasi-PDFs, in\nan RI' scheme. The proposed prescription addresses simultaneously all aspects\nof renormalization: logarithmic divergences, finite renormalization as well as\nthe linear divergence which is present in the matrix elements of fermion\noperators with Wilson lines. Furthermore, for the case of the unpolarized\nquasi-PDFs, we describe how to eliminate the unwanted mixing with the twist-3\nscalar operator. We utilize perturbation theory for the one-loop conversion\nfactor that brings the renormalization functions to the MS-scheme at a scale of\n2 GeV. We also explain how to improve the estimates on the renormalization\nfunctions by eliminating lattice artifacts. The latter can be computed in\none-loop perturbation theory and to all orders in the lattice spacing. We apply\nthe methodology for the renormalization to an ensemble of twisted mass fermions\nwith Nf=2+1+1 dynamical light quarks, and a pion mass of around 375 MeV.", "category": "hep-lat" }, { "text": "Excited states in the full QCD hadron spectrum on a $16^3 \\times 40$\n lattice: We report the hadron mass spectrum obtained on a $16^3 \\times 40$ lattice at\n$\\beta = 5.7$ using two flavors of staggered fermions with $m a = 0.01$. We\ncalculate the masses of excited states that have the same quantum numbers as\nthe $\\pi$, $\\rho$ and $N$. They are obtained by a combined analysis of the\nhadron correlators from sources of size $16^3$ and $8^3$. We also report on the\nhadron spectrum for a wide range of valence quark masses.", "category": "hep-lat" }, { "text": "Renormalisation of lattice currents and the calculation of decay\n constants for dynamical staggered fermions: A numerical calculation of the lattice staggered renormalisation constants at\n$\\beta = 5.35$, $m = 0.01$ is presented. It is seen that there are considerable\nnon-perturbative effects present. As an application the vector decay constant\n$f_\\rho$ is estimated. (LAT92 contribution, one LATEX file with 3 postscript\nfigures appended.)", "category": "hep-lat" }, { "text": "Quenched QCD at finite temperature with chiral Fermions: We study physics at temperatures just above the QCD phase transition (Tc)\nusing chiral (overlap) Fermions in the quenched approximation of lattice QCD.\nExact zero modes of the overlap Dirac operator are localized and their\nfrequency of occurrence drops with temperature. This is closely related to\naxial U(1) symmetry, which remains broken up to 2Tc. After subtracting the\neffects of these zero modes, chiral symmetry is restored, as indicated by the\nbehavior of the chiral condensate. The pseudoscalar and vector screening masses\nare close to ideal gas values.", "category": "hep-lat" }, { "text": "A method to measure the antikaon-nucleon scattering length in lattice\n QCD: We propose a method to determine the isoscalar \\bar K N scattering length on\nthe lattice. Our method represents the generalization of L\\\"uscher's approach\nin the presence of inelastic channels (complex scattering length). In addition,\nthe proposed approach allows one to find the position of the S-matrix pole\ncorresponding the the Lambda(1405) resonance.", "category": "hep-lat" }, { "text": "Light hadron masses with 4-GeV cutoff and L=2.4fm: We discuss preliminary results from our quenched light hadron mass\ncalculation on a $48^3 \\times 64$ lattice at the coupling of $\\beta = 6.5$.\nStaggered quarks with masses of $m_q = 0.01, 0.005, 0.0025$ and $0.00125$ are\nused.", "category": "hep-lat" }, { "text": "Exploring a hidden symmetry with electrically charged quarks: It is usual to study confinement via quantum chromodynamics (QCD) alone. The\ndeconfinement transition of the pure gauge theory (i.e. with static quarks) is\nthen characterized by the breaking of center symmetry. Center vortices offer an\nintuitive and quantitative description of the transition. Dynamical quarks\nexplicitly break center symmetry, and the phase transition becomes a crossover.\nHowever, it may be misleading to study QCD in isolation. Quarks also carry\nfractional electric charge. This bestows the Standard Model with a global\ncenter symmetry that combines color center phases with an appropriate\nelectromagnetic phase. Is this symmetry relevant to confinement? We begin our\ninvestigation by studying a 2-color model of QCD with half-integer electrically\ncharged quarks.", "category": "hep-lat" }, { "text": "Continuum limit of the leading order HQET form factor in $B_s \\to\n K\\ell\u03bd$ decays: We discuss the computation of form factors for semi-leptonic decays of $\\rm\nB$-, $\\rm B_s$- mesons in lattice QCD. Considering in particular the example of\nthe static $\\rm B_s$ form factors we demonstrate that after non-perturbative\nrenormalization the continuum limit can be taken with confidence. The resulting\nprecision is of interest for extractions of $V_{\\rm ub}$. The size of the\ncorrections of order $1/m_{\\rm b}$ is just estimated at present but it is\nexpected that their inclusion does not pose significant difficulties.", "category": "hep-lat" }, { "text": "Non-Perturbative Gauge-Higgs Unification in Five Dimensions: We study the phase diagram and mass spectrum of an $SU(2)$ Gauge-Higgs\nUnification scenario on a five-dimensional orbifold.We observe spontaneous\nsymmetry breaking within the Higgs phase of the theory and, in the vicinity of\na newly discovered phase, we find that the ratio of Higgs to gauge boson masses\ntakes a Standard Model-like value. Precisely in this region of the phase\ndiagram, we observe dimensional reduction via localisation.", "category": "hep-lat" }, { "text": "Numerical methods for the sign problem in Lattice Field Theory: The great majority of algorithms employed in the study of lattice field\ntheory are based on Monte Carlo's importance sampling method, i.e. on\nprobability interpretation of the Boltzmann weight. Unfortunately in many\ntheories of interest one cannot associated a real and positive weight to every\nconfiguration, that is because their action is explicitly complex or because\nthe weight is multiplied by some non positive term. In this cases one says that\nthe theory on the lattice is affected by the sign problem. An outstanding\nexample of sign problem preventing a quantum field theory to be studied, is QCD\nat finite chemical potential. Whenever the sign problem is present, standard\nMonte Carlo methods are problematic to apply and, in general, new approaches\nare needed to explore the phase diagram of the complex theory. Here we will\nreview three of the main candidate methods to deal with the sign problem,\nnamely complex Langevin dynamics, Lefschetz thimbles and density of states\nmethod. We will first study complex Langevin dynamics, combined with the gauge\ncooling method, on the one-dimensional Polyakov line model, and then we will\napply it to pure gauge Yang-Mills theory with a topological theta-term. It\nfollows a comparison between complex Langevin dynamics and the Lefschetz\nthimbles method on three toy models, which are the quartic model, the U(1)\none-link model with a mu dependent determinant, and the SU(2) non abelian\none-link model with complex beta parameter. Lastly, we introduce the density of\nstate method, based on the LLR algorithm, and we will employ it in the study of\nthe relativistic Bose gas at finite chemical potential.", "category": "hep-lat" }, { "text": "Lattice Study of the Extent of the Conformal Window in Two-Color\n Yang-Mills Theory: We perform a lattice calculation of the Schr\\\"odinger functional running\ncoupling in SU(2) Yang-Mills theory with six massless Wilson fermions in the\nfundamental representation. The aim of this work is to determine whether the\nabove theory has an infrared fixed point. Due to sensitivity of the $SF$\nrenormalized coupling to the tuning of the fermion bare mass we were unable to\nreliably extract the running coupling for stronger bare couplings.", "category": "hep-lat" }, { "text": "Semileptonic form factor ratio B_s->D_s/B->D and its application to\n BR(B^0_s->\u03bc^+\u03bc^-): We present a (2+1)-flavor lattice QCD calculation of the form factor ratio\nbetween the semileptonic decays $\\bar{B}^0_s \\to D^+_sl^-\\bar{\\nu} $ and\n$\\bar{B}^0 \\to D^+l^-\\bar{\\nu} $. This ratio is an important theoretical input\nto the hadronic determination of the $B$ meson fragmentation fraction ratio\n$f_s/f_d$ which enters in the measurement of $\\mathrm{BR}(B^0_s\\to\n\\mu^+\\mu^-)$. Small lattice spacings and high statistics enable us to simulate\nthe decays with a dynamic final $D$ meson of small momentum and reliably\nextract the hadronic matrix elements at nonzero recoil. We report our\npreliminary result for the form factor ratio at the corresponding momentum\ntransfer of the two decays $f_0^{(s)}(M^2_\\pi)/f_0^{(d)}(M^2_K)$.", "category": "hep-lat" }, { "text": "Thermodynamical quantities for overlap fermions with chemical potential: Recently a formulation of overlap fermions at finite density based on an\nanalytic continuation of the sign function was proposed. We study this proposal\nby analyzing the energy and number densities for free fermions as a function of\nthe chemical potential and the temperature. Our results show that overlap\nfermions with chemical potential give rise to the correct continuum behavior.", "category": "hep-lat" }, { "text": "Controlling Excited-State Contributions with Distillation in Lattice QCD\n Calculations of Nucleon Isovector Charges $g_S^{u-d}$, $g_A^{u-d}$,\n $g_T^{u-d}$: We investigate the application of the distillation smearing approach, and the\nuse of the variational method with an extended basis of operators facilitated\nby this approach, on the calculation of the nucleon isovector charges\n$g_S^{u-d}$, $g_A^{u-d}$, and $g_T^{u-d}$. We find that the better sampling of\nthe lattice enabled through the use of distillation yields a substantial\nreduction in the statistical uncertainty in comparison with the use of\nalternative smearing methods, and furthermore, appears to offer better control\nover the contribution of excited-states compared to use of a single, local\ninterpolating operator. The additional benefit arising through the use of the\nvariational method in the distillation approach is less dramatic, but\nnevertheless significant given that it requires no additional Dirac inversions.", "category": "hep-lat" }, { "text": "Eigenvalues and Eigenvectors of the Staggered Dirac Operator at Finite\n Temperature: We examine the eigenvalues and eigenvectors of the staggered Dirac operator\non thermal ensembles created in QCD with two flavours of staggered quarks. We\nsee that across the phase transition a gap opens in the spectrum. For finite\nvolume lattices in the low-temperature phase the eigenvectors are extended, but\ngeneric field configurations in the high temperature phase give rise to\nlocalized eigenstates. We examine measures of the stability of such\nlocalization and find that at finite volumes localization occurs through Mott's\nmechanism of the formation of mobility edges. However, the band gap between the\nlocalized and extended states seem to scale to zero in the limit of large\nvolume.", "category": "hep-lat" }, { "text": "Monopole and instanton effects on connected and disconnected\n correlations for scalar density: This study investigates the effects on the connected and disconnected\ncorrelations for the scalar density that are induced by created monopoles and\ninstantons in the QCD vacuum. To reveal the effects, we add a monopole and\nanti-monopole pair in the gauge field configurations in \\textit{SU}(3) by\napplying the monopole creation operator to the vacuum. We vary the magnetic\ncharges of the monopole and anti-monopole and increase the number of monopoles\nand anti-monopoles in the configurations. The Dirac operator of overlap\nfermions preserves the exact chiral symmetry in lattice gauge theory and exact\nzero-modes exist in its spectrum. The eigenvalues and eigenvectors of the\noverlap Dirac operator have been calculated using these configurations, and the\nnumbers of instantons and anti-instantons which are created by these additional\nmonopoles and anti-monopoles have been estimated from the numbers of\ntopological charges in our previous studies. In this study, we demonstrate the\npreliminary results that instantons and monopoles influence the masses that are\nevaluated from the connected and disconnected correlation functions for the\nscalar density using low-lying eigenvalues and eigenvectors of the overlap\nDirac operator.", "category": "hep-lat" }, { "text": "Critical point phase transition for finite temperature 3-flavor QCD with\n non-perturbatively O($a$) improved Wilson fermions at $N_{\\rm t}=10$: We study the finite temperature phase structure for three-flavor QCD with a\nfocus on locating the critical point which separates crossover and first order\nphase transition region in the chiral regime of the Columbia plot. In this\nstudy, we employ the Iwasaki gauge action and the non-perturvatively O($a$)\nimproved Wilson-Clover fermion action. We discuss the finite size scaling\nanalysis including the mixing of magnetization-like and energy-like\nobservables. We carry out the continuum extrapolation of the critical point\nusing newly generated data at $N_{\\rm t}=8$, $10$ and estimate the upper bound\nof the critical pseudo-scalar meson mass $m_{\\rm PS,E} \\lesssim 170 {\\rm MeV}$\nand the critical temperature $T_{\\rm E}=134(3){\\rm MeV}$. Our estimate of the\nupper bound is derived from the existence of the critical point as an edge of\nthe 1st order phase transition while that of the staggered-type fermions is\nbased on its absence.", "category": "hep-lat" }, { "text": "Chiral condensate, susceptibilities, critical coupling and indices in\n QED$_4$: We measure chiral susceptibilities in the Coulomb phase of noncompact QED$_4$\nin $8^4, 10^4$ and $12^4$ lattices. The MFA approach allows simulations in the\nchiral limit which are therefore free from arbitrary mass extrapolations. Using\nthe critical couplings extracted from these calculations, we study the critical\nbehaviour of the chiral condensate, which we find in disagreement with the\npredictions of logarithmically improved scalar Mean Field theory.", "category": "hep-lat" }, { "text": "Quark number susceptibility at high temperature: We use three dimensional reduced effective field theory (EQCD) and lattice\ncalculations to determine the quark number susceptibility of QCD at high\ntemperature. We find our results to agree well with known perturbative\nexpansion as well as with other lattice data.", "category": "hep-lat" }, { "text": "Angular momentum content of the rho-meson in lattice QCD: The variational method allows one to study the mixing of interpolators with\ndifferent chiral transformation properties in the non-perturbatively determined\nphysical state. It is then possible to define and calculate in a\ngauge-invariant manner the chiral as well as the partial wave content of the\nquark-antiquark component of a meson in the infrared, where mass is generated.\nUsing a unitary transformation from the chiral basis to the LSJ basis one may\nextract a partial wave content of a meson. We present results for the ground\nstate of the rho-meson using quenched simulations as well as simulations with\ntwo dynamical quarks, all for lattice spacings close to 0.15 fm. We point out\nthat these results indicate a simple 3S1-wave composition of the rho-meson in\nthe infrared, like in the SU(6) flavor-spin quark model.", "category": "hep-lat" }, { "text": "The Kaon B-parameter in Mixed Action Chiral Perturbation Theory: We calculate the kaon B-parameter, B_K, in chiral perturbation theory for a\npartially quenched, mixed action theory with Ginsparg-Wilson valence quarks and\nstaggered sea quarks. We find that the resulting expression is similar to that\nin the continuum, and in fact has only two additional unknown parameters. At\none-loop order, taste-symmetry violations in the staggered sea sector only\ncontribute to flavor-disconnected diagrams by generating an O(a^2) shift to the\nmasses of taste-singlet sea-sea mesons. Lattice discretization errors also give\nrise to an analytic term which shifts the tree-level value of B_K by an amount\nof O(a^2). This term, however, is not strictly due to taste-breaking, and is\ntherefore also present in the expression for B_K for pure G-W lattice fermions.\nWe also present a numerical study of the mixed B_K expression in order to\ndemonstrate that both discretization errors and finite volume effects are small\nand under control on the MILC improved staggered lattices.", "category": "hep-lat" }, { "text": "Moments of generalized parton distributions and quark angular momentum\n of the nucleon: The internal structure of hadrons is important for a variety of topics,\nincluding the hadron form factors, proton spin and spin asymmetry in polarized\nproton scattering.\n For a systematic study generalized parton distributions (GPDs) encode\nimportant information on hadron structure in the entire impact parameter space.\nWe report on a computation of nucleon GPDs based on simulations with two\ndynamical non-perturbatively improved Wilson quarks with pion masses down to\n350MeV. We present results for the total angular momentum of quarks with chiral\nextrapolation based on covariant baryon chiral perturbation theory.", "category": "hep-lat" }, { "text": "Fermions obstruct dimensional reduction in hot QCD: We have studied, for the first time, screening masses obtained from\nglueball-like correlators in Quantum Chromodynamics with four light dynamical\nflavours of quarks in the temperature range 1.5T_c < T < 3T_c, where T_c is the\ntemperature at which the chiral transition occurs. We have also studied\npion-like and sigma-like screening masses, and found that they are degenerate\nin the entire range of T. These obstruct perturbative dimensional reduction\nsince the lowest glueball screening mass is heavier than them. Extrapolation of\nour results suggests that this obstruction may affect the entire range of\ntemperature expected to be reached even at the Large Hadron Collider.", "category": "hep-lat" }, { "text": "Mean-Field Gauge Interactions in Five Dimensions II. The Orbifold: We study Gauge-Higgs Unification in five dimensions on the lattice by means\nof the mean-field expansion. We formulate it for the case of an SU(2) pure\ngauge theory and orbifold boundary conditions along the extra dimension, which\nexplicitly break the gauge symmetry to U(1) on the boundaries. Our main result\nis that the gauge boson mass computed from the static potential along\nfour-dimensional hyperplanes is nonzero implying spontaneous symmetry breaking.\nThis observation supports earlier data from Monte Carlo simulations [12].", "category": "hep-lat" }, { "text": "Probing the Region of Massless Quarks in Quenched Lattice QCD using\n Wilson Fermions: We study the spectrum of $H(m)=\\gamma_5 W(-m)$ with $W(m)$ being the\nWilson-Dirac operator on the lattice with bare mass equal to $m$. The\nbackground gauge fields are generated using the SU(3) Wilson action at\n$\\beta=5.7$ on an $8^3\\times 16$ lattice. We find evidence that the spectrum of\n$H(m)$ is gapless for $1.02 < m < 2.0$, implying that the physical quark is\nmassless in this whole region.", "category": "hep-lat" }, { "text": "Spectral Analysis of Causal Dynamical Triangulations via Finite Element\n Method: We examine the dual graph representation of simplicial manifolds in Causal\nDynamical Triangulations (CDT) as a mean to build observables, and propose a\nnew representation based on the Finite Element Methods (FEM). In particular,\nwith the application of FEM techniques, we extract the (low-lying) spectrum of\nthe Laplace-Beltrami (LB) operator on the Sobolev space $H^1$ of scalar\nfunctions on piecewise flat manifolds, and compare them with corresponding\nresults obtained by using the dual graph representation. We show that, besides\nfor non-pathological cases in two dimensions, the dual graph spectrum and\nspectral dimension do not generally agree, neither quantitatively nor\nqualitatively, with the ones obtained from the LB operator on the continuous\nspace. We analyze the reasons of this discrepancy and discuss its possible\nimplications on the definition of generic observables built from the dual graph\nrepresentation.", "category": "hep-lat" }, { "text": "Higgs mechanism in five-dimensional gauge theories: Lattice simulations of five-dimensional gauge theories on an orbifold\nrevealed that there is spontaneous symmetry breaking. Some of the\nextra-dimensional components of the gauge field play the role of a Higgs field\nand some of the four-dimensional components become massive gauge bosons. The\neffect is confirmed by computing the Coleman-Weinberg potential with a cutoff.\nWe compare the results of this computation with the lattice data.", "category": "hep-lat" }, { "text": "Nuclear Physics Review: Anchoring low-energy nuclear physics to the fundamental theory of strong\ninteractions remains an outstanding challenge. I review the current progress\nand challenges of the endeavor to use lattice QCD to bridge this connection.\nThis is a particularly exciting time for this line of research as demonstrated\nby the spike in the number of different collaborative efforts focussed on this\nproblem and presented at this conference. I first digress and discuss the 2013\nKen Wilson Award.", "category": "hep-lat" }, { "text": "The three-loop beta function in SU(N) lattice gauge theories: We calculate the third coefficient of the lattice $\\beta$ function in pure\nYang-Mills theory. We make use of a computer code for solving perturbation\ntheory analytically on the lattice. We compute the divergent integrals by using\na method based on a Taylor expansion of the integrand in powers of the external\nmomenta in $4 - \\epsilon$ dimensions. Our results are in agreement with a\nprevious calculation by M. L\\\"uscher and P. Weisz where the authors used a\ndifferent technique. We also show how this new coefficient modifies the scaling\nfunction on the lattice in both the standard and energy schemes. In particular\nwe show that asymptotic scaling is extremely well achieved in the energy\nscheme.", "category": "hep-lat" }, { "text": "A note on the vacuum structure to lattice Euclidean quantum gravity: It is shown that the ground state or vacuum to the lattice Euclidean quantum\ngravity is significantly different from the ground states to the well-known\nvacua in QED, QCD, et cetera. In the case of the lattice Euclidean quantum\ngravity, the long-wavelength scale vacuum structure is similar to that in QED,\nmoreover the quantum fluctuations to gravity are very reduced in comparison\nwith the situation in QED. But the small scale (of the order of the lattice\nscale) vacuum structure to gravity is significantly different from that to the\nlong-wavelength scales: the fluctuation values of geometrical degrees of\nfreedom (tetrads) are commensurable with theirs most probable values.", "category": "hep-lat" }, { "text": "Composite flavor-singlet scalar in twelve-flavor QCD: We report the calculation of the flavor-singlet scalar in the SU(3) gauge\ntheory with the degenerate twelve fermions in the fundamental representation\nusing a HISQ-type action at a fixed $\\beta$. In order to reduce the large\nstatistical error coming from the vacuum-subtracted disconnected correlator, we\nemploy a noise reduction method and a large number of configurations. We\nobserve that the flavor-singlet scalar is lighter than the pion in this theory\nfrom the calculations with the fermion bilinear and gluonic operators. This\npeculiar feature is considered to be due to the infrared conformality of this\ntheory, and it is a promissing signal for a walking technicolor, where a light\ncomposite Higgs boson is expected to emerge by approximate conformal dynamics.", "category": "hep-lat" }, { "text": "Landau gauge gluon and ghost propagators from two-flavor lattice QCD at\n T > 0: In this contribution we extend our unquenched computation of the Landau gauge\ngluon and ghost propagators in lattice QCD at non-zero temperature. The study\nwas aimed at providing input for investigations employing continuum functional\nmethods. We show data which correspond to pion mass values between 300 and 500\nMeV and are obtained for a lattice size 32**3 x 12. The longitudinal and\ntransversal components of the gluon propagator turn out to change smoothly\nthrough the crossover region, while the ghost propagator exhibits only a very\nweak temperature dependence. For a pion mass of around 400 MeV and the\nintermediate temperature value of approx. 240 MeV we compare our results with\nadditional data obtained on a lattice with smaller Euclidean time extent N_t =\n8, 10 and find a reasonable scaling behavior.", "category": "hep-lat" }, { "text": "A numerical and theoretical study of multilevel performance for\n two-point correlator calculations: An investigation of the performance of the multilevel algorithm in the\napproach to criticality has been undertaken using the Ising model, performing\nsimulations across a range of temperatures. Numerical results show that the\nperformance of multilevel in this system deteriorates as the correlation length\nis increased with respect to the lattice size. The statistical error of the\nlongest correlator in the system is reduced in a multilevel setup when the\ncorrelation length is less than one-tenth of the lattice size, while for longer\ncorrelation lengths multilevel performs more poorly than a computer-time\nequivalent single level algorithm. A theoretical model of this performance\nscaling is outlined, and shows remarkable accuracy when compared to numerical\nresults. This theoretical model may be applied to other systems with more\ncomplex spectra to predict if multilevel techniques are likely to result in\nimproved statistics.", "category": "hep-lat" }, { "text": "SU(4) lattice gauge theory with decuplet fermions: Schr\u00f6dinger\n functional analysis: We complete a program of study of SU(N) gauge theories coupled to two flavors\nof fermions in the two-index symmetric representation by performing numerical\nsimulations in SU(4). The beta function, defined and calculated via the\nSchr\\\"odinger functional, runs more slowly than the two-loop perturbative\nresult. The mass anomalous dimension levels off in strong coupling at a value\nof about 0.45, rendering this theory unsuitable for walking technicolor. A\nlarge-N comparison of this data with results from SU(2) and SU(3) reveals\nstriking regularities.", "category": "hep-lat" }, { "text": "Irregular parameter dependence of numerical results in tensor\n renormalization group analysis: We study the parameter dependence of numerical results obtained by the tensor\nrenormalization group. We often observe an irregular behavior as the parameters\nare varied with the method, which makes it difficult to perform the numerical\nderivatives in terms of the parameter. With the use of two-dimensional Ising\nmodel we explicitly show that the sharp cutoff used in the truncated singular\nvalue decomposition causes this unwanted behavior when the level crossing\nhappens between singular values below and above the truncation order as the\nparameters are varied. We also test a smooth cutoff, instead of the sharp one,\nas a truncation scheme and discuss its effects.", "category": "hep-lat" }, { "text": "Quantum Field Theories with Tensor Renormalization Group: We report recent progress on the application of the tensor renormalization\ngroup (TRG) to quantum field theories pursued by the Tsukuba group. We explain\nhow to treat the scalar, fermion, and gauge theories with the TRG method\npresenting the results for the phase transitions in the (3+1)-dimensional\n((3+1)$d$) complex $\\phi^4$ theory at finite density, (1+1)$d$ pure U(1)\nlattice gauge theory with a $\\theta$ term, (3+1)$d$ Nambu--Jona-Lasinio model\nat finite density and (1+1)$d$ and (2+1)$d$ Hubbard models at an arbitrary\nchemical potential. It is demonstrated that the TRG method is free from the\nsign problem in practical calculations and applicable to the four-dimensional\nmodels.", "category": "hep-lat" }, { "text": "Lattice Gauge Fixing, Gribov Copies and BRST Symmetry: We show that a modification of the BRST lattice quantization allows to\ncircumvent an old paradox, formulated by Neuberger, related to lattice Gribov\ncopies and non-perturbative BRST invariance. In the continuum limit the usual\nBRST formulation is recovered.", "category": "hep-lat" }, { "text": "Multi-block/multi-core SSOR preconditioner for the QCD quark solver for\n K computer: We study the algorithmic optimization and performance tuning of the Lattice\nQCD clover-fermion solver for the K computer. We implement the L\\\"uscher's SAP\npreconditioner with sub-blocking in which the lattice block in a node is\nfurther divided to several sub-blocks to extract enough parallelism for the\n8-core CPU SPARC64$^{\\mathrm{TM}}$ VIIIfx of the K computer. To achieve a\nbetter convergence property we use the symmetric successive over-relaxation\n(SSOR) iteration with {\\it locally-lexicographical} ordering for the sub-blocks\nin obtaining the block inverse. The SAP preconditioner is included in the\nsingle precision BiCGStab solver of the nested BiCGStab solver. The single\nprecision part of the computational kernel are solely written with the SIMD\noriented intrinsics to achieve the best performance of the \\SPARC on the K\ncomputer. We benchmark the single precision BiCGStab solver on the three\nlattice sizes: $12^3\\times 24$, $24^3\\times 48$ and $48^3\\times 96$, with\nfixing the local lattice size in a node at $6^3\\times 12$. We observe an ideal\nweak-scaling performance from 16 nodes to 4096 nodes. The performance of a\ncomputational kernel exceeds 50% efficiency, and the single precision BiCGstab\nhas $\\sim26% susutained efficiency.", "category": "hep-lat" }, { "text": "Light hadron masses with a tadpole-improved next-nearest-neighbour\n lattice fermion action: Calculations of hadron masses are done in quenched approximation using gauge\nfield and fermion actions which are both corrected for discretization errors to\n$O(a^2)$ at the classical level and which contain tadpole improvement factors.\nThe fermion action has both nearest-neighbour and next-nearest-neighbour\ncouplings in the kinetic and Wilson terms. Simulations done at lattice spacings\nof $0.27$ and $0.4$fm yield hadron masses which are already quite close to\nexperimental values. The results are compared to Wilson action calculations\ndone at comparable lattice spacings.", "category": "hep-lat" }, { "text": "Perfect Lattice Actions for the Gross-Neveu Model: We apply the method of Hasenfratz and Niedermayer to analytically construct\nperfect lattice actions for the Gross--Neveu model. In the large $N$ limit\nthese actions display an exactly perfect scaling, i.e. cut-off artifacts are\ncompletely eliminated even at arbitrarily short correlation length. Also the\nenergy spectrum coincides with the spectrum in the continuum and continuous\ntranslation and rotation symmetries are restored in physical observables. This\nis the first (analytic) construction of an exactly perfect lattice action at\nfinite correlation length.", "category": "hep-lat" }, { "text": "Asymptotic scaling in the two-dimensional $SU(3)$ $\u03c3$-model at\n correlation length $4 \\times 10^5$: We carry out a high-precision simulation of the two-dimensional $SU(3)$\nprincipal chiral model at correlation lengths $\\xi$ up to $\\approx\\! 4 \\times\n10^5$, using a multi-grid Monte Carlo (MGMC) algorithm. We extrapolate the\nfinite-volume Monte Carlo data to infinite volume using finite-size-scaling\ntheory, and we discuss carefully the systematic and statistical errors in this\nextrapolation. We then compare the extrapolated data to the\nrenormalization-group predictions. For $\\xi \\gtapprox 10^3$ we observe good\nasymptotic scaling in the bare coupling; at $\\xi \\approx 4 \\times 10^5$ the\nnonperturbative constant is within 2--3\\% of its predicted limiting value.", "category": "hep-lat" }, { "text": "Precise Determinations of the Decay Constants of B and D mesons: Recently we studied the B, Bs, D and Ds meson decay constants using various\ntreatments for the heavy quark. For B mesons, we determined fB, fBs, and fBs/fB\nwith NRQCD bottom quarks. We then combined the ratio fBs/fB and another very\nprecise determination from HPQCD for fBs using heavy HISQ quarks, and extracted\nfB with 2% total errors. We also calculated fD, fDs, and fDs/fD using HISQ\ncharm quarks. Here we review our results and briefly discuss their implications\nfor the determination of the CKM matrix elements |Vcd| and |Vcs|.", "category": "hep-lat" }, { "text": "Status of the Finite Temperature Electroweak Phase Transition on the\n Lattice: I review the status of non-perturbative investigations of the finite\ntemperature electroweak phase transition by means of lattice simulations.", "category": "hep-lat" }, { "text": "Leading Isospin Breaking effects in nucleon and $\u0394$ masses: We present a lattice calculation of the leading corrections to the masses of\nnucleons and $\\Delta$ resonances. These are obtained in QCD+QED at $1$st order\nin the Isospin Breaking parameters $\\alpha_{EM}$, the electromagnetic coupling,\nand $\\frac{{\\hat{m}}_d - {\\hat{m}}_u}{\\Lambda_{QCD}}$, coming from the mass\ndifference between $u$ and $d$ quarks.", "category": "hep-lat" }, { "text": "Form factors for semi-leptonic B decays: We report on form factors for the B->K l^+ l^- semi-leptonic decay process.\nWe use several lattice spacings from a=0.12 fm down to 0.06 fm and a variety of\ndynamical quark masses with 2+1 flavors of asqtad quarks provided by the MILC\nCollaboration. These ensembles allow good control of the chiral and continuum\nextrapolations. The b-quark is treated as a clover quark with the Fermilab\ninterpretation. We update our results for f_\\parallel and f_\\perp, or,\nequivalently, f_+ and f_0. In addition, we present new results for the tensor\nform factor f_T. Model independent results are obtained based upon the\nz-expansion.", "category": "hep-lat" }, { "text": "Strong-coupling expansion of lattice O(N) sigma models: We report progress in the computation and analysis of strong-coupling series\nof two- and three-dimensional ${\\rm O}(N)$ $\\sigma$ models. We show that,\nthrough a combination of long strong-coupling series and judicious choice of\nobservables, one can compute continuum quantities reliably and with a precision\nat least comparable with the best available Monte Carlo data.", "category": "hep-lat" }, { "text": "Critical exponents of a three dimensional O(4) spin model: By Monte Carlo simulation we study the critical exponents governing the\ntransition of the three-dimensional classical O(4) Heisenberg model, which is\nconsidered to be in the same universality class as the finite-temperature QCD\nwith massless two flavors. We use the single cluster algorithm and the\nhistogram reweighting technique to obtain observables at the critical\ntemperature. After estimating an accurate value of the inverse critical\ntemperature $\\Kc=0.9360(1)$, we make non-perturbative estimates for various\ncritical exponents by finite-size scaling analysis. They are in excellent\nagreement with those obtained with the $4-\\epsilon$ expansion method with\nerrors reduced to about halves of them.", "category": "hep-lat" }, { "text": "An ideal toy model for confining, walking and conformal gauge theories:\n the O(3) sigma model with theta-term: A toy model is proposed for four dimensional non-abelian gauge theories\ncoupled to a large number of fermionic degrees of freedom. As the number of\nflavors is varied the gauge theory may be confining, walking or conformal. The\ntoy model mimicking this feature is the two dimensional O(3) sigma model with a\ntheta-term. For all theta the model is asymptotically free. For small theta the\nmodel is confining in the infra red, for theta = pi the model has a non-trivial\ninfra red fixed point and consequently for theta slightly below pi the coupling\nwalks. The first step in investigating the notoriously difficult systematic\neffects of the gauge theory in the toy model is to establish non-perturbatively\nthat the theta parameter is actually a relevant coupling. This is done by\nshowing that there exist quantities that are entirely given by the total\ntopological charge and are well defined in the continuum limit and are\nnon-zero, despite the fact that the topological susceptibility is divergent.\nMore precisely it is established that the differences of connected correlation\nfunctions of the topological charge (the cumulants) are finite and non-zero and\nconsequently there is only a single divergent parameter in Z(theta) but\notherwise it is finite. This divergent constant can be removed by an\nappropriate counter term rendering the theory completely finite even at theta >\n0.", "category": "hep-lat" }, { "text": "A lattice calculation of the pion form factor with Ginsparg-Wilson-type\n fermions: Results for Monte Carlo calculations of the electromagnetic vector and scalar\nform factors of the pion in a quenched simulation are presented. We work with\ntwo different lattice volumes up to a spatial size of 2.4 fm at a lattice\nspacing of 0.148 fm. The pion form factors in the space-like region are\ndetermined for pion masses down to 340 MeV.", "category": "hep-lat" }, { "text": "'Bs --> Ds l nu' near zero recoil in and beyond the Standard Model: We compute the normalization of the form factor entering the Bs --> Ds l nu\ndecay amplitude by using numerical simulations of QCD on the lattice. From our\nstudy with Nf=2 dynamical light quarks, and by employing the maximally twisted\nWilson quark action, we obtain in the continuum limit G(1) = 1.052(46). We also\ncompute the scalar and tensor form factors in the region near zero recoil and\nfind f0(t0)/f+(t0)=0.77(2), fT(t0,mb)/f+(t0)=1.08(7), for t0=11.5 GeV^2. These\nlatter results are useful for searching the effects of physics beyond the\nStandard Model in Bs --> Ds l nu decays. Our results for the similar form\nfactors relevant to the non-strange case indicate that the method employed here\ncan be used to achieve the precision determination of the B --> D l nu decay\namplitude as well.", "category": "hep-lat" }, { "text": "A direct relation between confinement and chiral symmetry breaking in\n temporally odd-number lattice QCD: In the lattice QCD formalism, we derive a gauge-invariant analytical relation\nconnecting the Polyakov loop and the Dirac modes on a temporally odd-number\nlattice, where the temporal lattice size is odd, with the normal (nontwisted)\nperiodic boundary condition. This analytical relation indicates that low-lying\nDirac modes have little contribution to the Polyakov loop. Using lattice QCD\nsimulations, we numerically confirm the analytical relation and the negligible\ncontribution of low-lying Dirac modes to the Polyakov loop at the quenched\nlevel, i.e., the Polyakov loop is almost unchanged by removing low-lying\nDirac-mode contribution from the QCD vacuum generated by lattice QCD in both\nconfinement and deconfinement phases. Thus, we conclude that there is no\none-to-one correspondence between confinement and chiral symmetry breaking in\nQCD. As a new method, modifying the Kogut-Susskind formalism, we develop a\nmethod for spin-diagonalizing the Dirac operator on the temporally odd-number\nlattice.", "category": "hep-lat" }, { "text": "Physics from the lattice: glueballs in QCD; topology; SU(N) for all N: Lectures given at the Isaac Newton Institute, NATO-ASI School on\n\"Confinement, Duality and Non-Perturbative Aspects of QCD\", 23 June - 4 July,\n1997.", "category": "hep-lat" }, { "text": "Perturbation theory predictions and Monte Carlo simulations for the 2-d\n O(n) non-linear sigma-model: By using the results of a high-statistics (O(10^7) measurements) Monte Carlo\nsimulation we test several predictions of perturbation theory on the O(n)\nnon-linear sigma-model in 2 dimensions. We study the O(3) and O(8) models on\nlarge enough lattices to have a good control on finite-size effects. The\nmagnetic susceptibility and three different definitions of the correlation\nlength are measured. We check our results with large-n expansions as well as\nwith standard formulae for asymptotic freedom up to 4 loops in the standard and\neffective schemes.\n For this purpose the weak coupling expansions of the energy up to 4 loops for\nthe standard action and up to 3 loops for the Symanzik action are calculated.\nFor the O(3) model we have used two different effective schemes and checked\nthat they lead to compatible results. A great improvement in the results is\nobtained by using the effective scheme based on the energy at 3 and 4 loops. We\nfind that the O(8) model follows very nicely (within few per mille) the\nperturbative predictions. For the O(3) model an acceptable agreement (within\nfew per cent) is found.", "category": "hep-lat" }, { "text": "A simple approach towards the sign problem using path optimisation: We suggest an approach for simulating theories with a sign problem that\nrelies on optimisation of complex integration contours that are not restricted\nto lie along Lefschetz thimbles. To that end we consider the toy model of a\none-dimensional Bose gas with chemical potential. We identify the main\ncontribution to the sign problem in this case as coming from a nearest\nneighbour interaction and approximately cancel it by an explicit deformation of\nthe integration contour. We extend the obtained expressions to more general\nones, depending on a small set of parameters. We find the optimal values of\nthese parameters on a small lattice and study their range of validity. We also\nidentify precursors for the onset of the sign problem. A fast method of\nevaluating the Jacobian related to the contour deformation is proposed and its\nnumerical stability is examined. For a particular choice of lattice parameters,\nwe find that our approach increases the lattice size at which the sign problem\nbecomes serious from $L \\approx 32$ to $L \\approx 700$. The efficient\nevaluation of the Jacobian ($O(L)$ for a sweep) results in running times that\nare of the order of a few minutes on a standard laptop.", "category": "hep-lat" }, { "text": "Colorful plane vortices and Chiral Symmetry Breaking in $SU(2)$ Lattice\n Gauge Theory: We investigate plane vortices with color structure. The topological charge\nand gauge action of such colorful plane vortices are studied in the continuum\nand on the lattice. These configurations are vacuum to vacuum transitions\nchanging the winding number between the two vacua, leading to a topological\ncharge $Q=-1$ in the continuum. After growing temporal extent of these\nvortices, the lattice topological charge approaches $-1$ and the index theorem\nis fulfilled. We analyze the low lying modes of the overlap Dirac operator in\nthe background of these colorful plane vortices and compare them with those of\nspherical vortices. They show characteristic properties for spontaneous chiral\nsymmetry breaking.", "category": "hep-lat" }, { "text": "Anomalous Fermion Number Non-Conservation on the Lattice: The anomaly for the fermion number current is calculated on the lattice in a\nsimple prototype model with an even number of fermion doublets.", "category": "hep-lat" }, { "text": "The Renormalization Group and Dynamical Triangulations: A block spin renormalization group approach is introduced which can be\napplied to dynamical triangulations in any dimension.", "category": "hep-lat" }, { "text": "Trivializing maps, the Wilson flow and the HMC algorithm: In lattice gauge theory, there exist field transformations that map the\ntheory to the trivial one, where the basic field variables are completely\ndecoupled from one another. Such maps can be constructed systematically by\nintegrating certain flow equations in field space. The construction is worked\nout in some detail and it is proposed to combine the Wilson flow (which\ngenerates approximately trivializing maps for the Wilson gauge action) with the\nHMC simulation algorithm in order to improve the efficiency of lattice QCD\nsimulations.", "category": "hep-lat" }, { "text": "The static energy of a quark-antiquark pair from Laplacian eigenmodes: We test a method for computing the static quark-antiquark potential in\nlattice QCD, which is not based on Wilson loops, but where the trial states are\nformed by eigenvector components of the covariant lattice Laplace operator. The\nruntime of this method is significantly smaller than the standard Wilson loop\ncalculation, when computing the static potential not only for on-axis, but also\nfor many off-axis quark-antiquark separations, i.e., when a fine spatial\nresolution is required. We further improve the signal by using multiple\neigenvector pairs, weighted with Gaussian profile functions of the eigenvalues,\nproviding a basis for a generalized eigenvalue problem (GEVP), as it was\nrecently introduced to improve distillation in meson spectroscopy. We show\nresults with the new method for the static potential with dynamical fermions\nand demonstrate its efficiency compared to traditional Wilson loop\ncalculations. The method presented here can also be applied to compute hybrid\nor tetra-quark potentials and to static-light systems.", "category": "hep-lat" }, { "text": "Static quark anti-quark interactions at non-zero temperature from\n lattice QCD: We present results on the in-medium interactions of static quark anti-quark\npairs using realistic 2+1 HISQ flavor lattice QCD. Focus is put on the\nextraction of spectral information from Wilson line correlators in Coulomb\ngauge using four complementary methods. Our results indicate that on HISQ\nlattices, the position of the dominant spectral peak associated with the\nreal-part of the interquark potential remains unaffected by temperature. This\nis in contrast to prior work in quenched QCD and we present follow up\ncomparisons to newly generated quenched ensembles.", "category": "hep-lat" }, { "text": "Perturbative calculations for the HISQ action: the gluon action at\n $O(N_f\u03b1_sa^2)$: We present a new (and general) algorithm for deriving lattice Feynman rules\nwhich is capable of handling actions as complex as the Highly Improved\nStaggered Quark (HISQ) action. This enables us to perform a perturbative\ncalculation of the influence of dynamical HISQ fermions on the perturbative\nimprovement of the gluonic action in the same way as we have previously done\nfor asqtad fermions. We find the fermionic contributions to the radiative\ncorrections in the L\\\"uscher-Weisz gauge action to be somewhat larger for HISQ\nfermions than for asqtad.", "category": "hep-lat" }, { "text": "A new fermion Hamiltonian for lattice gauge theory: We formulate Hamiltonian vector-like lattice gauge theory using the overlap\nformula for the spatial fermionic part, $H_f$. We define a chiral charge, $Q_5$\nwhich commutes with $H_f$, but not with the electric field term. There is an\ninteresting relation between the chiral charge and the fermion energy with\nconsequences for chiral anomalies.", "category": "hep-lat" }, { "text": "Lattice Models of Quantum Gravity: Standard Regge Calculus provides an interesting method to explore quantum\ngravity in a non-perturbative fashion but turns out to be a CPU-time demanding\nenterprise. One therefore seeks for suitable approximations which retain most\nof its universal features. The $Z_2$-Regge model could be such a desired\nsimplification. Here the quadratic edge lengths $q$ of the simplicial complexes\nare restricted to only two possible values $q=1+\\epsilon\\sigma$, with\n$\\sigma=\\pm 1$, in close analogy to the ancestor of all lattice theories, the\nIsing model. To test whether this simpler model still contains the essential\nqualities of the standard Regge Calculus, we study both models in two\ndimensions and determine several observables on the same lattice size. In order\nto compare expectation values, e.g. of the average curvature or the Liouville\nfield susceptibility, we employ in both models the same functional integration\nmeasure. The phase structure is under current investigation using mean field\ntheory and numerical simulation.", "category": "hep-lat" }, { "text": "Hadronic vacuum polarization with C* boundary conditions: We present a progress report on the calculation of the connected hadronic\ncontribution to the muon g-2 with C* boundary conditions. For that purpose we\nuse a QCD gauge ensemble with 3+1 flavors and two QCD+QED gauge ensembles with\n1+2+1 flavors of dynamical quarks generated by the RC* collaboration. We detail\nthe calculation of the vector mass and elaborate on both statistical and\nsystematic errors.", "category": "hep-lat" }, { "text": "Delta I = 3/2, K to Pi Pi Decays with a Nearly Physical Pion Mass: The Delta I = 3/2 K to Pi Pi decay amplitude is calculated on RBC/UKQCD 32^3\nx 64, L_s=32 dynamical lattices with 2+1 flavors of domain wall fermions using\nthe DSDR and Iwasaki gauge action. The calculation is performed with a single\npion mass (m_pi=141.9(2.3) MeV, partially quenched) and kaon mass\n(m_K=507.4(8.5) MeV) which are nearly physical, and with nearly energy\nconserving kinematics. Antiperiodic boundary conditions in two spatial\ndirections are used to give the two pions non-zero ground state momentum.\nResults for time separations of 20, 24, 28 and 32 between the kaon and two-pion\nsources are computed and an error weighted average is performed to reduce the\nerror. We find prelimenary results for Re(A_2)=1.396(081)_stat(160)_sys x\n10^(-8) GeV and Im(A_2) = -8.46(45)_stat(1.95)_sys x 10^(-13) GeV.", "category": "hep-lat" }, { "text": "Colorful vortex intersections in SU(2) lattice gauge theory and their\n influencs on chiral properties: We introduce topological non-trivial colorful regions around intersection\npoints of two perpendicular vortex pairs and investigate their influence on\ntopological charge density and eigenmodes of the Dirac operator. With\nincreasing distance between the vortices the eigenvalues of the lowest modes\ndecrease. We show that the maxima and minima of the chiral densities of the low\nmodes follow mainly the distributions of the topological charge densities. The\ntopological non-trivial color structures lead in some low modes to distinct\npeaks in the chiral densities. The other low modes reflect the topological\ncharge densities of the intersection points.", "category": "hep-lat" }, { "text": "First experience with classical-statistical real-time simulations of\n anomalous transport with overlap fermions: We present first results of classical-statistical real-time simulations of\nanomalous transport phenomena with overlap fermions. We find that even on small\nlattices overlap fermions reproduce the real-time anomaly equation with much\nbetter precision than Wilson-Dirac fermions on an order of magnitude larger\nlattices. The difference becomes much more pronounced for quickly changing\nelectromagnetic fields, especially if one takes into account the back-reaction\nof fermions on electromagnetism. As test cases, we consider chirality pumping\nin parallel electric and magnetic fields and mixing between the plasmon and the\nChiral Magnetic Wave.", "category": "hep-lat" }, { "text": "Magnetic properties of the nucleon in a uniform background field: We present results for the magnetic moment and magnetic polarisability of the\nneutron and the magnetic moment of the proton. These results are calculated\nusing the uniform background field method on 32^3 x 64 dynamical QCD lattices\nprovided by the PACS-CS collaboration as part of the ILDG. We use a uniform\nbackground magnetic field quantised by the periodic spatial volume. We\ninvestigate ways to improve the effective energy plots used to calculate\nmagnetic polarisabilities, including the use of correlation matrix techniques\nwith various source smearings.", "category": "hep-lat" }, { "text": "The order of the phase transition in 3d U(1)+Higgs theory: We study the order of the phase transition in the 3d U(1)+Higgs theory, which\nis the Ginzburg-Landau theory of superconductivity. We confirm that for small\nscalar self-coupling the transition is of first order. For large scalar\nself-coupling the transition ceases to be of first order, and a non-vanishing\nscalar mass suggests that the transition may even be of higher than second\norder.", "category": "hep-lat" }, { "text": "Correlated Dirac Eigenvalues and Axial Anomaly in Chiral Symmetric QCD: We investigate the Dirac eigenvalue spectrum ($\\rho(\\lambda,m_l)$) to study\nthe microscopic origin of axial anomaly in high temperature phase of QCD. We\npropose novel relations between the derivatives ($\\partial^n\n\\rho(\\lambda,m_l)/\\partial m_l^n$) of the Dirac eigenvalue spectrum with\nrespect to the quark mass ($m_l$) and the $(n+1)$-point correlations among the\neigenvalues ($\\lambda$) of the massless Dirac operator. Based on these\nrelations, we present lattice QCD results for $\\partial^n\n\\rho(\\lambda,m_l)/\\partial m_l^n$ ($n=1, 2, 3$) with $m_l$ corresponding to\npion masses $m_\\pi=160-55$ MeV, and at a temperature of about 1.6 times the\nchiral phase transition temperature. Calculations were carried out using\n(2+1)-flavors of highly improved staggered quarks and the tree-level Symanzik\ngauge action with the physical strange quark mass, three lattice spacings\n$a=0.12, 0.08, 0.06$ fm, and lattices having aspect ratios $4-9$. We find that\n$\\rho(\\lambda\\to0,m_l)$ develops a peaked structure. This peaked structure,\nwhich arises due to non-Poisson correlations within the infrared part of the\nDirac eigenvalue spectrum, becomes sharper as $a\\to0$, and its amplitude is\nproportional to $m_l^2$. After continuum and chiral extrapolations, we find\nthat the axial anomaly remains manifested in two-point correlation functions of\nscalar and pseudo-scalar mesons in the chiral limit. We demonstrate that the\nbehavior of $\\rho(\\lambda\\to0,m_l)$ is responsible for it.", "category": "hep-lat" }, { "text": "Monte Carlo approach to the string/M-theory: It has long been conjectured that certain supersymmetric Yang-Mills (SYM)\ntheories provide us with nonperturbative formulations of the string/M-theory.\nAlthough the supersymmetry (SUSY) on lattice is notoriously difficult in\ngeneral, for a class of theories important for the string/M-theory various\nlattice and non-lattice methods, which enable us to study them on computers,\nhave been proposed by now. In this talk, firstly I explain how SYM and\nstring/M-theory are related. Then I explain why the lattice SUSY is difficult\nin general, and how the difficulties are solved in theories related to\nstring/M-theory. Then I review the status of the simulations. It is explained\nthat some stringy effects are correctly incorporated in SYM. Furthermore,\nconcrete values can be obtained from the SYM side, even when a direct\ncalculation on the string theory side is impossible by the state-of-the-art\ntechniques. We also comment on other recent developments, including the\nmembrane mini-revolution in 2008 and simulation of the matrix model formulation\nof the string theory.", "category": "hep-lat" }, { "text": "Asymptotic scaling from strong coupling: Strong-coupling analysis of two-dimensional chiral models, extended to 15th\norder, allows for the identification of a scaling region where known continuum\nresults are reproduced with great accuracy, and asymptotic scaling predictions\nare fulfilled. The properties of the large-$N$ second-order phase transition\nare quantitatively investigated.", "category": "hep-lat" }, { "text": "Polyakov loops and spectral properties of the staggered Dirac operator: We study the spectrum of the staggered Dirac operator in SU(2) gauge fields\nclose to the free limit, for both the fundamental and the adjoint\nrepresentation. Numerically we find a characteristic cluster structure with\nspacings of adjacent levels separating into three scales. We derive an\nanalytical formula which explains the emergence of these different spectral\nscales. The behavior on the two coarser scales is determined by the lattice\ngeometry and the Polyakov loops, respectively. Furthermore, we analyze the\nspectral statistics on all three scales, comparing to predictions from random\nmatrix theory.", "category": "hep-lat" }, { "text": "Uses of Effective Field Theory in Lattice QCD: Several physical problems in particle physics, nuclear physics, and\nastrophysics require information from non-perturbative QCD to gain a full\nunderstanding. In some cases the most reliable technique for quantitative\nresults is to carry out large-scale numerical calculations in lattice gauge\ntheory. As in any numerical technique, there are several sources of\nuncertainty. This chapter explains how effective field theories are used to\nkeep them under control and, then, obtain a sensible error bar. After a short\nsurvey of the numerical technique, we explain why effective field theories are\nnecessary and useful. Then four important cases are reviewed: Symanzik's\neffective field theory of lattice spacing effects; heavy-quark effective theory\nas a tool for controlling discretization effects of heavy quarks; chiral\nperturbation theory as a tool for reaching the chiral limit; and a general\nfield theory of hadrons for deriving finite volume corrections.", "category": "hep-lat" }, { "text": "A microscopic semiclassical confining field equation for $U(1)$ lattice\n gauge theory in 2+1 dimensions: We present a semiclassical nonlinear field equation for the confining field\nin 2+1--dimensional $U(1)$ lattice gauge theory (compact QED). The equation is\nderived directly from the underlying microscopic quantum Hamiltonian by means\nof truncation. Its nonlinearities express the dynamic creation of magnetic\nmonopole currents leading to the confinement of the electric field between two\nstatic electric charges. We solve the equation numerically and show that it can\nbe interpreted as a London relation in a dual superconductor.", "category": "hep-lat" }, { "text": "Review on Algorithms for dynamical fermions: This review gives an overview on the research of algorithms for dynamical\nfermions used in large scale lattice QCD simulations.\n First a short overview on the state-of-the-art of ensemble generation at the\nphysical point is given.\n Followed by an overview on necessary steps towards simulation of large\nlattices with the Hybrid Monte Carlo algorithm. Here, the status of iterative\nsolvers and tuning procedures for numerical integrators within the molecular\ndynamics are discussed.\n This is followed by a review on the on-going developments for algorithms,\nwith a focus on methods which are potentially useful to simulate gauge theories\nat very fine lattice spacings, i.e. well suited to overcome freezing of the\ntopological charge. This includes modification of the HMC algorithm as well as\na discussion of algorithms which includes the fermion weight via global\ncorrection steps. Parts of the discussions are on the application of generative\nmodels via gauge equivariant flows as well as multi-level algorithms.", "category": "hep-lat" }, { "text": "Non-perturbative calculation of Z_m using Asqtad fermions: We report progress on a non-perturbative calculation of the light quark mass\nrenormalization factor Z_m, using dynamical Asqtad fermions. This quantity is\nused to determine the light quark masses in the conventional MS-bar scheme.\nSuch a non-perturbative determination of Z_m removes uncertainties due to\ntruncation of its perturbative expansion, currently known to two loops. These\ncalculations have been carried out using publicly available MILC lattices with\nspacings of approximately 0.125 and 0.09 fm.", "category": "hep-lat" }, { "text": "Supercurrent conservation in the lattice Wess-Zumino model with\n Ginsparg-Wilson fermions: We study supercurrent conservation for the four-dimensional Wess-Zumino model\nformulated on the lattice. The formulation is one that has been discussed\nseveral times, and uses Ginsparg-Wilson fermions of the overlap (Neuberger)\nvariety, together with an auxiliary fermion (plus superpartners), such that a\nlattice version of U(1)_R symmetry is exactly preserved in the limit of\nvanishing bare mass. We show that the almost naive supercurrent is conserved at\none loop. By contrast we find that this is not true for Wilson fermions and a\ncanonical scalar action. We provide nonperturbative evidence for the\nnonconservation of the supercurrent in Monte Carlo simulations.", "category": "hep-lat" }, { "text": "Numerical sign problem and the tempered Lefschetz thimble method: The numerical sign problem is a major obstacle to the quantitative\nunderstanding of many important physical systems with first-principles\ncalculations. Typical examples for such systems include finite-density QCD,\nstrongly-correlated electron systems and frustrated spin systems, as well as\nthe real-time dynamics of quantum systems. In this talk, we argue that the\n\"tempered Lefschetz thimble method\" (TLTM) [M. Fukuma and N. Umeda,\narXiv:1703.00861] and its extension, the \"worldvolume tempered Lefschetz\nthimble method\" (WV-TLTM) [M. Fukuma and N. Matsumoto, arXiv:2012.08468], may\nbe a reliable and versatile solution to the sign problem. We demonstrate the\neffectiveness of the algorithm by exemplifying a successful application of\nWV-TLTM to the Stephanov model, which is an important toy model of\nfinite-density QCD. We also discuss the computational scaling of WV-TLTM.", "category": "hep-lat" }, { "text": "Condensation of vortices in the X-Y model in 3d: a disorder parameter: A disorder parameter is constructed which signals the condensation of\nvortices. The construction is tested by numerical simulations on lattice.", "category": "hep-lat" }, { "text": "From confinement to new states of dense QCD matter: Transitions between centre sectors are related to confinement in pure\nYang-Mills theories. We study the impact of these transitions in QCD-like\ntheories for which centre symmetry is explicitly broken by the presence of\nmatter. For low temperatures, we provide numerical evidence that centre\ntransitions do occur with matter merely providing a bias towards the trivial\ncentre sector until centre symmetry is spontaneously broken at high\ntemperatures. The phenomenological consequences of these transitions for dense\nhadron matter are illustrated in an SU(3) effective quark theory: centre\ndressed quarks undergo condensation due to Bose-type statistics forming a\nhitherto unknown state of dense but cold quark matter.", "category": "hep-lat" }, { "text": "A density of states approach to the hexagonal Hubbard model at finite\n density: We apply the Linear Logarithmic Relaxation (LLR) method, which generalizes\nthe Wang-Landau algorithm to quantum systems with continuous degrees of\nfreedom, to the fermionic Hubbard model with repulsive interactions on the\nhoneycomb lattice. We compute the generalized density of states of the average\nHubbard field and divise two reconstruction schemes to extract physical\nobservables from this result. By computing the particle density as a function\nof chemical potential we assess the utility of LLR in dealing with the sign\nproblem of this model, which arises away from half filling. We show that the\nrelative advantage over brute-force reweighting grows as the interaction\nstrength is increased and discuss possible future improvements.", "category": "hep-lat" }, { "text": "Status of the QCDOC project: A status report is given of the QCDOC project, a massively parallel computer\noptimized for lattice QCD using system-on-a-chip technology. We describe\nseveral of the hardware and software features unique to the QCDOC architecture\nand present performance figures obtained from simulating the current VHDL\ndesign of the QCDOC chip with single-cycle accuracy.", "category": "hep-lat" }, { "text": "Ordering monomial factors of polynomials in the product representation: The numerical construction of polynomials in the product representation (as\nused for instance in variants of the multiboson technique) can become\nproblematic if rounding errors induce an imprecise or even unstable evaluation\nof the polynomial. We give criteria to quantify the effects of these rounding\nerrors on the computation of polynomials approximating the function $1/s$. We\nconsider polynomials both in a real variable $s$ and in a Hermitian matrix. By\ninvestigating several ordering schemes for the monomials of these polynomials,\nwe finally demonstrate that there exist orderings of the monomials that keep\nrounding errors at a tolerable level.", "category": "hep-lat" }, { "text": "The Renormalized Trajectory of the O(N) Non-linear Sigma Model: The renormalized trajectory (RT) is determined from two different Monte Carlo\nrenormalization group techniques with $\\delta$-function block spin\ntransformation in the multi-dimensional coupling parameter space of the\ntwo-dimensional non-linear sigma model with O(3) symmetry. At a correlation\nlength $\\xi \\approx 3$-$5$, the RT is shown to break away from the straight\nline of the fixed point trajectory (FPT) which is orthogonal to the critical\nsurface and originates from the ultraviolet fixed point (UVFP). The large $N$\ncalculation of the RT is also presented in the coupling parameter space of the\nmost general bilinear Hamiltonian. The RT in the large $N$ approximation\nexhibits a similar shape with the sharp break occurring at a somewhat smaller\ncorrelation length.", "category": "hep-lat" }, { "text": "Polynomial Hybrid Monte Carlo algorithm for lattice QCD with an odd\n number of flavors: We present a polynomial hybrid Monte Carlo (PHMC) algorithm for lattice QCD\nwith odd numbers of flavors of O(a)-improved Wilson quark action. The algorithm\nmakes use of the non-Hermitian Chebyshev polynomial to approximate the inverse\nsquare root of the fermion matrix required for an odd number of flavors. The\nsystematic error from the polynomial approximation is removed by a noisy\nMetropolis test for which a new method is developed. Investigating the property\nof our PHMC algorithm in the N_f=2 QCD case, we find that it is as efficient as\nthe conventional HMC algorithm for a moderately large lattice size (16^3 times\n48) with intermediate quark masses (m_{PS}/m_V ~ 0.7-0.8). We test our\nodd-flavor algorithm through extensive simulations of two-flavor QCD treated as\nan N_f = 1+1 system, and comparing the results with those of the established\nalgorithms for N_f=2 QCD. These tests establish that our PHMC algorithm works\non a moderately large lattice size with intermediate quark masses (16^3 times\n48, m_{PS}/m_V ~ 0.7-0.8). Finally we experiment with the (2+1)-flavor QCD\nsimulation on small lattices (4^3 times 8 and 8^3 times 16), and confirm the\nagreement of our results with those obtained with the R algorithm and\nextrapolated to a zero molecular dynamics step size.", "category": "hep-lat" }, { "text": "Cascade Baryon Spectrum from Lattice QCD: A comprehensive study of the cascade baryon spectrum using lattice QCD\naffords the prospect of predicting the masses of states not yet discovered\nexperimentally, and determining the spin and parity of those states for which\nthe quantum numbers are not yet known. The study of the cascades, containing\ntwo strange quarks, is particularly attractive for lattice QCD in that the\nchiral effects are reduced compared to states composed only of u/d quarks, and\nthe states are typically narrow. We report preliminary results for the cascade\nspectrum obtained by using anisotropic N_f = 2 Wilson lattices with temporal\nlattice spacing inverse 5.56 GeV.", "category": "hep-lat" }, { "text": "Domain-wall fermions with U(1) dynamical gauge fields in\n (4+1)-dimensions: We carry out a numerical simulation of a domain-wall model in (4+1)\ndimensions, in the presence of a quenched U(1) dynamical gauge field only in an\nextra dimension, corresponding to the weak coupling limit of a (4-dimensional)\nphysical gauge coupling. Our numerical data suggest that the zero mode seems\nabsent in the symmetric phase, so that it is difficult to construct a lattice\nchiral gauge theory in the continuum limit.", "category": "hep-lat" }, { "text": "Towards reduction of autocorrelation in HMC by machine learning: In this paper we propose new algorithm to reduce autocorrelation in Markov\nchain Monte-Carlo algorithms for euclidean field theories on the lattice. Our\nproposing algorithm is the Hybrid Monte-Carlo algorithm (HMC) with restricted\nBoltzmann machine. We examine the validity of the algorithm by employing the\nphi-fourth theory in three dimension. We observe reduction of the\nautocorrelation both in symmetric and broken phase as well. Our proposing\nalgorithm provides consistent central values of expectation values of the\naction density and one-point Green's function with ones from the original HMC\nin both the symmetric phase and broken phase within the statistical error. On\nthe other hand, two-point Green's functions have slight difference between one\ncalculated by the HMC and one by our proposing algorithm in the symmetric\nphase. Furthermore, near the criticality, the distribution of the one-point\nGreen's function differs from the one from HMC. We discuss the origin of\ndiscrepancies and its improvement.", "category": "hep-lat" }, { "text": "On Scale Determination in Lattice QCD with Dynamical Quarks: Dependence of a/r_c (inverse Sommer parameter in units of lattice spacing a)\non am_q (quark mass in lattice unit) has been observed in all lattice QCD\nsimulations with sea quarks including the ones with improved actions. How much\nof this dependence is a scaling violation has remained an intriguing question.\nOur approach has been to investigate the issue with an action with known\nlattice artifacts, i.e., the standard Wilson quark and gauge action with\nbeta=5.6 and 2 degenerate flavors of sea quarks on 16^3 times 32 lattices. In\norder to study in detail the sea quark mass dependence, measurements are\ncarried out at eight values of the PCAC quark mass values am_q from about 0.07\nto below 0.015. Though scaling violations may indeed be present for relatively\nlarge am_q, a consistent scenario at sufficiently small am_q seems to emerge in\nthe mass-independent scheme where for a fixed beta, 1/r_0 and sqrt{sigma} have\nlinear dependence on m_q as physical effects similar to the quark mass\ndependence of the rho mass. We present evidence for this scenario and\naccordingly extract the lattice scale (a = 0.0805(7) fm, a^{-1} = 2.45(2) GeV)\nby chiral extrapolation to the physical point.", "category": "hep-lat" }, { "text": "Split of the pseudo-critical temperatures of chiral and\n confine/deconfine transitions by temperature gradient: Searching of the critical endpoint of the phase transition of Quantum\nChromodynamics~(QCD) matter in experiments is of great interest. The\ntemperature in the fireball of a collider is location dependent, however, most\ntheoretical studies address the scenario of uniform temperature. In this work,\nthe effect of temperature gradients is investigated using lattice QCD approach.\nWe find that the temperature gradient catalyzes chiral symmetry breaking,\nmeanwhile the temperature gradient increases the Polyakov loop in the confined\nphase but suppresses the Polyakov loop in the deconfined phase. Furthermore,\nthe temperature gradient decreases the pseudo-critical temperature of chiral\ntransition but increases the pseudo-critical temperature of the\nconfine/deconfine transition.", "category": "hep-lat" }, { "text": "B- and D-meson leptonic decay constants and quark masses from\n four-flavor lattice QCD: We describe a recent lattice-QCD calculation of the leptonic decay constants\nof heavy-light pseudoscalar mesons containing charm and bottom quarks and of\nthe masses of the up, down, strange, charm, and bottom quarks. Results for\nthese quantities are of the highest precision to date. Calculations use 24\nisospin-symmetric ensembles of gauge-field configurations with six different\nlattice spacings as small as approximately 0.03 fm and several values of the\nlight quark masses down to physical values of the average up- and\ndown-sea-quark masses. We use the highly-improved staggered quark (HISQ)\nformulation for valence and sea quarks, including the bottom quark. The\nanalysis employs heavy-quark effective theory (HQET). A novel HQET method is\nused in the determination of the quark masses.", "category": "hep-lat" }, { "text": "Taste breaking effects in scalar meson correlators: As a consistency check of the staggered-fermion fourth-root approximation, we\nanalyze the a_0 and f_0 correlators, including the effects of two-meson\ntaste-multiplet intermediate states. Rooted staggered chiral perturbation\ntheory describes the contributions from the pseudoscalar taste multiplets in\nterms of only a few low energy constants, which have all been previously\ndetermined by the MILC collaboration. In previous work one of us (Prelovsek)\nshowed that the two-meson ``bubble'' contributions could explain the observed\nanomalies in the lattice data for the isovector a_0 channel. In the present\nwork we extend this analysis to the f_0 channel. On a MILC collaboration\nlattice ensemble at 0.12 fm with 2+1 flavors of Asqtad-improved staggered\nfermions, we have made new measurements of correlators in both channels for a\nvariety of momenta. A fit to these correlators gives low energy constants that\nare reasonably consistent with previous determinations by the MILC\ncollaboration.}", "category": "hep-lat" }, { "text": "Pion condensation at lower than physical quark masses: In QCD at large enough isospin chemical potential Bose-Einstein Condensation\n(BEC) takes place, separated from the normal phase by a phase transition. From\nprevious studies the location of the BEC line at the physical point is known.\nIn the chiral limit the condensation happens already at infinitesimally small\nisospin chemical potential for zero temperature according to chiral\nperturbation theory. The thermal chiral transition at zero density might then\nbe affected, depending on the shape of the BEC boundary, by its proximity. As a\nfirst step towards the chiral limit, we perform simulations of 2+1 flavors QCD\nat half the physical quark masses. The position of the BEC transition is then\nextracted and compared with the results at physical masses.", "category": "hep-lat" }, { "text": "Recent progress in finite temperature lattice QCD: I review recent progress in the determination of the QCD phase diagram at\nfinite temperature, in investigations of the nature of the transition or\ncrossover from the hadronic phase to the quark-gluon plasma phase and in the\ndetermination of the equation of state. This talk will focus on results at zero\nchemical potential.", "category": "hep-lat" }, { "text": "Lattice Calculations of B to K/K*l+l- form factors: This paper gives a brief review on the recent lattice QCD calculations of the\nB to K/K*l+l- semi-leptonic decay form factors.", "category": "hep-lat" }, { "text": "Meson spectral functions at nonzero momentum in hot QCD: We present preliminary results for meson spectral functions at nonzero\nmomentum, obtained from quenched lattice QCD simulations at finite temperature\nusing the Maximal Entropy Method. Twisted boundary conditions are used to have\naccess to many momenta p~T. For light quarks, we observe a drastic modification\nwhen heating the system from below to above Tc. In particular, for the vector\nspectral density we find a nonzero spectral weight at all energies.", "category": "hep-lat" }, { "text": "No coincidence of center percolation and deconfinement in SU(4) lattice\n gauge theory: We study the behavior of center sectors in pure SU(4) lattice gauge theory at\nfinite temperature. The center sectors are defined as spatial clusters of\nneighboring sites with values of their local Polyakov loops near the same\ncenter elements. We study the connectedness and percolation properties of the\ncenter clusters across the deconfinement transition. We show that for SU(4)\ngauge theory deconfinement cannot be described as a percolation transition of\ncenter clusters, a finding which is different from pure SU(2) or pure SU(3)\nYang Mills theory, where the percolation description even allows for a\ncontinuum limit.", "category": "hep-lat" }, { "text": "Asymptotically free models and discrete non-Abelian groups: We study the two-dimensional renormalization-group flow induced by\nperturbations that reduce the global symmetry of the O(3) sigma-model to the\ndiscrete symmetries of Platonic solids. We estimate the value of the\ncorrelation length at which differences in the behaviour of the various models\nshould be expected. For the icosahedron model, we find xi > 200. We provide an\nexplanation for the recent numerical results of Patrascioiu and Seiler and of\nHasenfratz and Niedermayer.", "category": "hep-lat" }, { "text": "Precise Determination of the Charm Quark Mass: The determination of the charm quark mass is now possible to 1% from QCD,\nwith lattice QCD pushing the error down below 1%. I will describe the\ningredients of this approach and how it can achieve this accuracy. Results for\nquark mass ratios, m_c/m_s and m_b/m_c, can also be determined to 1% from\nlattice QCD, allowing accuracy for the heavy quark masses to be leveraged into\nthe light quark sector. I will discuss the prospects for, and importance of,\nimproving results in future calculations.", "category": "hep-lat" }, { "text": "Improved Error Estimate for the Valence Approximation: We construct a systematic mean-field-improved coupling constant and quark\nloop expansion for corrections to the valence (quenched) approximation to\nvacuum expectation values in the lattice formulation of QCD. Terms in the\nexpansion are evaluated by a combination of weak coupling perturbation theory\nand a Monte Carlo algorithm.", "category": "hep-lat" }, { "text": "Restoring rotational invariance for lattice QCD propagators: This note presents a method to reduce the discretization errors appearing\nwhen solving a Quantum Field Theory in a hypercubic lattice in both position\nand momentum-space. The method exploits the artifacts that break rotational\nsymmetry to recover rotationally invariant results for two-point Green\nfunctions. We show that a combination of the results obtained in position and\nmomentum space can be useful to signal the presence of rotationally invariant\nartifacts making use of their approximate Fourier transforms in the continuum.\nThe method will be introduced using a Klein-Gordon propagator, and a direct\napplication to gluon propagator in quenched lattice QCD will be given.", "category": "hep-lat" }, { "text": "Progress Towards finding Quark Masses and the QCD scale Lambda from the\n Lattice: We discuss recent work trying to extract the renormalised quark masses and\nLambda, the QCD scale, from dynamical simulations in lattice gauge theory.", "category": "hep-lat" }, { "text": "Topological Features in a Two-Dimensional Higgs Model: Topological properties of the gauge field in a two-dimensional Higgs model\nare investigated. Results of exploratory numerical simulations are presented.", "category": "hep-lat" }, { "text": "Confinement Physics in Quantum Chromodynamics: We study the confinement physics in QCD in the maximally abelian (MA) gauge\nusing the SU(2) lattice QCD, based on the dual-superconductor picture. In the\nMA gauge, off-diagonal gluon components are forced to be small, and the\noff-diagonal angle variable $\\chi_\\mu(s)$ tends to be random. Within the\nrandom-variable approximation for $\\chi_\\mu(s)$, we analytically prove the\nperimeter law of the off-diagonal gluon contribution to the Wilson loop in the\nMA gauge, which leads to abelian dominance on the string tension. To clarify\nthe origin of abelian dominance for the long-range physics, we study the\ncharged-gluon propagator in the MA gauge using the lattice QCD, and find that\nthe effective mass $m_{ch} \\simeq 0.9 {\\rm GeV}$ of the charged gluon is\ninduced by the MA gauge fixing. In the MA gauge, there appears the macroscopic\nnetwork of the monopole world-line covering the whole system, which would be\nidentified as monopole condensation at a large scale. To prove monopole\ncondensation in the field-theoretical manner, we derive the inter-monopole\npotential from the dual Wilson loop in the monopole part of QCD, which carries\nthe nonperturbative QCD aspects, in the MA gauge. The dual gluon mass is\nevaluated as $m_B \\simeq $0.5GeV in the monopole part in the infrared region,\nwhich is the evidence of the dual Higgs mechanism by monopole condensation.", "category": "hep-lat" }, { "text": "The lattice Schwinger model as a discrete sum of filled Wilson loops: Using techniques from hopping expansion we identically map the lattice\nSchwinger model with Wilson fermions to a model of oriented loops on the\nlattice. This is done by first computing the explicit form of the fermion\ndeterminant in the external field. Subsequent integration of the gauge fields\nrenders a sum over all loop configurations with simple Gaussian weights\ndepending on the number of plaquettes enclosed by the loops. In our new\nrepresentation vacuum expectation values of local fermionic operators (scalars,\nvectors) can be computed by simply counting the loop flow through the sites\n(links) supporting the scalars (vectors). The strong coupling limit, possible\napplications of our methods to 4-D models and the introduction of a chemical\npotential are discussed.", "category": "hep-lat" }, { "text": "Toward the excited isoscalar meson spectrum from lattice QCD: We report on the extraction of an excited spectrum of isoscalar mesons using\nlattice QCD. Calculations on several lattice volumes are performed with a range\nof light quark masses corresponding to pion masses down to about 400 MeV. The\ndistillation method enables us to evaluate the required disconnected\ncontributions with high statistical precision for a large number of meson\ninterpolating fields. We find relatively little mixing between light and\nstrange in most JPC channels; one notable exception is the pseudoscalar sector\nwhere the approximate SU(3)F octet, singlet structure of the {\\eta}, {\\eta}' is\nreproduced. We extract exotic JPC states, identified as hybrid mesons in which\nan excited gluonic field is coupled to a color-octet qqbar pair, along with\nnon-exotic hybrid mesons embedded in a qqbar-like spectrum.", "category": "hep-lat" }, { "text": "The finite temperature QCD using 2+1 flavors of domain wall fermions at\n N_t = 8: We study the region of the QCD phase transition using 2+1 flavors of domain\nwall fermions (DWF) and a $16^3 \\times 8$ lattice volume with a fifth dimension\nof $L_s = 32$. The disconnected light quark chiral susceptibility, quark number\nsusceptibility and the Polyakov loop suggest a chiral and deconfining crossover\ntransition lying between 155 and 185 MeV for our choice of quark mass and\nlattice spacing. In this region the lattice scale deduced from the Sommer\nparameter $r_0$ is $a^{-1} \\approx 1.3$ GeV, the pion mass is $\\approx 300$ MeV\nand the kaon mass is approximately physical. The peak in the chiral\nsusceptibility implies a pseudo critical temperature $T_c = 171(10)(17)$ MeV\nwhere the first error is associated with determining the peak location and the\nsecond with our unphysical light quark mass and non-zero lattice spacing. The\neffects of residual chiral symmetry breaking on the chiral condensate and\ndisconnected chiral susceptibility are studied using several values of the\nvalence $L_s$.", "category": "hep-lat" }, { "text": "Charm quark mass and D-meson decay constants from two-flavour lattice\n QCD: We present a computation of the charm quark's mass and the leptonic D-meson\ndecay constants f_D and f_{D_s} in two-flavour lattice QCD with\nnon-perturbatively O(a) improved Wilson quarks. Our analysis is based on the\nCLS configurations at two lattice spacings (a=0.065 and 0.048 fm, where the\nlattice scale is set by f_K) and pion masses ranging down to ~ 190 MeV at\nL*m_pi > 4, in order to perform controlled continuum and chiral extrapolations\nwith small systematic uncertainties.", "category": "hep-lat" }, { "text": "Thermodynamic Study for Conformal Phase in Large Nf Gauge Theory: We investigate the chiral phase transition at finite temperature (T) in\ncolour SU(3) Quantum Chromodynamics (QCD) with six species of fermions (Nf = 6)\nin the fundamental representation. The simulations have been performed by using\nlattice QCD with improved staggered fermions. The critical couplings (bc) for\nthe chiral phase transition are observed for several temporal extensions Nt,\nand the two-loop asymptotic scaling of the dimensionless ratio Tc/Lambda_L\n(Lambda_L = Lattice Lambda-parameter) is found to be achieved for Nt >= 6.\nFurther, we collect bc at Nf = 0 (quenched), and Nf = 4 at a fixed Nt = 6 as\nwell as Nf = 8 at Nt = 6 and 12, the latter relying on our earlier study. The\nresults are consistent with enhanced fermionic screening at larger Nf. The\nratio Tc/Lambda_L depends very mildly on Nf in the Nf = 0-4 region, begins\nincreasing at Nf = 6, and significantly grows up at Nf = 8, as Nf reaches to\nthe edge of the conformal window. We discuss the interrelation of the results\nwith preconformal dynamics in the light of a functional renormalization group\nanalysis.", "category": "hep-lat" }, { "text": "Wilson Fermions, Random Matrix Theory and the Aoki Phase: The QCD partition function for the Wilson Dirac operator, $D_W$, at nonzero\nlattice spacing $a$ can be expressed in terms of a chiral Lagrangian as a\nsystematic expansion in the quark mass, the momentum and $a^2$. Starting from\nthis chiral Lagrangian we obtain an analytical expression for the spectral\ndensity of $\\gamma_5 (D_W+m)$ in the microscopic domain. It is shown that the\n$\\gamma_5$-Hermiticity of the Dirac operator necessarily leads to a coefficient\nof the $a^2$ term that is consistent with the existence of an Aoki phase. The\ntransition to the Aoki phase is explained, and the interplay of the index of\n$D_W$ and nonzero $a$ is discussed. We formulate a random matrix theory for the\nWilson Dirac operator with index $\\nu$ (which, in the continuum limit, becomes\nequal to the topological charge of gauge field configurations). It is shown by\nan explicit calculation that this random matrix theory reproduces the\n$a^2$-dependence of the chiral Lagrangian in the microscopic domain, and that\nthe sign of the $a^2$-term is directly related to the $\\gamma_5$-Hermiticity of\n$D_W$.", "category": "hep-lat" }, { "text": "Proton and neutron electromagnetic radii and magnetic moments from\n lattice QCD: We present results for the electromagnetic form factors of the proton and\nneutron computed on the $(2 + 1)$-flavor Coordinated Lattice Simulations (CLS)\nensembles including both quark-connected and -disconnected contributions. The\n$Q^2$-, pion-mass, lattice-spacing, and finite-volume dependence of our form\nfactor data is fitted simultaneously to the expressions resulting from\ncovariant chiral perturbation theory including vector mesons amended by models\nfor lattice artefacts. From these fits, we determine the electric and magnetic\nradii and the magnetic moments of the proton and neutron, as well as the Zemach\nradius of the proton. To assess the influence of systematic effects, we average\nover various cuts in the pion mass and the momentum transfer, as well as over\ndifferent models for the lattice-spacing and finite-volume dependence, using\nweights derived from the Akaike Information Criterion (AIC).", "category": "hep-lat" }, { "text": "Glueball spectroscopy in lattice QCD using gradient flow: Removing ultraviolet noise from the gauge fields is necessary for glueball\nspectroscopy in lattice QCD. It is known that the Yang-Mills gradient flow\nmethod is an alternative approach instead of link smearing or link fuzzing in\nvarious aspects. In this work we study the application of the gradient flow\ntechnique to the construction of the extended glueball operators. We examine a\nsimple application of the gradient flow method, which has some problems in\nglueball mass calculations at large flow time because of its nature of\ndiffusion in space-time. To avoid this problem, the spatial links are evolved\nby the ``spatial gradient flow'', that is defined to restrict the diffusion to\nspatial directions only. We test the spatial gradient flow in calculations of\nglueball two-point functions and Wilson loops as a new smearing method, and\nthen discuss its efficiency in comparison with the original gradient flow\nmethod and the conventional method. Furthermore, to demonstrate the feasibility\nof our proposed method, we determine the masses of the three lowest-lying\nglueball states, corresponding to the $0^{++}$, $2^{++}$ and $0^{-+}$\nglueballs, in the continuum limit in the pure Yang-Mills theory.", "category": "hep-lat" }, { "text": "Current status of $\\varepsilon_K$ in lattice QCD: We present the current status of $\\varepsilon_K$ evaluated directly from the\nstandard model using lattice QCD inputs. The lattice QCD inputs include\n$\\hat{B}_K$, $\\xi_0$, $\\xi_2$, $|V_{us}|$, $m_c(m_c)$, and $|V_{cb}|$.\nRecently, FLAG has updated $\\hat{B}_K$, exclusive $|V_{cb}|$ has been updated\nwith new lattice data in the $\\bar{B}\\to D\\ell\\bar{\\nu}$ decay mode, and\nRBC-UKQCD has updated $\\xi_0$ and $\\xi_2$. We find that the standard model\nevaluation of $\\varepsilon_K$ with exclusive $|V_{cb}|$ (lattice QCD inputs) is\n$3.2\\sigma$ lower than the experimental value, while that with inclusive\n$|V_{cb}|$ (heavy quark expansion) shows no tension.", "category": "hep-lat" }, { "text": "Sensitivity of the Polyakov loop to chiral symmetry restoration: In the heavy, static quark mass regime of QCD, the Polyakov loop is well\nknown to be an order parameter of the deconfinement phase transition; however,\nthe sensitivity of the Polyakov loop to the deconfinement of light, dynamical\nquarks is less clear. On the other hand, from the perspective of an effective\nLagrangian written in the vicinity of the chiral transition, the Polyakov loop\nis an energy-like operator and should hence scale as any energy-like operator\nwould. We show here that the Polyakov loop and heavy-quark free energy are\nsensitive to the chiral transition, i.e. their scaling is consistent with\nenergy-like observables in 3-$d$ $O(N)$ universality classes.", "category": "hep-lat" }, { "text": "Numerical Evaluation of a Soliton Pair with Long Range Interaction: Within the model of topological particles (MTP) we determine the interaction\nenergy of monopole pairs, sources and sinks of a Coulombic field. The monopoles\nare represented by topological solitons of finite size and mass, described by a\nfield without any divergences. We fix the soliton centres in numerical\ncalculations at varying distance. Due to the finite size of the solitons we get\ndeviations from the Coulomb potential at distances of a few soliton radii. We\ncompare the numerical results for these deviations with the running of the\ncoupling in perturbative QED.", "category": "hep-lat" }, { "text": "Recent Developments in Dual Lattice Algorithms: We review recent progress in numerical simulations with dually transformed\nSU(2) LGT, starting with a discussion of explicit dual amplitudes and\nalgorithms for SU(2) pure Yang Mills in D=3 and D=4. In the D=3 case, we\ndiscuss results that validate the dual algorithm against conventional\nsimulations. We also review how a local, exact dynamical fermion algorithm can\nnaturally be incorporated into the dual framework. We conclude with an outlook\nfor this technique and a look at some of the current challenges we've\nencountered with this method, specifically critical slowing down and the sign\nproblem.", "category": "hep-lat" }, { "text": "Renormalization Group Therapy: We point out a general problem with the procedures commonly used to obtain\nimproved actions from MCRG decimated configurations. Straightforward\nmeasurement of the couplings from the decimated configurations, by one of the\nknown methods, can result into actions that do not correctly reproduce the\nphysics on the undecimated lattice. This is because the decimated\nconfigurations are generally not representative of the equilibrium\nconfigurations of the assumed form of the effective action at the measured\ncouplings. Curing this involves fine-tuning of the chosen MCRG decimation\nprocedure, which is also dependent on the form assumed for the effective\naction. We illustrate this in decimation studies of the SU(2) LGT using\nSwendsen and Double Smeared Blocking decimation procedures. A single-plaquette\nimproved action involving five group representations and free of this pathology\nis given.", "category": "hep-lat" }, { "text": "Lattice QCD Impact on Determination of the CKM Matrix: We review many lattice QCD calculations that impact the precise determination\nof the CKM matrix. We focus on decay constants and semileptonic form factors of\nboth light ($\\pi$ and K) and heavy-light ($D_{(s)}$ and $B_{(s)}$) mesons.\nImplication of $\\Lambda_b$ form factors will be shown. When combined with\nexperimental results for branching fractions and differential decay rates, the\nabove calculations strongly constrain the first two rows of the CKM matrix. We\ndiscuss a long standing difference between $|V_{ub}|$ and $|V_{cb}|$ as\ndetermined from exclusive or inclusive decays.", "category": "hep-lat" }, { "text": "Confining Classical Configurations: We construct a family of smooth, almost self-dual, non-thermalized SU(2)\ngauge field configurations, and measure the average of the fundamental, adjoint\nand spin $\\frac{3}{2}$ representation Wilson loops on them. We get area law in\nall three cases. We also study thermalised configurations at $\\beta= 2.325$\nafter cooling. The ratio of string tension in the spin j representation over\nthat in the fundamental, stays constant with cooling.", "category": "hep-lat" }, { "text": "A classification of 2-dim Lattice Theory: A unified classification and analysis is presented of two dimensional Dirac\noperators of QCD-like theories in the continuum as well as in a naive lattice\ndiscretization. Thereby we consider the quenched theory in the strong coupling\nlimit. We do not only consider the case of a lattice which has an even number\nof lattice sites in both directions and is thus equivalent to the case of\nstaggered fermions. We also study lattices with one or both directions with an\nodd parity to understand the general mechanism of changing the universality\nclass via a discretization. Furthermore we identify the corresponding random\nmatrix ensembles sharing the global symmetries of these QCD-like theories.\nDespite the Mermin-Wagner-Coleman theorem we find good agreement of lattice\ndata with our random matrix predictions.", "category": "hep-lat" }, { "text": "QCD with domain wall quarks: We present lattice calculations in QCD using a variant of Kaplan fermions\nwhich retain the continuum SU(N)xSU(N) chiral symmetry on the lattice in the\nlimit of an infinite extra dimension. In particular, we show that the pion mass\nand the four quark matrix element related to K_0-K_0-bar mixing have the\nexpected behavior in the chiral limit, even on lattices with modest extent in\nthe extra dimension, e.g. N_s=10.", "category": "hep-lat" }, { "text": "Improved gradient flow for step scaling function and scale setting: The gradient flow renormalized coupling offers a simple and relatively\ninexpensive way to calculate the step scaling function and the lattice scale,\nbut both applications can be hindered by large lattice artifacts. Recently we\nintroduced an empirical non-perturbative improvement that can reduce, even\nremove $\\mathcal{O}(a^2)$ lattice artifacts. The method is easy to implement\nand can be applied to any lattice gauge theory of interest both in step scaling\nstudies and for scale setting. In this talk I will briefly review this\nimprovement method and discuss its application for determining the discrete\n$\\beta$ function of the 8 and 12 flavor SU(3) systems and for improved scale\nsetting in 2+1+1 flavor QCD", "category": "hep-lat" }, { "text": "Radiative transitions in charmonium from $N_f=2$ twisted mass lattice\n QCD: We present a study for charmonium radiative transitions:\n$J/\\psi\\rightarrow\\eta_c\\gamma$, $\\chi_{c0}\\rightarrow J/\\Psi\\gamma$ and\n$h_c\\rightarrow\\eta_c\\gamma$ using $N_f=2$ twisted mass lattice QCD gauge\nconfigurations. The single-quark vector form factors for $\\eta_c$ and\n$\\chi_{c0}$ are also determined. The simulation is performed at a lattice\nspacing of $a= 0.06666$ fm and the lattice size is $32^3\\times 64$. After\nextrapolation of lattice data at nonzero $Q^2$ to 0, we compare our results\nwith previous quenched lattice results and the available experimental values.", "category": "hep-lat" }, { "text": "Warped Domain Wall Fermions: We consider Kaplan's domain wall fermions in the presence of an Anti-de\nSitter (AdS) background in the extra dimension. Just as in the flat space case,\nin a completely vector-like gauge theory defined after discretizing this extra\ndimension, the spectrum contains a very light charged fermion whose chiral\ncomponents are localized at the ends of the extra dimensional interval. The\ncomponent on the IR boundary of the AdS space can be given a large mass by\ncoupling it to a neutral fermion via the Higgs mechanism. In this theory, gauge\ninvariance can be restored either by taking the limit of infinite proper length\nof the extra dimension or by reducing the AdS curvature radius towards zero. In\nthe latter case, the Kaluza-Klein modes stay heavy and the resulting classical\ntheory approaches a chiral gauge theory, as we verify numerically. Potential\ndifficulties for this approach could arise from the coupling of the\nlongitudinal mode of the light gauge boson, which has to be treated\nnon-perturbatively.", "category": "hep-lat" }, { "text": "Rigidity and percolation of center vortices: Effective action of center vortices in SU(2) lattice gauge theory is\ninvestigated by studying the correlation between the action density on their\nworldsheets and their geometric properties. It turns out that center vortices\nare rigid, however, their dynamics is more complicated than that of rigid\nrandom surfaces, since some coupling constants have nonstandard scaling\ndimensions. As a result, the properties of center vortices are almost\ncompletely determined by curvature-dependent effects. This, in turn, provides a\nqualitative explanation of vortex percolation.", "category": "hep-lat" }, { "text": "Study of intermediate states in the inclusive semileptonic $B\n \\rightarrow X_c l \u03bd$ decay structure function: We analyze the inclusive semileptonic $B \\to X_c \\ell\\nu$ structure functions\nin 2+1-flavor lattice QCD. The M\\\"obius domain-wall fermion action is used for\nlight, strange, charm and bottom quarks. The structure function receives\ncontributions from various exclusive modes, including the dominant S-wave\nstates $D^{(*)}_s$ as well as the P-wave states $D_s^{**}$. We can identify\nthem in the lattice data, from which we put some constraints on the $B_s \\to\nD_s^{**}\\ell\\nu$ form factors.", "category": "hep-lat" }, { "text": "Excited States of U(1)$_{2+1}$ Lattice Gauge Theory from Monte Carlo\n Hamiltonian: We address an old problem in lattice gauge theory - the computation of the\nspectrum and wave functions of excited states. Our method is based on the\nHamiltonian formulation of lattice gauge theory. As strategy, we propose to\nconstruct a stochastic basis of Bargmann link states, drawn from a physical\nprobability density distribution. Then we compute transition amplitudes between\nstochastic basis states. From a matrix of transition elements we extract energy\nspectra and wave functions. We apply this method to U(1)$_{2+1}$ lattice gauge\ntheory. We test the method by computing the energy spectrum, wave functions and\nthermodynamical functions of the electric Hamiltonian of this theory and\ncompare them with analytical results. We observe a reasonable scaling of\nenergies and wave functions in the variable of time. We also present first\nresults on a small lattice for the full Hamiltonian including the magnetic\nterm.", "category": "hep-lat" }, { "text": "Hadron Spectrum and Matrix Elements in QCD with Dynamical Wilson\n Fermions at 6/g^2=5.3: We present results of a lattice simulation of quantum chromodynamics with two\ndegenerate flavors of dynamic Wilson fermions at $6/g^2=5.3$ at each of two\ndynamical fermion hopping parameters, $\\kappa=0.1670$ and 0.1675, corresponding\nto pion masses in lattice units of about 0.45 and 0.31. The simulations include\nthree other values of valence quark mass, in addition to the dynamical quarks.\nWe present calculations of masses and of the decay constants of vector mesons\nand of pseudoscalars, including the D-meson decay constant. The effects of sea\nquarks on matrix elements and spectroscopy are small.", "category": "hep-lat" }, { "text": "Topological Fluctuations in Dense Matter with Two Colors: We study the topological charge fluctuations of an SU(2) lattice gauge theory\ncontaining both N_f=2 and 4 flavors of Wilson fermion, at low temperature with\nnon-zero chemical potential $\\mu$. The topological susceptibility, chi_T, is\nused to characterize differing physical regimes as mu is varied between the\nonset of matter at mu_o and and color deconfinement at mu_d. Suppression of\ninstantons by matter via Debye screening is also investigated, revealing\neffects not captured by perturbative predictions. In particular, the breaking\nof scale invariance leads to the mean instanton size rho becoming mu-dependent\nin the regime between onset and deconfinement, with a scaling rho~1/mu^2 over\nthe range mu_o 0.5 \\, \\text{fm}$ the system essentially corresponds to a pair of $B$ mesons.\nFor the meson-meson to diquark-antidiquark ratio of the tetraquark we obtain\naround $58\\%/42\\%$.", "category": "hep-lat" }, { "text": "Numerical Study of Dense Adjoint Matter in Two Color QCD: We identify the global symmetries of SU(2) lattice gauge theory with N\nflavors of staggered fermion in the presence of a quark chemical potential mu,\nfor fermions in both fundamental and adjoint representations, and anticipate\nlikely patterns of symmetry breaking at both low and high densities. Results\nfrom numerical simulations of the model with N=1 adjoint flavor on a 4^3x8\nlattice are presented, using both hybrid Monte Carlo and Two-Step Multi-Boson\nalgorithms. It is shown that the sign of the fermion determinant starts to\nfluctuate once the model enters a phase with non-zero baryon charge density.\nHMC simulations are not ergodic in this regime, but TSMB simulations retain\nergodicity even in the dense phase, and in addition appear to show superior\ndecorrelation. The HMC results for the equation of state and the pion mass show\ngood quantitative agreement with the predictions of chiral perturbation theory,\nwhich should hold only for N>=2. The TSMB results incorporating the sign of the\ndeterminant support a delayed onset transition, consistent with the pattern of\nsymmetry breaking expected for N=1.", "category": "hep-lat" }, { "text": "Meson screening masses at finite temperature with Highly Improved\n Staggered Quarks: We report on the first study of the screening properties of the mesonic\nexcitations with strange ($s$) and charm ($c$) quarks, specifically the ground\nstates of the pseudo-scalar and vector meson excitations for the $\\bar{s}s$,\n$\\bar{s}c$ and $\\bar{c}c$ flavor combinations, using the Highly Improved\nStaggered Quark action with dynamical physical strange quark and\nnearly-physical up and down quarks. By comparing with their respective vacuum\nmeson masses and by investigating the influence of the changing temporal\nboundary conditions of the valence quarks we study the thermal modifications of\nthese mesonic excitations. While the $\\bar{s}s$ states show significant\nmodifications even below the chiral crossover temperature $T_c$, the\nmodifications of the open-charm and charmonium like states become visible only\nfor temperatures $T\\gtrsim T_c$ and $T\\gtrsim1.2T_c$, respectively.", "category": "hep-lat" }, { "text": "The pion quasiparticle in the low-temperature phase of QCD: We investigate the properties of the pion quasiparticle in the\nlow-temperature phase of two-flavor QCD on the lattice with support from chiral\neffective theory. We find that the pion quasiparticle mass is significantly\nreduced compared to its value in the vacuum, in contrast to the static\nscreening mass, which increases with temperature. By a simple argument, the two\nmasses are expected to determine the quasiparticle dispersion relation near the\nchiral limit. Analyzing two-point functions of the axial charge density at\nnon-vanishing spatial momentum, we find that the predicted dispersion relation\nand the residue of the pion pole are simultaneously consistent with the lattice\ndata at low momentum. The test, based on fits to the correlation functions, is\nconfirmed by a second analysis using the Backus-Gilbert method.", "category": "hep-lat" }, { "text": "Matrix product states for gauge field theories: The matrix product state formalism is used to simulate Hamiltonian lattice\ngauge theories. To this end, we define matrix product state manifolds which are\nmanifestly gauge invariant. As an application, we study 1+1 dimensional one\nflavour quantum electrodynamics, also known as the massive Schwinger model, and\nare able to determine very accurately the ground state properties and\nelementary one-particle excitations in the continuum limit. In particular, a\nnovel particle excitation in the form of a heavy vector boson is uncovered,\ncompatible with the strong coupling expansion in the continuum. We also study\nnon-equilibrium dynamics by simulating the real-time evolution of the system\ninduced by a quench in the form of a uniform background electric field.", "category": "hep-lat" }, { "text": "Comparison of Improved and Unimproved Quenched Hadron Spectroscopy: We make a comparison between our quenched-hadron-spectroscopy results for the\nnon-perturbatively-improved Wilson action and the corresponding unimproved\ncase, at beta=6.2 on the same set of gauge configurations. Within our\nstatistics, we find a sizeable improvement for the baryon spectrum and for the\ndetermination of the strange-quark mass.", "category": "hep-lat" }, { "text": "Direct detection of metal-insulator phase transitions using the modified\n Backus-Gilbert method: The detection of the (semi)metal-insulator phase transition can be extremely\ndifficult if the local order parameter which characterizes the ordered phase is\nunknown.In some cases, it is even impossible to define a local order parameter:\nthe most prominent example of such system is the spin liquid state. This state\nwas proposed to exist in theHubbard model on the hexagonal lattice in a region\nbetween the semimetal phase and the antiferromagnetic insulator phase. The\nexistence of this phase has been the subject of a long debate. In order to\ndetect these exotic phases we must use alternative methods to those used for\nmore familiar examples of spontaneous symmetry breaking. We have modified the\nBackus-Gilbert method of analytic continuation which was previously used in the\ncalculation of the pion quasiparticle mass in lattice QCD. The modification of\nthe method consists of the introduction of the Tikhonov regularization scheme\nwhich was used to treat the ill-conditioned kernel. This modified\nBackus-Gilbert method is applied to the Euclidean propagators in momentum space\ncalculated using the hybridMonte Carlo algorithm. In this way, it is possible\nto reconstruct the full dispersion relation and to estimate the mass gap, which\nis a direct signal of the transition to the insulating state. We demonstrate\nthe utility of this method in our calculations for the Hubbard model on the\nhexagonal lattice. We also apply the method to the metal-insulator phase\ntransition in the Hubbard-Coulomb model on the square lattice.", "category": "hep-lat" }, { "text": "Cluster Percolation and Critical Behaviour in Spin Models and SU(N)\n Gauge Theories: The critical behaviour of several spin models can be simply described as\npercolation of some suitably defined clusters, or droplets: the onset of the\ngeometrical transition coincides with the critical point and the percolation\nexponents are equal to the thermal exponents. It is still unknown whether,\ngiven a model, one can define at all the droplets. In the cases where this is\npossible, the droplet definition depends in general on the specific model at\nstudy and can be quite involved. We propose here a simple general definition\nfor the droplets: they are clusters obtained by joining nearest-neighbour spins\nof the same sign with some bond probability p_B, which is the minimal\nprobability that still allows the existence of a percolating cluster at the\ncritical temperature T_c. By means of lattice Monte Carlo simulations we find\nthat this definition indeed satisfies the conditions required for the droplets,\nfor many classical spin models, discrete and continuous, both in two and in\nthree dimensions. In particular, our prescription allows to describe exactly\nthe confinement-deconfinement transition of SU(N) gauge theories as Polyakov\nloop percolation.", "category": "hep-lat" }, { "text": "Nucleon Properties at Finite Volume: the Epsilon Prime Regime: We study the properties of the nucleon in highly asymmetric volumes where the\nspatial dimensions are small but the time dimension is large in comparison to\nthe inverse pion mass. To facilitate power-counting at the level of Feynman\ndiagrams, we introduce $\\epsilon^\\prime$-power-counting which is a special case\nof Leutwyler's $\\delta$-power-counting. Pion zero-modes enter the\n$\\epsilon^\\prime$-counting perturbatively, in contrast to both the $\\epsilon$-\nand $\\delta$-power-countings, since $m_q < q\\bar{q}> V$ remains large. However,\nthese modes are enhanced over those with non-zero momenta and enter at lower\norders in the $\\epsilon^\\prime$-expansion than they would in large volume\nchiral perturbation theory. We discuss an application of\n$\\epsilon^\\prime$-counting by determining the nucleon mass, magnetic moment and\naxial matrix element at the first nontrivial order in the\n$\\epsilon^\\prime$-expansion.", "category": "hep-lat" }, { "text": "Hadron form factors using density-density correlators: Gauge invariant density-density correlators yield detailed information on\nhadron structure. Hadron deformation and form factors can be extracted for\nmomentum transfers up to about 6 GeV$^2$. We use stochastic techniques and\ndilution to compute the all to all propagator required for the exact evaluation\nof density-density correlators. We present first results for the pion form\nfactor.", "category": "hep-lat" }, { "text": "Proton momentum and angular momentum decompositions with overlap\n fermions: We present a calculation of the proton momentum and angular momentum\ndecompositions using overlap fermions on a $2+1$-flavor RBC/UKQCD domain-wall\nlattice at 0.143 fm with a pion mass of 171 MeV which is close to the physical\none. A complete determination of the momentum and angular momentum fractions\ncarried by up, down, strange and glue inside the proton has been done with\nvalence pion masses varying from 171 to 391 MeV. We have utilized fast Fourier\ntransform on the stochastic-sandwich method for connected-insertion parts and\nthe cluster-decomposition error reduction technique for disconnected-insertion\nparts has been used to reduce statistical errors. The full nonperturbative\nrenormalization and mixing between the quark and glue operators are carried\nout. The final results are normalized with the momentum and angular momentum\nsum rules and reported at the physical valence pion mass at ${\\overline{\\rm\n{MS}}}\\, (\\mu = 2\\ {\\rm{GeV}})$. The renormalized momentum fractions for the\nquarks and glue are $\\langle x \\rangle^q = 0.491(20)(23)$ and $\\langle x\n\\rangle^g = 0.509(20)(23)$, respectively, and the renormalized total angular\nmomentum fractions for quarks and glue are $2 J^q = 0.539(22)(44)$ and $2 J^g =\n0.461(22)(44)$, respectively. The quark spin fraction is $\\Sigma =\n0.405(25)(37)$ from our previous work and the quark orbital angular momentum\nfraction is deduced from $2 L^q = 2 J^q - \\Sigma$ to be $0.134(22)(44)$.", "category": "hep-lat" }, { "text": "Improved determination of $B_K$ with staggered quarks: We present results for the kaon mixing parameter $B_K$ obtained using\nimproved staggered fermions on a much enlarged set of MILC asqtad lattices.\nCompared to our previous publication, which was based largely on a single\nensemble at each of the three lattice spacings $a\\approx 0.09\\;$fm, $0.06\\;$fm\nand $0.045\\;$fm, we have added seven new fine and four new superfine ensembles,\nwith a range of values of the light and strange sea-quark masses. We have also\nincreased the number of measurements on one of the original ensembles. This\nallows us to do controlled extrapolations in the light and strange sea-quark\nmasses, which we do simultaneously with the continuum extrapolation. This\nreduces the extrapolation error and improves the reliability of our error\nestimates. Our final result is $\\hat{B}_K = 0.7379 \\pm 0.0047 (\\text{stat}) \\pm\n0.0365 (\\text{sys})$.", "category": "hep-lat" }, { "text": "The spectrum of lattice QCD with staggered fermions at strong coupling: Using 4 flavors of staggered fermions at infinite gauge coupling, we compare\nvarious analytic results for the hadron spectrum with exact Monte Carlo\nsimulations. Agreement with Ref. \\cite{Martin_etal} is very good, at the level\nof a few percent.\n Our results give credence to a discrepancy between the baryon mass and the\ncritical chemical potential, for which baryons fill the lattice at zero\ntemperature and infinite gauge coupling. Independent determinations of the\nlatter set it at about 30% less than the baryon mass. One possible explanation\nis that the nuclear attraction becomes strong at infinite gauge coupling.", "category": "hep-lat" }, { "text": "Twist free energy and critical behavior of 3D U(1) LGT at finite\n temperature: The twist free energy is computed in the Villain formulation of the 3D U(1)\nlattice gauge theory at finite temperature. This enables us to obtain\nrenormalization group equations describing a critical behavior of the model in\nthe vicinity of the deconfinement phase transition. These equations are used to\ncheck the validity of the Svetitsky-Yaffe conjecture regarding the critical\nbehavior of the lattice U(1) model. In particular, we calculate the two-point\ncorrelation function of the Polyakov loops and determine some critical indices.", "category": "hep-lat" }, { "text": "Gauge-invariant nonlocal quark condensates in QCD: We study, by numerical simulations on a lattice, the behaviour of the\ngauge-invariant nonlocal quark condensates in the QCD vacuum both in the\nquenched approximation and with four flavours of dynamical staggered fermions.\nThe correlation length of the condensate is determined to be roughly twice as\nbig as in the case of the gluon field strength correlators.", "category": "hep-lat" }, { "text": "The phase diagram of the three-dimensional Z2 gauge Higgs system at zero\n and finite temperature: We study the effect of adding a matter field to the Z2 gauge model in three\ndimensions at zero and finite temperature. Up to a given value of the parameter\nregulating the coupling, the matter field produces a slight shift of the\ntransition line without changing the universality class of the pure gauge\ntheory, as seen by finite size scaling analysis or by comparison, in the finite\ntemperature case, to exact formulas of conformal field theory. At zero\ntemperature the critical line turns into a first-order transition. The fate of\nthis kind of transition in the finite temperature case is discussed.", "category": "hep-lat" }, { "text": "Static quark-antiquark potential in the quark-gluon plasma from lattice\n QCD: We present a state-of-the-art determination of the complex valued static\nquark-antiquark potential at phenomenologically relevant temperatures around\nthe deconfinement phase transition. Its values are obtained from\nnon-perturbative lattice QCD simulations using spectral functions extracted via\na novel Bayesian inference prescription. We find that the real part, both in a\ngluonic medium as well as in realistic QCD with light $u$, $d$ and $s$ quarks,\nlies close to the color singlet free energies in Coulomb gauge and shows Debye\nscreening above the (pseudo) critical temperature $T_c$. The imaginary part is\nestimated in the gluonic medium, where we find that it is of the same order of\nmagnitude as in hard-thermal loop resummed perturbation theory in the\ndeconfined phase.", "category": "hep-lat" }, { "text": "Numerical study of chiral magnetic effect in quenched SU(2) lattice\n gauge theory: A possible experimental observation of the chiral magnetic effect in heavy\nion collisions at RHIC was recently reported by the STAR Collaboration. We\nstudy signatures of this effect in SU(2) lattice gluodynamics with the chirally\ninvariant Dirac operator. We find that at zero temperature the local\nfluctuations of an electric current of quarks and chirality fluctuations\nincrease with external Abelian magnetic field. The external magnetic field\nleads to spatial separation of the quark's electric charges. The separation\nincreases with the strength of the magnetic field. As temperature gets higher\nthe dependence of these quantities on the strength of the magnetic field\nbecomes weaker. In the deconfinement phase the local fluctuations of the chiral\ndensity and of the spatial components of the quarks electric current are large\nand are almost independent on the external magnetic field. The local\nfluctuations of the electric charge density decrease with the strength of the\nmagnetic field in this phase.", "category": "hep-lat" }, { "text": "On isospin breaking in $\u03c4$ decays for $(g-2)_\u03bc$ from Lattice QCD: Hadronic spectral functions of $\\tau$ decays have been used in the past to\nprovide an alternative determination of the LO Hadronic Vacuum Polarization\nrelevant for the (g-2) of the muon. Following recent developments and results\nin Lattice QCD+QED calculations, we explore the possibility of studying the\nisospin breaking corrections of $\\tau$ spectral functions for this prediction.\nWe present preliminary results at physical pion mass based on Domain Wall\nFermion ensembles generated by the RBC/UKQCD collaboration.", "category": "hep-lat" }, { "text": "N=2 Wess-Zumino model on the d=2 Euclidean lattice: We examine the N=2 Wess-Zumino model defined on the $d=2$ Euclidean lattice\nin connection with a restoration of the Leibniz rule in the limit $a\\to0$ in\nperturbatively finite theory. We are interested in the difference between the\nWilson and Ginsparg-Wilson fermions and in the effects of extra interactions\nintroduced by an analysis of Nicolai mapping. As for the Wilson fermion, it\ninduces a linear divergence to individual tadpole diagrams in the limit\n$a\\to0$, which is absent in the Ginsparg-Wilson fermion. This divergence\nsuggests that a careful choice of lattice regularization is required in a\nreliable numerical simulation. As for the effects of the extra couplings\nintroduced by an analysis of Nicolai mapping, the extra couplings do not\ncompletely remedy the supersymmetry breaking in correlation functions induced\nby the failure of the Leibniz rule in perturbation theory, though those\ncouplings ensure the vanishing of vacuum energy arising from disconnected\ndiagrams. Supersymmetry in correlation functions is recovered in the limit\n$a\\to 0$ {\\em with or without} those extra couplings. In the context of lattice\ntheory, it may be properly said that supersymmetry does not improve ultraviolet\nproperties but rather it is well accommodated in theories with good ultraviolet\nproperties.", "category": "hep-lat" }, { "text": "Scaling Properties of the Probability Distribution of Lattice Gribov\n Copies: We study the problem of the Landau gauge fixing in the case of the SU(2)\nlattice gauge theory. We show that the probability to find a lattice Gribov\ncopy increases considerably when the physical size of the lattice exceeds some\ncritical value $\\approx2.75/\\sqrt{\\sigma}$, almost independent of the lattice\nspacing. The impact of the choice of the copy on Green functions is presented.\nWe confirm that the ghost propagator depends on the choice of the copy, this\ndependence decreasing for increasing volumes above the critical one. The gluon\npropagator as well as the gluonic three-point functions are insensitive to\nchoice of the copy (within present statistical errors). Finally we show that\ngauge copies which have the same value of the minimisation functional ($\\int\nd^4x (A^a_\\mu)^2$) are equivalent, up to a global gauge transformation, and\nyield the same Green functions.", "category": "hep-lat" }, { "text": "Lattice-QCD Determination of the Hyperon Axial Couplings in the\n Continuum Limit: We present the first continuum extrapolation of the hyperon octet axial\ncouplings ($g_{\\Sigma \\Sigma}$ and $g_{\\Xi \\Xi}$) from $N_f=2+1+1$ lattice QCD.\nThese couplings are important parameters in the low-energy effective field\ntheory description of the octet baryons and fundamental to the nonleptonic\ndecays of hyperons and to hyperon-hyperon and hyperon-nucleon scattering with\napplication to neutron stars. We use clover lattice fermion action for the\nvalence quarks with sea quarks coming from configurations of $N_f=2+1+1$ highly\nimproved staggered quarks (HISQ) generated by MILC Collaboration. Our work\nincludes the first calculation of $g_{\\Sigma \\Sigma}$ and $g_{\\Xi \\Xi}$\ndirectly at the physical pion mass on the lattice, and a full account of\nsystematic uncertainty, including excited-state contamination, finite-volume\neffects and continuum extrapolation, all addressed for the first time. We find\nthe continuum-limit hyperon coupling constants to be $g_{\\Sigma\n\\Sigma}=0.4455(55)_\\text{stat}(65)_\\text{sys}$ and $g_{\\Xi \\Xi}\n=-0.2703(47)_\\text{stat}(13)_\\text{sys}$, which correspond to low-energy\nconstants of $D = 0.708(10)_\\text{stat}(6)_\\text{sys}$ and $F =\n0.438(7)_\\text{stat}(6)_\\text{sys}$. The corresponding SU(3) symmetry breaking\nis 9\\% which is about a factor of 2 smaller than the earlier lattice estimate.", "category": "hep-lat" }, { "text": "Wilson fermions with imaginary chemical potential: We study the phase structure of imaginary chemical potential.\n We calculate the Polyakov loop using clover-improved Wilson action and\nrenormalization improved gauge action. We obtain a two-state signals indicating\nthe first order phase transition for $\\beta = 1.9, \\mu_I = 0.2618,\n\\kappa=0.1388$ on $8^3\\times 4$ lattice volume We also present a result of the\nmatrix reduction formula for the Wilson fermion.", "category": "hep-lat" }, { "text": "Light Meson Distribution Amplitudes: We calculated the first two moments of the light-cone distribution amplitudes\nfor the pseudoscalar mesons ($\\pi$ and $K$) and the longitudinally polarised\nvector mesons ($\\rho$, $K^*$ and $\\phi$) as part of the UKQCD and RBC\ncollaborations' $N_f=2+1$ domain-wall fermion phenomenology programme. These\nquantities were obtained with a good precision and, in particular, the expected\neffects of $SU(3)$-flavour symmetry breaking were observed. Operators were\nrenormalised non-perturbatively and extrapolations to the physical point were\nmade, guided by leading order chiral perturbation theory. The main results\npresented are for two volumes, $16^3\\times 32$ and $24^3\\times 64$, with a\ncommon lattice spacing. Preliminary results for a lattice with a finer lattice\nspacing, $32^3\\times64$, are discussed and a first look is taken at the use of\ntwisted boundary conditions to extract distribution amplitudes.", "category": "hep-lat" }, { "text": "Wilson fermions with chirally twisted mass: Lattice formulations of QCD with Wilson fermions and a chirally twisted quark\nmass matrix provide an attractive framework for non-perturbative numerical\nstudies. Owing to reparameterization invariance, the limiting continuum theory\nis just QCD. No spurious quark zero modes, which are responsible for the\nproblem with exceptional configurations, can occur at finite values of the\nquark mass. Moreover, the details of the lattice formulation can be adjusted so\nas to simplify the renormalization and the O($a$) improvement of several\nquantities of phenomenological relevance. The first exploratory studies in the\nquenched approximation yield very encouraging results.", "category": "hep-lat" }, { "text": "Scattering of two and three physical pions at maximal isospin from\n lattice QCD: We present the first direct $N_f=2$ lattice QCD computation of two- and\nthree-$\\pi^+$ scattering quantities that includes an ensemble at the physical\npoint. We study the quark mass dependence of the two-pion phase shift, and the\nthree-particle interaction parameters. We also compare to phenomenology and\nchiral perturbation theory (ChPT). In the two-particle sector, we observe good\nagreement to the phenomenological fits in $s$- and $d$-wave, and obtain $M_\\pi\na_0 = -0.0481(86)$ at the physical point from a direct computation. In the\nthree-particle sector, we observe reasonable agreement at threshold to the\nleading order chiral expansion, i.e.\\@ a mildly attractive three-particle\ncontact term. In contrast, we observe that the energy-dependent part of the\nthree-particle quasilocal scattering quantity is not well described by leading\norder ChPT.", "category": "hep-lat" }, { "text": "Non-perturbative renormalization of tensor currents: strategy and\n results for $N_f = 0$ and $N_f = 2$ QCD: Tensor currents are the only quark bilinear operators lacking a\nnon-perturbative determination of their renormalisation group (RG) running\nbetween hadronic and electroweak scales. We develop the setup to carry out the\ncomputation in lattice QCD via standard recursive finite-size scaling\ntechniques, and provide results for the RG running of tensor currents in $N_f =\n0$ and $N_f = 2$ QCD in the continuum for various Schr\u007f\\\"odinger Functional\nschemes. The matching factors between bare and renormalisation group invariant\ncurrents are also determined for a range of values of the lattice spacing\nrelevant for large-volume simulations, thus enabling a fully non-perturbative\nrenormalization of physical amplitudes mediated by tensor currents.", "category": "hep-lat" }, { "text": "Gap in the Dirac spectrum and quark propagator symmetries in lattice QCD: Recent studies on lattice QCD have shown the emergence of large symmetries at\nhigh temperature. This includes not only the restoration $SU(n_F)_L \\times\nSU(n_F)_R$, but also the effective emergence of an unexpected symmetry group,\nnamely $SU(2)_{CS}$, which contains $U(1)_A$ as subgroup. At the same time, at\nhigh $T$, a gap in Dirac spectrum appears. As it is argued in several works of\n\\textit{L. Glozman et al.}, there should be a connection between a gap in the\nDirac spectrum and the presence of $SU(2)_{CS}$.In this paper, we analyze\nwhether the quark propagator can be invariant under $SU(n_F)_L \\times\nSU(n_F)_R$ and $SU(2)_{CS}$ transformations, in case of a gap in the Dirac\nspectrum, and consequently the invariance of hadron correlators, giving the\ncondition for a quark propagator to be invariant under $SU(2)_{CS}$.", "category": "hep-lat" }, { "text": "\u0394S=2 and \u0394C=2 bag parameters in the SM and beyond from\n Nf=2+1+1 twisted-mass LQCD: We present unquenched lattice QCD results for the matrix elements of\nfour-fermion operators relevant to the description of the neutral K and D\nmixing in the Standard Model and its extensions. We have employed simulations\nwith Nf = 2 + 1 + 1 dynamical sea quarks at three values of the lattice\nspacings in the interval 0.06 - 0.09 fm and pseudoscalar meson masses in the\nrange 210 - 450 MeV. Our results are extrapolated to the continuum limit and to\nthe physical pion mass. Renormalization constants have been determined\nnon-perturbatively in the RI-MOM scheme. In particular, for the Kaon\nbag-parameter, which is relevant for the \\overline{K}^0-K^0 mixing in the\nStandard Model, we obtain B_K^{RGI} = 0.717(24).", "category": "hep-lat" }, { "text": "Algorithms for Lattice QCD with Dynamical Fermions: We consider recent progress in algorithms for generating gauge field\nconfigurations that include the dynamical effects of light fermions. We survey\nwhat has been achieved in recent state-of-the-art computations, and examine the\ntrade-offs between performance and control of systematic errors. We briefly\nreview the use of polynomial and rational approximations in Hybrid Monte Carlo\nalgorithms, and some of the theory of on-shell chiral fermions on the lattice.\nThis provides a theoretical framework within which we compare algorithmic\nalternatives for their implementation; and again we examine the trade-offs\nbetween speed and error control.", "category": "hep-lat" }, { "text": "A Lattice Study of Spectator Effects in Inclusive Decays of B-Mesons: We compute the matrix elements of the operators which contribute to spectator\neffects in inclusive decays of $B$-mesons. The results agree well with\nestimates based on the vacuum saturation (factorization) hypothesis. For the\nratio of lifetimes of charged and neutral mesons we find\n$\\tau(B^-)/\\tau(B_d)=1.03\\pm 0.02\\pm 0.03$, where the first error represents\nthe uncertainty in our evaluation of the matrix elements, and the second is an\nestimate of the uncertainty due to the fact that the Wilson coefficient\nfunctions have only been evaluated at tree-level in perturbation theory. This\nresult is in agreement with the experimental measurement. We also discuss the\nimplications of our results for the semileptonic branching ratio and the charm\nyield.", "category": "hep-lat" }, { "text": "Gauge theory of things alive and universal dynamics: Positing complex adaptive systems made of agents with relations between them\nthat can be composed, it follows that they can be described by gauge theories\nsimilar to elementary particle theory and general relativity. By definition, a\nuniversal dynamics is able to determine the time development of any such system\nwithout need for further specification. The possibilities are limited, but one\nof them - reproduction fork dynamics - describes DNA replication and is the\nbasis of biological life on earth. It is a universal copy machine and a\nrenormalization group fixed point. A universal equation of motion in continuous\ntime is also presented.", "category": "hep-lat" }, { "text": "Nucleon axial form factors using lattice QCD simulations with a physical\n value of the pion mass: We present results on the nucleon axial and induced pseudo-scalar form\nfactors using an ensemble of two degenerate twisted mass clover-improved\nfermions generated at the physical value of the pion mass. We evaluate the\nisovector and the isoscalar, as well as, the strange and the charm axial form\nfactors. The disconnected contributions are evaluated using recently developed\nmethods that include deflation of the lower eigenstates, allowing us to extract\nthe isoscalar, strange and charm axial form factors. We find that the\ndisconnected quark loop contributions are non-zero and particularly large for\nthe induced pseudo-scalar form factor.", "category": "hep-lat" }, { "text": "Large center vortices and confinement in 3D Z(2) gauge theory: We study the role of large clusters of center vortices in producing\nconfinement in 3D Z(2) gauge theory. First, we modify each configuration of a\nMonte Carlo-generated ensemble in the confined phase by removing the largest\ncluster of center vortices, and show that the ensemble thus obtained does not\nconfine. Conversely, we show that removing all of the small clusters of center\nvortices and leaving the largest one only, confinement is preserved, albeit\nwith a string tension significantly smaller than the original one. Remarkably,\nalso the string corrections due to the quantum fluctuations of the confining\nflux tube are preserved by this transformation.", "category": "hep-lat" }, { "text": "The Lefschetz thimble and the sign problem: In this talk I review the proposal to formulate quantum field theories (QFTs)\non a Lefschetz thimble, which was put forward to enable Monte Carlo simulations\nof lattice QFTs affected by sign problem. First I will review the theoretical\njustification of the approach, and comment on some open issues. Then, I will\nreview the algorithms that have been proposed and are being tested to represent\nand simulate a lattice QFT on a Lefschetz thimble. In particular, I will review\nthe lessons from the very first models of QFTs that have been studied with this\napproach.", "category": "hep-lat" }, { "text": "Correlation functions and critical behaviour on fluctuating geometries: We study the two-point correlation function in the model of branched polymers\nand its relation to the critical behaviour of the model. We show that the\ncorrelation function has a universal scaling form in the generic phase with the\nonly scale given by the size of the polymer. We show that the origin of the\nsingularity of the free energy at the critical point is different from that in\nthe standard statistical models. The transition is related to the change of the\ndimensionality of the system.", "category": "hep-lat" }, { "text": "Two topics from lattice NRQCD at non-zero temperature: heavy quark mass\n dependence and S-wave bottomonium states moving in a thermal bath: Using Non-Relativistic QCD (NRQCD), we study heavy quark mass dependence of\nS-wave and P-wave bottomonium correlators for 0.42Tc <= T <= 2.09Tc and study\nspectral functions of S-wave bottomonium states moving in a thermal bath at\nthese temperatures using Maximum Entropy Method with NRQCD kernel. For the\nstudied momentum range, the energy of moving states shows quadratic\nmomentum-dependence and the width of moving states does not show significant\nchanges as the momentum of bottomonium is increased. Also, we find that in\ncorrelator ratios, the temperature effect is larger than the effect caused by\n20% change in the bottom quark mass.", "category": "hep-lat" }, { "text": "On the possibility of the critical behavior of LGT in the area of\n asymptotically large \u03b2: Coupling dependence on lattice spacing and size is estimated analytically at\n\\beta -> \\infty region where for a->0 the critical area is shifted in\naccordance with Callan-Symanzik relation. In considered approximation no trace\nof critical behavior is found in this area.", "category": "hep-lat" }, { "text": "Impact of stout-link smearing in lattice fermion actions: The impact of stout-link smearing in lattice fermion actions is examined\nthrough the consideration of the mass and renormalization functions of the\noverlap quark propagator over a variety of smeared configurations. Up to six\nsweeps of stout-link smearing are investigated. For heavy quark masses, the\nquark propagator is strongly affected by the smearing procedure. For moderate\nmasses, the effect appears to be negligible. A small effect is seen for light\nquark masses, where dynamical mass generation is suppressed through the\nsmearing procedure.", "category": "hep-lat" }, { "text": "Charmonium Potentials at Finite Temperature: The charmonium states at non-zero temperature are studied on anisotropic\nlattices with 2 dynamical quark flavours. Non-local operators are used to\ndetermine the Nambu-Bethe-Salpeter (NBS) wavefunctions via both conventional\nfitting methods and the Maximum Entropy Method. The interquark potential is\ndetermined from the solution of the Schrodinger equation, given the NBS\nwavefunction as input following the HAL QCD method. We observe a temperature\ndependent potential which becomes steeper as the temperature decreases.", "category": "hep-lat" }, { "text": "Quark Propagation in the Instantons of Lattice QCD: We quantitatively examine the extent to which instanton degress of freedom,\ncontained within standard Monte-carlo generated gauge-field configurations, can\nmaintain the characteristic features of the mass and renormalisation functions\nof the non-perturbative quark propagator. We use over-improved stout-link\nsmearing to isolate instanton effects on the lattice. Using a variety of\nmeasures, we illustrate how gauge fields consisting almost solely of\ninstanton-like objects are produced after only 50 sweeps of smearing. We find a\nfull vacuum, with a packing fraction more than three times larger than\nphenomenological models predict. We calculate the overlap quark propagator on\nthese smeared configurations, and find that even at high levels of smearing the\nmajority of the characteristic features of the propagator are reproduced. We\nthus conclude that instantons contained within standard Monte-carlo generated\ngauge-field configurations are the degrees of freedom responsible for the\ndynamical generation of mass observed in lattice QCD.", "category": "hep-lat" }, { "text": "Bottomonium above deconfinement in lattice nonrelativistic QCD: We study the temperature dependence of bottomonium for temperatures in the\nrange $0.4 T_c < T < 2.1 T_c$, using nonrelativistic dynamics for the bottom\nquark and full relativistic lattice QCD simulations for $N_f=2$ light flavors\non a highly anisotropic lattice. We find that the $\\Upsilon$ is insensitive to\nthe temperature in this range, while the $\\chi_b$ propagators show a crossover\nfrom the exponential decay characterizing the hadronic phase to a power-law\nbehaviour consistent with nearly-free dynamics at $T \\simeq 2 T_c$.", "category": "hep-lat" }, { "text": "SU(3) Lattice Gauge Theory in the Fundamental--Adjoint Plane and Scaling\n Along the Wilson Axis: We present further evidence for the bulk nature of the phase transition line\nin the fundamental--adjoint action plane of SU(3) lattice gauge theory.\nComputing the string tension and some glueball masses along the thermal phase\ntransition line of finite temperature systems with $N_t=4$, which was found to\njoin onto the bulk transition line at its endpoint, we find that the ratio\n$\\sqrt{\\sigma} / T_c$ remains approximately constant. However, the mass of the\n$0^{++}$ glueball decreases as the endpoint of the bulk transition line is\napproached, while the other glueball masses appear unchanged. This is\nconsistent with the notion that the bulk transition line ends in a critical\nendpoint, with the continuum limit there being a $\\phi^4$ theory with a\ndiverging correlation length only in the $0^{++}$ channel. We comment on the\nimplications for the scaling behavior along the fundamental or Wilson axis.", "category": "hep-lat" }, { "text": "Calculation of the running coupling in non-Abelian gauge theories from\n Jarzynski's equality: We discuss the theoretical foundations of non-equilibrium Monte Carlo\nsimulations based on Jarzynski's equality and present, as an example of\napplication, the determination of the running coupling in the\nSchr\\\"odinger-functional scheme.", "category": "hep-lat" }, { "text": "P-wave nucleon-pion scattering amplitude in the $\u0394(1232)$ channel\n from lattice QCD: We determine the $\\Delta(1232)$ resonance parameters using lattice QCD and\nthe L\\\"uscher method. The resonance occurs in elastic pion-nucleon scattering\nwith $J^P=3/2^+$ in the isospin $I = 3/2$, $P$-wave channel. Our calculation is\nperformed with $N_f=2+1$ flavors of clover fermions on a lattice with $L\\approx\n2.8$ fm. The pion and nucleon masses are $m_\\pi =255.4(1.6)$ MeV and\n$m_N=1073(5)$ MeV, and the strong decay channel $\\Delta \\rightarrow \\pi N$ is\nfound to be above the threshold. To thoroughly map out the energy-dependence of\nthe nucleon-pion scattering amplitude, we compute the spectra in all relevant\nirreducible representations of the lattice symmetry groups for total momenta up\nto $\\vec{P}=\\frac{2\\pi}{L}(1,1,1)$, including irreps that mix $S$ and $P$\nwaves. We perform global fits of the amplitude parameters to up to 21 energy\nlevels, using a Breit-Wigner model for the $P$-wave phase shift and the\neffective-range expansion for the $S$-wave phase shift. From the location of\nthe pole in the $P$-wave scattering amplitude, we obtain the resonance mass\n$m_\\Delta=1378(7)(9)$ MeV and the coupling $g_{\\Delta\\text{-}\\pi\nN}=23.8(2.7)(0.9)$.", "category": "hep-lat" }, { "text": "Running Gluon Mass from Landau Gauge Lattice QCD Propagator: The interpretation of the Landau gauge lattice gluon propagator as a massive\ntype bosonic propagator is investigated. Three different scenarios are\ndiscussed: i) an infrared constant gluon mass; ii) an ultraviolet constant\ngluon mass; iii) a momentum dependent mass. We find that the infrared data can\nbe associated with a massive propagator up to momenta $\\sim 500$ MeV, with a\nconstant gluon mass of 723(11) MeV, if one excludes the zero momentum gluon\npropagator from the analysis, or 648(7) MeV, if the zero momentum gluon\npropagator is included in the data sets. The ultraviolet lattice data is not\ncompatible with a massive type propagator with a constant mass. The scenario of\na momentum dependent gluon mass gives a decreasing mass with the momentum,\nwhich vanishes in the deep ultraviolet region. Furthermore, we show that the\nfunctional forms used to describe the decoupling like solution of the\nDyson-Schwinger equations are compatible with the lattice data with similar\nmass scales.", "category": "hep-lat" }, { "text": "The S, U and \u0394\u03c1parameters in the Zaragoza proposal for lattice\n chiral gauge fermions: Using the Zaragoza proposal for lattice chiral gauge fermions, the S, U and\n\\Delta\\rho parameters have been calculated at one loop. It is shown that the\ncontinuum values for these quantities can be reproduced without requiring\nexplicit fine tuning of counterterms. Furthermore, fermion fields doubling is\nnot necessary. To the best of our knowledge, the Zaragoza proposal is the only\nscheme which has these properties. A necessary (although not sufficient)\nsymmetry is found to support the calculations. Previous results for some of\nthese parameters in other lattice chiral regularizations are revisited in the\nlight of this symmetry.", "category": "hep-lat" }, { "text": "The chromomagnetic operator on the lattice: We present our study of the renormalization of the chromomagnetic\noperator,O(CM), which appears in the effective Hamiltonian describing Delta S =\n1 transitions in and beyond the Standard Model. We have computed,\nperturbatively to one-loop, the relevant Green's functions with two\n(quark-quark) and three (quark-quark-gluon) external fields, at nonzero quark\nmasses, using both the lattice and dimensional regularizations. The\nperturbative computation on the lattice is carried out using the maximally\ntwisted-mass action for the fermions, while for the gluons we employed the\nSymanzik improved gauge action for different sets of values of the Symanzik\ncoefficients. We have identified all the operators which can possibly mix with\nO(CM), including lower dimensional and non gauge invariant operators, and we\nhave calculated those elements of the mixing matrix which are relevant for the\nrenormalization of O(CM). We have also performed numerical lattice calculations\nto determine non-perturbatively the mixings of the chromomagnetic operator with\nlower dimensional operators, through proper renormalization conditions. For the\nfirst time the 1/a**2-divergent mixing of the chromomagnetic operator with the\nscalar density has been determined non-perturbatively with high precision.\nMoreover, the 1/a-divergent mixing with the pseudoscalar density, due to the\nbreaking of parity within the twisted-mass regularization of QCD, has been\ncalculated non-perturbatively and found to be smaller than its one-loop\nperturbative estimate. The QCD simulations have been carried out using the\ngauge configurations produced by the European Twisted Mass Collaboration with\nNf = 2 + 1 + 1 dynamical quarks, which include in the sea, besides two light\nmass degenerate quarks, also the strange and charm quarks with masses close to\ntheir physical values.", "category": "hep-lat" }, { "text": "General properties of logarithmically divergent one-loop lattice Feynman\n integrals: We prove that logarithmically divergent one-loop lattice Feynman integrals\nhave the general form I(p,a) = f(p)log(aM)+g(p,M) up to terms which vanish for\nlattice spacing a -> 0. Here p denotes collectively the external momenta and M\nis an arbitrary mass scale. The f(p) is shown to be universal and to coincide\nwith the analogous quantity in the corresponding continuum integral\n(regularized, e.g., by momentum cut-off). This is essential for universality of\nthe lattice QCD beta-function and anomalous dimensions of renormalized lattice\noperators at one loop. The result and argument presented here are simplified\nversions of ones given in arXiv:0709.0781. A noteworthy feature of the argument\nhere is that it does not involve Taylor expansion in external momenta, hence\ninfra-red divergences associated with that expansion do not arise.", "category": "hep-lat" }, { "text": "Hadronic Coupling Constants in Lattice QCD: We calculate the hadronic coupling constants $g_{NN\\pi}$ and $g_{\\rho\\pi\\pi}$\nin QCD, including dynamical quarks in the framework of staggered fermions in\nthe lattice approach. For the nucleon--pion coupling we obtain $g_{NN\\pi} =\n13.8 \\pm 5.8$, to be compared with the experimental value $13.13 \\pm 0.07$. The\n$\\rho\\pi\\pi$ coupling has been analysed for two different sets of operators\nwith the averaged result $g_{\\rho\\pi\\pi} = 4.2 \\pm 1.9$ which is to be compared\nwith the experimental value $6.06 \\pm 0.01$.", "category": "hep-lat" }, { "text": "Solution to new sign problems with Hamiltonian Lattice Fermions: We present a solution to the sign problem in a class of particle-hole\nsymmetric Hamiltonian lattice fermion models on bipartite lattices using the\nidea of fermion bags. The solution remains valid when the particle-hole\nsymmetry is broken through a staggered chemical potential term. This solution\nallows, for the first time, simulations of some massless four-fermion models\nwith minimal fermion doubling and with an odd number of fermion flavors using\nultra-local actions. One can thus study a variety of quantum phase transitions\nthat have remained unexplored so far due to sign problems.", "category": "hep-lat" }, { "text": "Convergence of chiral effective field theory: We formulate the expansion for the mass of the nucleon as a function of pion\nmass within chiral perturbation theory using a number of different ultra-violet\nregularisation schemes; including dimensional regularisation and various\nfinite-ranged regulators. Leading and next-to-leading order non-analytic\ncontributions are included through the standard one-loop Feynman graphs. In\naddition to the physical nucleon mass, the expansion is constrained by recent,\nextremely accurate, lattice QCD data obtained with two flavors of dynamical\nquarks. The extent to which different regulators can describe the chiral\nexpansion is examined, while varying the range of quark mass over which the\nexpansions are matched. Renormalised chiral expansion parameters are recovered\nfrom each regularisation prescription and compared. We find that the\nfinite-range regulators produce consistent, model-independent results over a\nwide range of quark mass sufficient to solve the chiral extrapolation problem\nin lattice QCD.", "category": "hep-lat" }, { "text": "Two-Baryon Systems with Twisted Boundary Conditions: We explore the use of twisted boundary conditions in extracting the nucleon\nmass and the binding energy of two-baryon systems, such as the deuteron, from\nLattice QCD calculations. Averaging the results of calculations performed with\nperiodic and anti-periodic boundary conditions imposed upon the light-quark\nfields, or other pair-wise averages, improves the volume dependence of the\ndeuteron binding energy from ~exp(-kappa*L)/L to ~exp(-sqrt(2)kappa*L)/L.\nHowever, a twist angle of pi/2 in each of the spatial directions improves the\nvolume dependence from ~exp(-kappa*L)/L to ~exp(-2kappa*L)/L. Twist averaging\nthe binding energy with a random sampling of twist angles improves the volume\ndependence from ~exp^(-kappa*L)/L to ~exp(-2kappa*L)/L, but with a standard\ndeviation of ~exp(-kappa*L)/L, introducing a signal-to-noise issue in modest\nlattice volumes. Using the experimentally determined phase shifts and mixing\nangles, we determine the expected energies of the deuteron states over a range\nof cubic lattice volumes for a selection of twisted boundary conditions.", "category": "hep-lat" }, { "text": "Chiral Determinant as an Overlap of Two Vacua: The effective action induced by chiral fermions can be written, formally, as\nan overlap of two states. These states are the Fock ground states of\nHamiltonians for fermions in even dimensional space with opposite sign mass\nterms coupled to identical static vector potentials. A perturbative analysis of\nthe overlap in the continuum framework produces the correct anomaly for Abelian\ngauge fields in two dimensions. When a lattice transfer matrix formalism is\napplied in the direction perpendicular to a domain wall on which chiral\nfermions live a lattice version of the overlap is obtained. The real part of\nthe overlap is nonperturbatively defined and previous work indicates that the\nreal part of the vacuum polarization tensor in four dimensions has the correct\ncontinuum limit for a chiral theory. The phase of the overlap represents the\nimaginary part of the chiral action and suffers from ambiguities.", "category": "hep-lat" }, { "text": "Effects of non-perturbatively improved dynamical fermions in UKQCD\n simulations: We present results for QCD with 2 degenerate flavours of quark using a\nnon-perturbatively improved action on a lattice volume of $16^3\\times32$ where\nthe bare gauge coupling and bare dynamical quark mass have been chosen to\nmaintain a fixed physical lattice spacing and volume (1.71 fm). By comparing\nmeasurements from these matched ensembles, including quenched ones, we find\nevidence of dynamical quark effects on the short distance static potential, the\nscalar glueball mass and the topological susceptibility. There is little\nevidence of effects on the light hadron spectrum over the range of quark masses\nstudied ($m_{\\pi}/m_{\\rho}\\geq 0.60$).", "category": "hep-lat" }, { "text": "Solving the left-hand cut problem in lattice QCD: $T_{cc}(3875)^+$ from\n finite volume energy levels: A novel effective-field-theory-based approach is implemented for extracting\ntwo-body scattering information from finite volume energies, serving as an\nalternative to L\\\"uscher's method. By explicitly incorporating one-pion\nexchange, the approach quantitatively accounts for effects related to left-hand\ncuts and range corrections from the longest-range interactions. The method\nutilizes the plane wave basis instead of the conventional partial wave\nexpansion, thereby also naturally including partial wave mixing effects\nresulting from rotational symmetry breaking in a cubic box. Applied to the\nlattice data for $DD^*$ scattering at a pion mass of 280 MeV, it reveals the\nsignificant impact of the one-pion exchange on P-wave and S-wave phase shifts.\nThe pole position of the $T_{cc}(3875)^+$ state, extracted from the\nfinite-volume energy levels while taking into account left-hand cut effects,\nrange corrections, and partial-wave mixing, appears to be consistent with a\nnear-threshold resonance.", "category": "hep-lat" }, { "text": "Schwinger-Keldysh on the lattice: a faster algorithm and its application\n to field theory: A new algorithm is developed allowing the Monte Carlo study of a 1 + 1\ndimensional theory in real time. The main algorithmic development is to avoid\nthe explicit calculation of the Jacobian matrix and its determinant in the\nupdate process. This improvement has a wide applicability and reduces the cost\nof the update in thimble-inspired calculations from O(N^3) to less than O(N^2).\nAs an additional feature, the algorithm leads to improved Monte Carlo\nproposals. We exemplify the use of the algorithm to the real time dynamics of a\nscalar {\\phi}^4 theory with weak and strong couplings.", "category": "hep-lat" }, { "text": "Test for a universal behavior of Dirac eigenvalues in the complex\n Langevin method: We apply the complex Langevin (CL) method to a chiral random matrix theory\n(ChRMT) at non-zero chemical potential and study the nearest neighbor spacing\n(NNS) distribution of the Dirac eigenvalues. The NNS distribution is extracted\nusing an unfolding procedure for the Dirac eigenvalues obtained in the CL\nmethod. For large quark mass, we find that the NNS distribution obeys the\nGinibre ensemble as expected. For small quark mass, the NNS distribution\nfollows the Wigner surmise for correct convergence case, while it follows the\nGinibre ensemble for wrong convergence case. The Wigner surmise is physically\nreasonable from the chemical potential independence of the ChRMT. The Ginibre\nensemble is known to be favored in a phase quenched QCD at finite chemical\npotential. Our result suggests a possibility that the originally universal\nbehavior of the NNS distribution is preserved even in the CL method for correct\nconvergence case.", "category": "hep-lat" }, { "text": "Polyakov loop effects on the phase diagram in strong-coupling lattice\n QCD: We investigate the Polyakov loop effects on the QCD phase diagram by using\nthe strong-coupling (1/g^2) expansion of the lattice QCD (SC-LQCD) with one\nspecies of unrooted staggered quark, including O}(1/g^4) effects. We take\naccount of the effects of Polyakov loop fluctuations in Weiss mean-field\napproximation (MFA), and compare the results with those in the Haar-measure MFA\n(no fluctuation from the mean-field). The Polyakov loops strongly suppress the\nchiral transition temperature in the second-order/crossover region at small\nchemical potential, while they give a minor modification of the first-order\nphase boundary at larger chemical potential. The Polyakov loops also account\nfor a drastic increase of the interaction measure near the chiral phase\ntransition. The chiral and Polyakov loop susceptibilities have their peaks\nclose to each other in the second-order/crossover region. In particular in\nWeiss MFA, there is no indication of the separated deconfinement transition\nboundary from the chiral phase boundary at any chemical potential. We discuss\nthe interplay between the chiral and deconfinement dynamics via the bare quark\nmass dependence of susceptibilities.", "category": "hep-lat" }, { "text": "A lattice regularization of Weyl fermions in a gravitational background: We report on a lattice fermion formulation with a curved domain-wall mass\nterm to nonperturbatively describe fermions in a gravitational background. In\nour previous work in 2022, we showed under the time-reversal symmetry that the\nedge-localized massless Dirac fermion appears on one and two-dimensional\nspherical domain-walls and the spin connection is induced on the lattice in a\nconsistent way with continuum theory. In this work, we extend our study to the\nShamir type curved domain-wall fermions without the time-reversal symmetry. We\nfind in the free fermion case that a single Weyl fermion appears on the edge,\nand feels gravity through the induced spin connection. With a topologically\nnontrivial $U(1)$ gauge potential, however, we find an oppositely chiral zero\nmode at the center where the gauge field is singular.", "category": "hep-lat" }, { "text": "Lattice real-time simulations with learned optimal kernels: We present a simulation strategy for the real-time dynamics of quantum\nfields, inspired by reinforcement learning. It builds on the complex Langevin\napproach, which it amends with system specific prior information, a necessary\nprerequisite to overcome this exceptionally severe sign problem. The\noptimization process underlying our machine learning approach is made possible\nby deploying inherently stable solvers of the complex Langevin stochastic\nprocess and a novel optimality criterion derived from insight into so-called\nboundary terms. This conceptual and technical progress allows us to both\nsignificantly extend the range of real-time simulations in 1+1d scalar field\ntheory beyond the state-of-the-art and to avoid discretization artifacts that\nplagued previous real-time field theory simulations. Limitations of and\npromising future directions are discussed.", "category": "hep-lat" }, { "text": "Double parton distributions in the nucleon from lattice QCD: We evaluate nucleon four-point functions in the framework of lattice QCD in\norder to extract the first Mellin moment of double parton distributions (DPDs)\nin the unpolarized proton. In this first study, we employ an nf = 2 + 1\nensemble with pseudoscalar masses of mpi = 355 MeV and mK = 441 MeV. The\nresults are converted to the scale mu = 2 GeV. Our calculation includes all\nWick contractions, and for almost all of them a good statistical signal is\nobtained. We analyze the dependence of the DPD Mellin moments on the quark\nflavor and the quark polarization. Furthermore, the validity of frequently used\nfactorization assumptions is investigated.", "category": "hep-lat" }, { "text": "Non-relativistic bound states in a finite volume: We derive general results for the mass shift of bound states with angular\nmomentum l >= 1 in a periodic cubic box in two and three spatial dimensions.\nOur results have applications to lattice simulations of hadronic molecules,\nhalo nuclei, and Feshbach molecules. The sign of the mass shift can be related\nto the symmetry properties of the state under consideration. We verify our\nanalytical results with explicit numerical calculations. Moreover, we comment\non the relations connecting the effective range parameter, the binding momentum\nof a given state and the asymptotic normalization coefficient of the\ncorresponding wave function. We give explicit expressions for this relation in\nthe shallow binding limit.", "category": "hep-lat" }, { "text": "Lattice QCD Calculation of Electroweak Box Contributions to Superallowed\n Nuclear and Neutron Beta Decays: We present the first lattice QCD calculation of the universal axial $\\gamma\nW$-box contribution $\\square_{\\gamma W}^{VA}$ to both superallowed nuclear and\nneutron beta decays. This contribution emerges as a significant component\nwithin the theoretical uncertainties surrounding the extraction of $|V_{ud}|$\nfrom superallowed decays. Our calculation is conducted using two domain wall\nfermion ensembles at the physical pion mass. To construct the nucleon 4-point\ncorrelation functions, we employ the random sparsening field technique.\nFurthermore, we incorporate long-distance contributions to the hadronic\nfunction using the infinite-volume reconstruction method. Upon performing the\ncontinuum extrapolation, we arrive at $\\square_{\\gamma\nW}^{VA}=3.65(8)_{\\mathrm{lat}}(1)_{\\mathrm{PT}}\\times10^{-3}$. Consequently,\nthis yields a slightly higher value of\n$|V_{ud}|=0.97386(11)_{\\mathrm{exp.}}(9)_{\\mathrm{RC}}(27)_{\\mathrm{NS}}$,\nreducing the previous $2.1\\sigma$ tension with the CKM unitarity to\n$1.8\\sigma$. Additionally, we calculate the vector $\\gamma W$-box contribution\nto the axial charge $g_A$, denoted as $\\square_{\\gamma W}^{VV}$, and explore\nits potential implications.", "category": "hep-lat" }, { "text": "Phase structure of four flavor QCD in the T \u03bcplane from a new method\n for simulations of lattice gauge theories at non zero baryon density: We review a method for numerical simulations of lattice gauge theories at\nnon-zero baryonic chemical potential we recently proposed. We first report on a\ntest of the method using a solvable model and then present results for the\nphase structure of four flavour QCD. For the first time the region of chemical\npotential up to 1.4 T_C is explored, finding a first order transition line.", "category": "hep-lat" }, { "text": "Light Quark Masses with Dynamical Wilson Fermions: We determine the masses of the light and the strange quarks in the\n$\\bar{MS}$-scheme using our high-statistics lattice simulation of QCD with\ndynamical Wilson fermions. For the light quark mass we find\n$m^{light}_{\\bar{MS}}(2 GeV) = 2.7(2) MeV$, which is lower than in quenched\nsimulations. For the strange quark, in a sea of two dynamical light quarks, we\nobtain $m^{strange}_{\\bar{MS}}(2 GeV) = 140(20) MeV$.", "category": "hep-lat" }, { "text": "Core -- a New Method for Solving Hamiltonian Lattice Systems: The COntractor REnormalization group (CORE) approximation, a new method for\nsolving Hamiltonian lattice systems, is introduced. The approach combines\nvariational and contraction techniques with the real-space renormalization\ngroup approach and is systematically improvable. Since it applies to lattice\nsystems of infinite extent, the method is suitable for studying critical\nphenomena and phase structure; systems with dynamical fermions can also be\ntreated. The method is tested using the 1+1-dimensional Ising model.", "category": "hep-lat" }, { "text": "Phases at finite winding number of an Abelian lattice gauge theory: Pure gauge theories are rather different from theories with pure scalar and\nfermionic matter, especially in terms of the nature of excitations. For\nexample, in scalar and fermionic theories, one can create ultra-local\nexcitations. For a gauge theory, such excitations need to be closed loops that\ndo not violate gauge invariance. In this proceedings, we present a study on the\ncondensation phenomenon associated with the string-like excitations of an\nAbelian lattice gauge theory. These phenomena are studied through numerical\nsimulations of a $U(1)$ quantum link model in 2+1 dimensions in a ladder\ngeometry using matrix product states. In this proceedings, we show the\nexistence of ground states characterized by the presence of such string-like\nexcitations. These are caused due to the condensation of torelons. We also\nstudy the relationship between the properties of the plaquettes in the ground\nstate and the presence of such condensation phenomenon.", "category": "hep-lat" }, { "text": "Quantum tunneling in the real-time path integral by the Lefschetz\n thimble method: Quantum tunneling is mostly discussed in the Euclidean path integral\nformalism using instantons. On the other hand, it is difficult to understand\nquantum tunneling based on the real-time path integral due to its oscillatory\nnature, which causes the notorious sign problem. We show that recent\ndevelopment of the Lefschetz thimble method enables us to investigate this\nissue numerically. In particular, we find that quantum tunneling occurs due to\ncomplex trajectories, which are actually observable experimentally by using the\nso-called weak measurement.", "category": "hep-lat" }, { "text": "Cutoff effects in twisted mass lattice QCD: We present a first numerical study of lattice QCD with O(a) improved Wilson\nquarks and a chirally twisted mass term. Renormalized correlation functions are\nderived from the Schroedinger functional and evaluated in an intermediate\nspace-time volume of size 0.75^3 x 1.5 fm^4. In the quenched approximation\nprecise results are then obtained with a moderate computational effort,\nallowing for a detailed study of the continuum approach. The latter is\ndiscussed in terms of observables which converge to meson masses and decay\nconstants in the limit of large space-time volume. In the O(a) improved theory\nwe find residual cutoff effects to be at the level of a few percent for lattice\nspacings of about 0.1 fm.", "category": "hep-lat" }, { "text": "Excited state baryon spectroscopy from lattice QCD with spin\n identification: Lattice QCD calculations are presented for the spectra of N* excited states\nwith spins up to J = 7/2. Ambiguities of the standard method of spin\nidentification are shown to be overcome by the use of lattice operators that\ntransform according to SU(2) symmetry restricted to the lattice. Such operators\nare labeled by their continuum spins. Overlaps of the operators with the states\nobtained by diagonalizing matrices of correlation functions provide a clear\nlink between continuum spins and lattice states, allowing spins to be\nidentified. Evidence for an approximate realization of rotational symmetry in\nthe N* spectrum is presented. In simulations with pion mass = 392 MeV, the\nlow-lying excited states of lattice QCD are found to have the same quantum\nnumbers as the states of SU(6)xO(3) symmetry. The lattice spectra are\ninconsistent with either a quark-diquark model or parity doubling of states and\nthey suggest that the J = 1/2 Roper resonance may have a complex structure\nconsisting of contributions from L=0, 1 and 2.", "category": "hep-lat" }, { "text": "Three-particle finite-volume formalism for $\u03c0^+\u03c0^+ K^+$ and related\n systems: We consider three-particle systems consisting of two identical particles and\na third that is different, with all being spinless. Examples include\n$\\pi^+\\pi^+ K^+$ and $K^+K^+\\pi^+$. We derive the formalism necessary to\nextract two- and three-particle infinite-volume scattering amplitudes from the\nspectrum of such systems in finite volume. We use a relativistic formalism\nbased on an all-orders diagrammatic analysis in generic effective field theory,\nadopting the methodology used recently to study the case of three nondegenerate\nparticles. We present both a direct derivation, and also a cross-check based on\nan appropriate limit and projection of the fully nondegenerate formalism. We\nalso work out the threshold expansions for the three-particle K matrix that\nwill be needed in practical applications, both for systems with two identical\nparticles plus a third, and also for the fully nondegenerate theory.", "category": "hep-lat" }, { "text": "Interplay between sign problem and Z_3 symmetry in three-dimensional\n Potts model: We construct four kinds of Z3-symmetric three-dimentional (3-d) Potts models,\neach with different number of states at each site on a 3-d lattice, by\nextending the 3-d three-state Potts model. Comparing the ordinary Potts model\nwith the four Z3-symmetric Potts models, we investigate how Z3 symmetry affects\nthe sign problem and see how the deconfinement transition line changes in the\n$\\mu-\\kappa$ plane as the number of states increases, where $\\mu$ $(\\kappa)$\nplays a role of chemical potential (temperature) in the models. We find that\nthe sign problem is almost cured by imposing Z3 symmetry. This mechanism may\nhappen in Z3-symmetric QCD-like theory. We also show that the deconfinement\ntransition line has stronger $\\mu$-dependence with respect to increasing the\nnumber of states.", "category": "hep-lat" }, { "text": "K^0--\\bar{K}^0 mixing in full lattice QCD: There are at least two methods to calculate $ B_K $ with staggered fermions:\none is the two spin trace formalism and the other is the one spin trace\nformalism. We have performed numerical simulations on a $ 16^3 \\times 40 $\nlattice in full QCD with $ \\beta = 5.7 $ and a dynamical quark mass 0.01 in\nlattice units. We try various sources to select only the pseudo-Goldstone\nbosons and compare the various results.", "category": "hep-lat" }, { "text": "Remarks on the quantum gravity interpretation of 4D dynamical\n triangulation: We review some of the phenomenology in 4D dynamical triangulation and explore\nits interpretation in terms of a euclidean effective action of the continuum\nform $\\intx \\sqrt{g} [\\mu -\\frac{1}{16\\pi G} R + \\cdots]$.", "category": "hep-lat" }, { "text": "Phase Quenched Lattice QCD at Finite Density and Temperature: We simulate 3-flavour lattice QCD at finite quark-number chemical potential\nmu in the phase-quenched approximation, close to the finite temperature\ntransition. Working close to the critical quark mass, we find no evidence for\nthe expected critical endpoint at small mu. We are performing further\nsimulations aimed at calculating the equation-of-state of this theory outside\nof the superfluid domain, where its phase structure is expected to mimic the\nfull theory.", "category": "hep-lat" }, { "text": "Light hadron spectroscopy with O(a) improved dynamical fermions: We present the first results for the static quark potential and the light\nhadron spectrum using dynamical fermions at $\\beta=5.2$ using an O(a) improved\nWilson fermion action together with the standard Wilson plaquette action for\nthe gauge part. Sea quark masses were chosen such that the pseudoscalar-vector\nmass ratio, m_PS/m_V$, varies from 0.86 to 0.67. Finite-size effects are\nstudied by using three different volumes, 8^3\\cdot 24, 12^3\\cdot 24 and\n16^3\\cdot 24. Comparing our results to previous ones obtained using the\nquenched approximation, we find evidence for sea quark effects in quantities\nlike the static quark potential and the vector-pseudoscalar hyperfine\nsplitting.", "category": "hep-lat" }, { "text": "High-loop perturbative renormalization constants for Lattice QCD (II):\n three-loop quark currents for tree-level Symanzik improved gauge action and\n n_f=2 Wilson fermions: Numerical Stochastic Perturbation Theory was able to get three- (and even\nfour-) loop results for finite Lattice QCD renormalization constants. More\nrecently, a conceptual and technical framework has been devised to tame finite\nsize effects, which had been reported to be significant for (logarithmically)\ndivergent renormalization constants. In this work we present three-loop results\nfor fermion bilinears in the Lattice QCD regularization defined by tree-level\nSymanzik improved gauge action and n_f=2 Wilson fermions. We discuss both\nfinite and divergent renormalization constants in the RI'-MOM scheme. Since\nrenormalization conditions are defined in the chiral limit, our results also\napply to Twisted Mass QCD, for which non-perturbative computations of the same\nquantities are available. We emphasize the importance of carefully accounting\nfor both finite lattice space and finite volume effects. In our opinion the\nlatter have in general not attracted the attention they would deserve.", "category": "hep-lat" }, { "text": "Renormalization constants for $N_{\\rm f}=2+1+1$ twisted mass QCD: We summarize recent non-perturbative results obtained for the renormalization\nconstants computed in the RI'-MOM scheme for $N_{\\rm f}=2+1+1$ twisted mass\nQCD. Our implementation employs the Iwasaki gauge action and four dynamical\ndegenerate twisted mass fermions. Renormalization constants for scalar,\npseudo-scalar, vector and axial operators, as well as the quark propagator\nrenormalization, are computed at three different values of the lattice spacing,\ntwo different volumes and several values of the twisted mass. Our method allows\nfor a precise cross-check of the running, because of the particular proper\ntreatment of the hypercubic artifacts. Preliminary results for twist-2\noperators are also presented.", "category": "hep-lat" }, { "text": "Rigidity and percolation of center vortices: Effective action of center vortices in SU(2) lattice gauge theory is\ninvestigated by studying the correlation between the action density on their\nworldsheets and their geometric properties. It turns out that center vortices\nare rigid, however, their dynamics is more complicated than that of rigid\nrandom surfaces, since some coupling constants have nonstandard scaling\ndimensions. As a result, the properties of center vortices are almost\ncompletely determined by curvature-dependent effects. This, in turn, provides a\nqualitative explanation of vortex percolation.", "category": "hep-lat" }, { "text": "Unpolarized gluon distribution in the nucleon from lattice quantum\n chromodynamics: In this study, we present a determination of the unpolarized gluon Ioffe-time\ndistribution in the nucleon from a first principles lattice quantum\nchromodynamics calculation. We carry out the lattice calculation on a\n$32^3\\times 64$ ensemble with a pion mass of $358$ MeV and lattice spacing of\n$0.094$ fm. We construct the nucleon interpolating fields using the\ndistillation technique, flow the gauge fields using the gradient flow, and\nsolve the summed generalized eigenvalue problem to determine the glounic matrix\nelements. Combining these techniques allows us to provide a statistically\nwell-controlled Ioffe-time distribution and unpolarized gluon PDF. We obtain\nthe flow time independent reduced Ioffe-time pseudo-distribution, and calculate\nthe light-cone Ioffe-time distribution and unpolarized gluon distribution\nfunction in the $\\overline{\\rm MS}$ scheme at $\\mu = 2$ GeV, neglecting the\nmixing of the gluon operator with the quark singlet sector. Finally, we compare\nour results to phenomenological determinations.", "category": "hep-lat" }, { "text": "Lattice QCD constraints on the parton distribution functions of\n ${}^3\\text{He}$: The fraction of the longitudinal momentum of ${}^3\\text{He}$ that is carried\nby the isovector combination of $u$ and $d$ quarks is determined using lattice\nQCD for the first time. The ratio of this combination to that in the\nconstituent nucleons is found to be consistent with unity at the few-percent\nlevel from calculations with quark masses corresponding to $m_\\pi\\sim 800$ MeV,\nextrapolated to the physical quark masses. This constraint is consistent with,\nand significantly more precise than, determinations from global nuclear parton\ndistribution function fits. Including the lattice QCD determination of the\nmomentum fraction in the nNNPDF global fitting framework results in the\nuncertainty on the isovector momentum fraction ratio being reduced by a factor\nof 2.5, and thereby enables a more precise extraction of the $u$ and $d$ parton\ndistributions in ${}^3\\text{He}$.", "category": "hep-lat" }, { "text": "SO(2N) and SU(N) gauge theories: We present our preliminary results of SO(2N) gauge theories, approaching the\nlarge-N limit. SO(2N) theories may help us to understand QCD at finite chemical\npotential since there is an orbifold equivalence between SO(2N) and SU(N) gauge\ntheories at large-N and SO(2N) theories do not have the sign problem present in\nQCD. We consider the string tensions, mass spectra, and deconfinement\ntemperatures in the SO(2N) pure gauge theories in 2+1 dimensions, comparing\nthem to their corresponding SU(N) theories.", "category": "hep-lat" }, { "text": "Multi-hadron interactions from lattice QCD: First-principles calculations of multi-hadron dynamics are a crucial goal in\nlattice QCD. Significant progress has been achieved in developing,\nimplementing, and applying theoretical tools that connect finite-volume\nquantities to their infinite-volume counterparts. Here, I review some recent\ntheoretical developments and numerical results regarding multi-particle\nquantities in a finite volume. These results include $N\\pi$ scattering, systems\nof two and three mesons at maximal isospin, three-body resonances in a toy\nmodel, and the formulation of effective theories in finite volume for\nmulti-nucleon systems.", "category": "hep-lat" }, { "text": "Lattice diffeomorphism invariance: We propose a lattice counterpart of diffeomorphism symmetry in the continuum.\nA functional integral for quantum gravity is regularized on a discrete set of\nspace-time points, with fermionic or bosonic lattice fields. When the\nspace-time points are positioned as discrete points of a continuous manifold,\nthe lattice action can be reformulated in terms of average fields within local\ncells and lattice derivatives. Lattice diffeomorphism invariance is realized if\nthe action is independent of the positioning of the space-time points. Regular\nas well as rather irregular lattices are then described by the same action.\nLattice diffeomorphism invariance implies that the continuum limit and the\nquantum effective action are invariant under general coordinate transformations\n- the basic ingredient for general relativity. In our approach the lattice\ndiffeomorphism invariant actions are formulated without introducing a metric or\nother geometrical objects as fundamental degrees of freedom. The metric rather\narises as the expectation value of a suitable collective field. As examples, we\npresent lattice diffeomorphism invariant actions for a bosonic non-linear\nsigma-model and lattice spinor gravity.", "category": "hep-lat" }, { "text": "Thermal monopole condensation in QCD with physical quark masses: Thermal monopoles, identified after Abelian projection as magnetic currents\nwrapping non-trivially around the thermal circle, are studied in $N_f = 2+1$\nQCD at the physical point. The distribution in the number of wrappings, which\nin pure gauge theories points to a condensation temperature coinciding with\ndeconfinement, points in this case to around 275 MeV, almost twice the QCD\ncrossover temperature $T_c$; similar indications emerge looking for the\nformation of a percolating current cluster. The possible relation with other\nnon-perturbative phenomena observed above $T_c$ is discussed.", "category": "hep-lat" }, { "text": "A non-perturbative calculation of the mass of the Bc: We present a calculation of the mass of the 1S0 pseudoscalar anti-b c (Bc)\nstate using a non-perturbative measurement from quenched lattice QCD. We find\nM_Bc = 6.386(9)(98)(15) GeV where the first error is statistical, the second\nsystematic due to the quark mass ambiguities and quenching and the third the\nsystematic error due to the estimation of mass of the eta_b.", "category": "hep-lat" }, { "text": "An estimate for the thermal photon rate from lattice QCD: We estimate the production rate of photons by the quark-gluon plasma in\nlattice QCD. We propose a new correlation function which provides better\ncontrol over the systematic uncertainty in estimating the photon production\nrate at photon momenta in the range {\\pi}T/2 to 2{\\pi}T. The relevant Euclidean\nvector current correlation functions are computed with $N_{\\mathrm f}$ = 2\nWilson clover fermions in the chirally-symmetric phase. In order to estimate\nthe photon rate, an ill-posed problem for the vector-channel spectral function\nmust be regularized. We use both a direct model for the spectral function and a\nmodel-independent estimate from the Backus-Gilbert method to give an estimate\nfor the photon rate.", "category": "hep-lat" }, { "text": "Quark contribution to the proton spin from 2+1+1-flavor lattice QCD: We present the first chiral-continuum extrapolated up, down and strange quark\nspin contribution to the proton spin using lattice QCD. For the connected\ncontributions, we use eleven ensembles of 2+1+1-flavor of Highly Improved\nStaggered Quarks (HISQ) generated by the MILC Collaboration. They cover four\nlattice spacings $a \\approx \\{0.15,0.12,0.09,0.06\\}$ fm and three pion masses,\n$M_\\pi \\approx \\{315,220,135\\}$ MeV, of which two are at the physical pion\nmass. The disconnected strange calculations are done on seven of these\nensembles, covering the four lattice spacings but only one with the physical\npion mass. The disconnected light quark calculation was done on six ensembles\nat two values of $M_\\pi \\approx \\{315,220\\}$ MeV. High-statistics estimates on\neach ensemble for all three quantities allow us to quantify systematic\nuncertainties and perform a simultaneous chiral-continuum extrapolation in the\nlattice spacing and the light-quark mass. Our final results are $\\Delta u\n\\equiv \\langle 1 \\rangle_{\\Delta u^+} = 0.777(25)(30)$, $\\Delta d \\equiv\n\\langle 1 \\rangle_{\\Delta d^+} = -0.438(18)(30)$, and $\\Delta s \\equiv \\langle\n1 \\rangle_{\\Delta s^+} = -0.053(8)$, adding up to a total quark contribution to\nproton spin of $\\sum_{q=u,d,s} (\\frac{1}{2} \\Delta q) = 0.143(31)(36)$. The\nsecond error is the systematic uncertainty associated with the chiral-continuum\nextrapolation. These results are obtained without model assumptions and are in\ngood agreement with the recent COMPASS analysis $0.13 < \\frac{1}{2} \\Delta\n\\Sigma < 0.18$, and with the $\\Delta q$ obtained from various global analyses\nof polarized beam or target data.", "category": "hep-lat" }, { "text": "Large N: I review some of the things we have learned about large N gauge theories (and\nQCD at N=oo) from lattice calculations in recent years. I point to some open\nproblems.", "category": "hep-lat" }, { "text": "Gauge-fixing approach to lattice chiral gauge theories: We review the status of our recent work on the gauge-fixing approach to\nlattice chiral gauge theories. New numerical results in the reduced version of\na model with a U(1) gauge symmetry are presented which strongly indicate that\nthe factorization of the correlation functions of the left-handed neutral and\nright-handed charged fermion fields, which we established before in\nperturbation theory, holds also nonperturbatively.", "category": "hep-lat" }, { "text": "Nucleon Structure in Lattice QCD using twisted mass fermions: We present results on the nucleon form factors and moments of generalized\nparton distributions obtained within the twisted mass formulation of lattice\nQCD. We include a discussion of lattice artifacts by examining results at\ndifferent volumes and lattice spacings. We compare our results with those\nobtained using different discretization schemes and to experiment.", "category": "hep-lat" }, { "text": "N=1 super Yang-Mills on a (3+1) dimensional transverse lattice with one\n exact supersymmetry: We formulate ${\\cal N}$=1 super Yang-Mills theory in 3+1 dimensions on a two\ndimensional transverse lattice using supersymmetric discrete light cone\nquantization in the large-$N_c$ limit. This formulation is free of fermion\nspecies doubling. We are able to preserve one supersymmetry. We find a rich,\nnon-trivial behavior of the mass spectrum as a function of the coupling\n$g\\sqrt{N_c}$, and see some sort of \"transition\" in the structure of a bound\nstate as we go from the weak coupling to the strong coupling. Using a toy model\nwe give an interpretation of the rich behavior of the mass spectrum. We present\nthe mass spectrum as a function of the winding number for those states whose\ncolor flux winds all the way around in one of the transverse directions. We use\ntwo fits to the mass spectrum and the one that has a string theory\njustification appears preferable. For those states whose color flux is\nlocalized we present an extrapolated value for $m^2$ for some low energy bound\nstates in the limit where the numerical resolution goes to infinity.", "category": "hep-lat" }, { "text": "The Chiral Condensate of One-Flavor QCD and the Dirac Spectrum at\n \u03b8=0: In a sector of fixed topological charge, the chiral condensate has a\ndiscontinuity given by the Banks-Casher formula also in the case of one-flavor\nQCD. However, at fixed \\theta-angle, the chiral condensate remains constant\nwhen the quark mass crosses zero. To reconcile these contradictory\nobservations, we have evaluated the spectral density of one-flavor QCD at\n\\theta=0. For negative quark mass, it becomes a strongly oscillating function\nwith a period that scales as the inverse space-time volume and an amplitude\nthat increases exponentially with the space-time volume. As we have learned\nfrom QCD at nonzero chemical potential, if this is the case, an alternative to\nthe Banks-Casher formula applies, and as we will demonstrate in this talk, for\none-flavor QCD this results in a continuous chiral condensate. A special role\nis played by the topological zero modes which have to be taken into account\nexactly in order to get a finite chiral condensate in the thermodynamic limit.", "category": "hep-lat" }, { "text": "The strange quark contribution to the spin of the nucleon: Quark line disconnected matrix elements of an operator, such as the axial\ncurrent, are difficult to compute on the lattice. The standard method uses a\nstochastic estimator of the operator, which is generally very noisy. We discuss\nand develop further our alternative approach using the Feynman-Hellmann theorem\nwhich involves only evaluating two-point correlation functions. This is applied\nto computing the contribution of the quark spin to the nucleon and in\nparticular for the strange quark. In this process we also pay particular\nattention to the development of an SU(3) flavour breaking expansion for singlet\noperators.", "category": "hep-lat" }, { "text": "Spectrum of the open QCD flux tube and its effective string description: I perform a high precision measurement of the static quark-antiquark\npotential in three-dimensional ${\\rm SU}(N)$ gauge theory with $N=2$ to 6. The\nresults are compared to the effective string theory for the QCD flux tube and I\nobtain continuum limit results for the string tension and the non-universal\nleading order boundary coefficient, including an extensive analysis of all\ntypes of systematic uncertainties. The magnitude of the boundary coefficient\ndecreases with increasing $N$, but remains non-vanishing in the large-$N$\nlimit. I also test for the presence of possible contributions from rigidity or\nmassive modes and compare the results for the string theory parameters to data\nfor the excited states.", "category": "hep-lat" }, { "text": "Nuclear force in Lattice QCD: We perform the quenched lattice QCD analysis on the nuclear force\n(baryon-baryon interactions). We employ $20^3\\times 24$ lattice at $\\beta=5.7$\n($a\\simeq 0.19$ fm) with the standard gauge action and the Wilson quark action\nwith the hopping parameters $\\kappa=0.1600, 0.1625, 0.1650$, and generate about\n200 gauge configurations. We measure the temporal correlators of the two-baryon\nsystem which consists of heavy-light-light quarks. We extract the inter-baryon\nforce as a function of the relative distance $r$. We also evaluate the\ncontribution to the nuclear force from each ``Feynman diagram'' such as the\nquark-exchange diagram individually, and single out the roles of Pauli-blocking\neffects or quark exchanges in the inter-baryon interactions.", "category": "hep-lat" }, { "text": "Two dimensional SU(N)xSU(N) Chiral Models on the Lattice (II): the\n Green's Function: Analytical and numerical methods are applied to principal chiral models on a\ntwo-dimensional lattice and their predictions are tested and compared. New\ntechniques for the strong coupling expansion of SU(N) models are developed and\napplied to the evaluation of the two-point correlation function. The\nmomentum-space lattice propagator is constructed with precision O(\\beta^{10})\nand an evaluation of the correlation length is obtained for several different\ndefinitions. Three-loop weak coupling contributions to the internal energy and\nto the lattice $\\beta$ and $\\gamma$ functions are evaluated for all N, and the\neffect of adopting the ``energy'' definition of temperature is computed with\nthe same precision. Renormalization-group improved predictions for the\ntwo-point Green's function in the weak coupling ( continuum ) regime are\nobtained and successfully compared with Monte Carlo data. We find that strong\ncoupling is predictive up to a point where asymptotic scaling in the energy\nscheme is observed. Continuum physics is insensitive to the effects of the\nlarge N phase transition occurring in the lattice model. Universality in N is\nalready well established for $N \\ge 10$ and the large N physics is well\ndescribed by a ``hadronization'' picture.", "category": "hep-lat" }, { "text": "Effects of the anomaly on the QCD chiral phase transition: We study a lattice field theory described by two flavors of massless\nstaggered fermions interacting with U(1) gauge fields in the strong coupling\nlimit. We show that the lattice model has a $SU(2)\\times SU(2)\\times U(1)$\nchiral symmetry and can be used to model the two-flavor QCD chiral phase\ntransition in the absence of the anomaly. It is also possible to add a coupling\nto this model which breaks the chiral symmetry to $SU(2)\\times SU(2)$ and thus\nmimics the effects of the anomaly in two-flavor QCD. We construct an efficient\ndirected loop algorithm to study such a model. We show that the chiral phase\ntransition in our model is first order in the absence of the anomaly, while it\nbecomes second order with O(4) exponents when the anomaly is turned on.", "category": "hep-lat" }, { "text": "Running Coupling and the Lambda-Parameter from SU(3) Lattice Simulations: We present new results on the static qq-potential from high statistics\nsimulations on 32^4 and smaller lattices, using the standard Wilson beta = 6.0,\n6.4, and 6.8. Within our statistical errors we do not observe any finite size\neffects affecting the potential values, on varying the spatial lattice extent\nfrom 0.9fm up to 3.3fm. We are able to see and quantify the running of the\ncoupling from the Coulomb behaviour of the interquark force. From this we\nextract the ratio \\sqrt{sigma}/Lambda_L. We demonstrate that scaling violations\non the string tension can be considerably reduced by introducing effective\ncoupling schemes, which allow for a safe extrapolation of \\Lambda_L to its\ncontinuum value. Both methods yield consistent values for Lambda: Lambda_MSbar\n= 0.558_{-0.007}^{+0.017}\\sqrt{sigma} = 246_{-3}^{+7}MeV. At the highest energy\nscale attainable to us we find alpha(5 GeV) = 0.150(3)", "category": "hep-lat" }, { "text": "Domain Decomposition method on GPU cluster: Pallalel GPGPU computing for lattice QCD simulations has a bottleneck on the\nGPU to GPU data communication due to the lack of the direct data exchanging\nfacility. In this work we investigate the performance of quark solver using the\nrestricted additive Schwarz (RAS) preconditioner on a low cost GPU cluster. We\nexpect that the RAS preconditioner with appropriate domaindecomposition and\ntask distribution reduces the communication bottleneck. The GPU cluster we\nconstructed is composed of four PC boxes, two GPU cards are attached to each\nbox, and we have eight GPU cards in total. The compute nodes are connected with\nrather slow but low cost Gigabit-Ethernet. We include the RAS preconditioner in\nthe single-precision part of the mixedprecision nested-BiCGStab algorithm and\nthe single-precision task is distributed to the multiple GPUs. The benchmarking\nis done with the O(a)-improved Wilson quark on a randomly generated gauge\nconfiguration with the size of $32^4$. We observe a factor two improvment on\nthe solver performance with the RAS precoditioner compared to that without the\npreconditioner and find that the improvment mainly comes from the reduction of\nthe communication bottleneck as we expected.", "category": "hep-lat" }, { "text": "Deflated BiCGStab for linear equations in QCD problems: The large systems of complex linear equations that are generated in QCD\nproblems often have multiple right-hand sides (for multiple sources) and\nmultiple shifts (for multiple masses). Deflated GMRES methods have previously\nbeen developed for solving multiple right-hand sides. Eigenvectors are\ngenerated during solution of the first right-hand side and used to speed up\nconvergence for the other right-hand sides. Here we discuss deflating\nnon-restarted methods such as BiCGStab. For effective deflation, both left and\nright eigenvectors are needed. Fortunately, with the Wilson matrix, left\neigenvectors can be derived from the right eigenvectors. We demonstrate for\ndifficult problems with kappa near kappa_c that deflating eigenvalues can\nsignificantly improve BiCGStab. We also will look at improving solution of\ntwisted mass problems with multiple shifts. Projecting over previous solutions\nis an easy way to reduce the work needed.", "category": "hep-lat" }, { "text": "Electroweak three-body decays in the presence of two- and three-body\n bound states: Recently, formalism has been derived for studying electroweak transition\namplitudes for three-body systems both in infinite and finite volumes. The\nformalism provides exact relations that the infinite-volume amplitudes must\nsatisfy, as well as a relationship between physical amplitudes and\nfinite-volume matrix elements, which can be constrained from lattice QCD\ncalculations. This formalism poses additional challenges when compared with the\nanalogous well-studied two-body equivalent one, including the necessary step of\nsolving integral equations of singular functions. In this work, we provide some\nnon-trivial analytical and numerical tests on the aforementioned formalism. In\nparticular, we consider a case where the three-particle system can have\nthree-body bound states as well as bound states in the two-body subsystem. For\nkinematics below the three-body threshold, we demonstrate that the scattering\namplitudes satisfy unitarity. We also check that for these kinematics the\nfinite-volume matrix elements are accurately described by the formalism for\ntwo-body systems up to exponentially suppressed corrections. Finally, we verify\nthat in the case of the three-body bound state, the finite-volume matrix\nelement is equal to the infinite-volume coupling of the bound state, up to\nexponentially suppressed errors.", "category": "hep-lat" }, { "text": "One dimensional supersymmetric Yang-Mills theory with 16 supercharges: We report on numerical simulations of one dimensional maximally\nsupersymmetric SU(N) Yang-Mills theory, by using the lattice action with two\nexact supercharges. Based on the gauge/gravity duality, the gauge theory\ncorresponds to N D0-branes system in type IIA superstring theory at finite\ntemperature. We aim to verify the gauge/gravity duality numerically by\ncomparing our results of the gauge side with analytic solutions of the gravity\nside. First of all, by examining the supersymmetric Ward-Takahashi relation, we\nshow that supersymmetry breaking effects from the cut-off vanish in the\ncontinuum limit and our lattice theory has the desired continuum limit. Then,\nwe find that, at low temperature, the black hole internal energy obtained from\nour data is close to the analytic solution of the gravity side. It suggests the\nvalidity of the duality.", "category": "hep-lat" }, { "text": "Confined Charged Particles in C-periodic Volumes: Charged particles in an Abelian Coulomb phase are non-local infraparticles\nthat are surrounded by a cloud of soft photons which extends to infinity.\nGauss' law prevents the existence of charged particles in a periodic volume. In\na $C$-periodic volume, which is periodic up to charge conjugation, on the other\nhand, charged particles can exist. This includes vortices in the $3$-d\nXY-model, magnetic monopoles in $4$-d $\\mathrm{U}(1)$ gauge theory, as well as\nprotons and other charged particles in QCD coupled to QED. In four dimensions\nnon-Abelian charges are confined. Hence, in an infinite volume non-Abelian\ninfraparticles cost an infinite amount of energy. However, in a $C$-periodic\nvolume non-Abelian infraparticles (whose energy increases linearly with the box\nsize) can indeed exist. Investigating these states holds the promise of\ndeepening our understanding of confinement.", "category": "hep-lat" }, { "text": "Toward solving the sign problem with path optimization method: We propose a new approach to circumvent the sign problem in which the\nintegration path is optimized to control the sign problem. We give a trial\nfunction specifying the integration path in the complex plane and tune it to\noptimize the cost function which represents the seriousness of the sign\nproblem. We call it the path optimization method. In this method, we do not\nneed to solve the gradient flow required in the Lefschetz-thimble method and\nthen the construction of the integration-path contour arrives at the\noptimization problem where several efficient methods can be applied. In a\nsimple model with a serious sign problem, the path optimization method is\ndemonstrated to work well; the residual sign problem is resolved and precise\nresults can be obtained even in the region where the global sign problem is\nserious.", "category": "hep-lat" }, { "text": "Scaling studies of QCD with the dynamical HISQ action: We study the lattice spacing dependence, or scaling, of physical quantities\nusing the highly improved staggered quark (HISQ) action introduced by the\nHPQCD/UKQCD collaboration, comparing our results to similar simulations with\nthe asqtad fermion action. Results are based on calculations with lattice\nspacings approximately 0.15, 0.12 and 0.09 fm, using four flavors of dynamical\nHISQ quarks. The strange and charm quark masses are near their physical values,\nand the light-quark mass is set to 0.2 times the strange-quark mass. We look at\nthe lattice spacing dependence of hadron masses, pseudoscalar meson decay\nconstants, and the topological susceptibility. In addition to the commonly used\ndetermination of the lattice spacing through the static quark potential, we\nexamine a determination proposed by the HPQCD collaboration that uses the decay\nconstant of a fictitious \"unmixed s bar s\" pseudoscalar meson. We find that the\nlattice artifacts in the HISQ simulations are much smaller than those in the\nasqtad simulations at the same lattice spacings and quark masses.", "category": "hep-lat" }, { "text": "Confinement-Deconfinement transition and $Z_2$ symmetry in $Z_2+$Higgs\n theory: We study the Polyakov loop and the $Z_2$ symmetry in the lattice $Z_2+$Higgs\ntheory in 4D Euclidean space using Monte Carlo simulations. The results show\nthat this symmetry is realised in the Higgs symmetric phase for large number of\ntemporal lattice sites. To understand the dependence on the number of temporal\nsites, we consider a one dimensional model by keeping terms of the original\naction corresponding to a single spatial site. In this approximation the\npartition function can be calculated exactly as a function of the Polyakov\nloop. The resulting free energy is found to have the $Z_2$ symmetry in the\nlimit of large temporal sites. We argue that this is due to $Z_2$ invariance as\nwell as dominance of the distribution or density of states corresponding to the\naction.", "category": "hep-lat" }, { "text": "Proton decay matrix element on the lattice with physical pion mass: Proton decay is one of possible signatures of baryon number violation, which\nhas to exist to explain the baryon asymmetry and the existence of nuclear\nmatter. Proton decays must be mediated through effective low-energy baryon\nnumber violating operators made of three quarks and a lepton. We calculate\nmatrix elements of these operators between the proton and various meson final\nstates using the direct method. We report on preliminary results of matrix\nelement calculation done with the 2+1 dynamical flavor domain wall fermions at\nthe physical point for the first time.", "category": "hep-lat" }, { "text": "Deriving exact results for Ising-like models from the cluster variation\n method: The cluster variation method (CVM) is an approximation technique which\ngeneralizes the mean field approximation and has been widely applied in the\nlast decades, mainly for finding accurate phase diagrams of Ising-like lattice\nmodels. Here we discuss in which cases the CVM can yield exact results,\nconsidering: (i) one-dimensional systems and strips (in which case the method\nreduces to the transfer matrix method), (ii) tree-like lattices and (iii) the\nso-called disorder points of euclidean lattice models with competitive\ninteractions in more than one dimension.", "category": "hep-lat" }, { "text": "Measurement of hybrid content of heavy quarkonia using lattice NRQCD: Using lowest-order lattice NRQCD to create heavy meson propagators and\napplying the spin-dependent interaction, $c_B^{}\n\\frac{-g}{2m_q}\\vec\\sigma\\cdot\\vec{B}$, at varying intermediate time slices, we\ncompute the off-diagonal matrix element of the Hamiltonian for the\nquarkonium-hybrid two-state system. Thus far, we have results for one set of\nquenched lattices with an interpolation in quark mass to match the bottomonium\nspectrum. After diagonalization of the two-state Hamiltonian, we find the\nground state of the $\\Upsilon$ to show a $0.0035(1)c_B^2$ (with $c_B^2 \\sim\n1.5-3.1$) probability admixture of hybrid, $|b\\bar{b}g>$.", "category": "hep-lat" }, { "text": "Pion form factor with twisted mass QCD: The pion form factor is calculated using quenched twisted mass QCD with\nbeta=6.0 and maximal twisting angle omega=pi/2. Two pion masses and several\nvalues of momentum transfer are considered. The momentum averaging procedure of\nFrezzotti and Rossi is used to reduce lattice spacing errors, and numerical\nresults are consistent with the expected O(a) improvement.", "category": "hep-lat" }, { "text": "Chiral Lattice Gauge Theories from Warped Domain Walls and\n Ginsparg-Wilson Fermions: We propose a construction of a 2-dimensional lattice chiral gauge theory. The\nconstruction may be viewed as a particular limit of an infinite warped\n3-dimensional theory. We also present a \"single-site'' construction using\nGinsparg-Wilson fermions which may avoid, in both 2 and 4 dimensions, the\nproblems of waveguide-Yukawa models.", "category": "hep-lat" }, { "text": "Logarithmic corrections to O($a$) and O($a^2$) effects in lattice QCD\n with Wilson or Ginsparg-Wilson quarks: We derive the asymptotic lattice spacing dependence\n$a^n[2b_0\\bar{g}^2(1/a)]^{\\hat{\\Gamma}_i}$ relevant for spectral quantities of\nlattice QCD, when using Wilson, O$(a)$ improved Wilson or Ginsparg-Wilson\nquarks. We give some examples for the spectra encountered for $\\hat{\\Gamma}_i$\nincluding the partially quenched case, mixed actions and using two different\ndiscretisations for dynamical quarks. This also includes maximally twisted mass\nQCD relying on automatic O$(a)$ improvement. At O$(a^2)$, all cases considered\nhave $\\min_i\\hat{\\Gamma}_i\\gtrsim -0.3$ if $N_\\mathrm{f}\\leq 4$, which ensures\nthat the leading order lattice artifacts are not severely logarithmically\nenhanced in contrast to the O$(3)$ non-linear sigma model [1,2]. However, we\nfind a very dense spectrum of these leading powers, which may result in major\npile-ups and cancellations. We present in detail the computational strategy\nemployed to obtain the 1-loop anomalous dimensions already used in [3].", "category": "hep-lat" }, { "text": "Exact calculation of disconnected loops: We present an implementation of the disconnected diagram contributions to\nquantities such as the flavor-singlet pseudoscalar meson mass which are\naccelerated by GPGPU technology utilizing the NVIDIA CUDA platform. To enable\nthe exact evaluation of the disconnected loops we use a $16^3 \\times 32$\nlattice and $N_f=2$ Wilson fermions simulated by the SESAM Collaboration. The\ndisconnected loops are also computed using stochastic methods with several\nnoise reduction techniques.\n In particular, we analyze various dilution schemes as well as the recently\nproposed truncated s olver method. We find consistency among the different\nmethods used for the determination of the $\\eta^\\prime$ mass, albeit that the\ngauge noise for the ensemble studied is large. We also find that the effect of\n'dilution' d oes not go beyond that of optimal statistical noise in many cases.\nIt has been observed, however, that spin dilution does have a significant\neffect for some quantities studied.", "category": "hep-lat" }, { "text": "Light hadronic physics using domain wall fermions in quenched lattice\n QCD: In the past year domain wall fermion simulations have moved from exploratory\nstages to the point where systematic effects can be studied with different\ngauge couplings, volumes, and lengths in the fifth dimension. Results are\npresented here for the chiral condensate, the light hadron spectrum, and the\nstrange quark mass. We focus especially on the pseudoscalar meson mass and show\nthat, in small volume, the correlators used to compute it can be contaminated\nto different degrees by topological zero modes. In large volume a nonlinear\nextrapolation to the chiral limit, e.g. as expected from quenched chiral\nperturbation theory, is needed in order to have a consistent picture of low\nenergy chiral symmetry breaking effects.", "category": "hep-lat" }, { "text": "Flux representation of an effective Polyakov loop model for QCD\n thermodynamics: We discuss an effective Polyakov loop model for QCD thermodynamics with a\nchemical potential. Using high temperature expansion techniques the partition\nsum is mapped exactly onto the partition sum of a flux model. In the flux\nrepresentation the complex action problem is resolved and a simulation with\nworm-type algorithms becomes possible also at finite chemical potential.", "category": "hep-lat" }, { "text": "The beta function and equation of state for QCD with two flavors of\n quarks: We measure the pressure and energy density of two flavor QCD in a wide range\nof quark masses and temperatures. The pressure is obtained from an integral\nover the average plaquette or psi-bar-psi. We measure the QCD beta function,\nincluding the anomalous dimension of the quark mass, in new Monte Carlo\nsimulations and from results in the literature. We use it to find the\ninteraction measure, E-3p, yielding non-perturbative values for both the energy\ndensity E and the pressure p. uuencoded compressed PostScript file Revised\nversion should work on more PostScript printers.", "category": "hep-lat" }, { "text": "A study of the (m,d,N)=(1,3,2) Lifshitz point and of the three-\n dimensional XY universality class by high-temperature bivariate series for\n the XY models with anisotropic competing interactions: High-temperature bivariate expansions have been derived for the two-spin\ncorrelation-function in a variety of classical lattice XY (planar rotator)\nmodels in which spatially isotropic interactions among first-neighbor spins\ncompete with spatially isotropic or anisotropic (in particular uniaxial)\ninteractions among next-to-nearest-neighbor spins. The expansions, calculated\nfor cubic lattices of dimension d=1,2 and 3, are expressed in terms of the two\nvariables K1=J1/kT and K2=J2/kT, where J1 and J2 are the nearest-neighbor and\nthe next-to-nearest-neighbor exchange couplings, respectively. This report\ndeals in particular with the properties of the d=3 uniaxial XY model (ANNNXY\nmodel) for which the bivariate expansions have been computed through the 18-th\norder, thus extending by 12 orders the results so far available and making a\nstudy of this model possible over a wide range of values of the competition\nparameter R=J2/J1.", "category": "hep-lat" }, { "text": "$\u03be/\u03be_{2nd}$ ratio as a tool to refine Effective Polyakov Loop models: Effective Polyakov line actions are a powerful tool to study the finite\ntemperature behaviour of lattice gauge theories. They are much simpler to\nsimulate than the original lattice model and are affected by a milder sign\nproblem, but it is not clear to which extent they really capture the rich\nspectrum of the original theories. We propose here a simple way to address this\nissue based on the so called second moment correlation length $\\xi_{2nd}$. The\nratio $\\xi/\\xi_{2nd}$ between the exponential correlation length and the second\nmoment one is equal to 1 if only a single mass is present in the spectrum, and\nit becomes larger and larger as the complexity of the spectrum increases. Since\nboth $\\xi$ and $\\xi_{2nd}$ are easy to measure on the lattice, this is a cheap\nand efficient way to keep track of the spectrum of the theory. As an example of\nthe information one can obtain with this tool we study the behaviour of\n$\\xi/\\xi_{2nd}$ in the confining phase of the ($D=3+1$) $\\mathrm{SU}(2)$ gauge\ntheory and show that it is compatible with 1 near the deconfinement transition,\nbut it increases dramatically as the temperature decreases. We also show that\nthis increase can be well understood in the framework of an effective string\ndescription of the Polyakov loop correlator. This non-trivial behaviour should\nbe reproduced by the Polyakov loop effective action; thus, it represents a\nstringent and challenging test of existing proposals and it may be used to\nfine-tune the couplings and to identify the range of validity of the\napproximations involved in their construction.", "category": "hep-lat" }, { "text": "Numerical simulations with two flavours of twisted-mass Wilson quarks\n and DBW2 gauge action: Discretisation errors in two-flavour lattice QCD with Wilson-quarks and DBW2\ngauge action are investigated by comparing numerical simulation data at two\nvalues of the bare gauge coupling. Both non-zero and zero twisted mass values\nare considered. The results, including also data from simulations using the\nWilson plaquette gauge action, are compared to next-to-leading order chiral\nperturbation theory formulas.", "category": "hep-lat" }, { "text": "4d Simplicial Quantum Gravity: Matter Fields and the Corresponding\n Effective Action: Four-dimensional simplicial quantum gravity is modified either by coupling it\nto U(1) gauge fields or by introducing a measure weighted by the orders of the\ntriangles. Strong coupling expansion and Monte Carlo simulations are used.\nAlthough the two modifications of the standard pure-gravity model are\napparently very distinct, they produce strikingly similar results, as far as\nthe geometry of random manifolds is concerned. In particular, for an\nappropriate choice of couplings, the branched polymer phase is replaced by a\ncrinkled phase, characterized by the susceptibility exponent $\\gamma < 0$ and\nthe fractal dimension $d_H > 2$. The quasi-equivalence between the two models\nis exploited to get further insight into the extended phase diagram of the\ntheory.", "category": "hep-lat" }, { "text": "Magnetic polarizability of hadrons from lattice QCD: We extract the magnetic polarizability from the quadratic response of a\nhadron's mass shift in progressively small static magnetic fields. The\ncalculation is done on a 24x12x12x24 lattice at a = 0.17 fm with an improved\ngauge action and the clover quark action. The results are compared to those\nfrom experiments and models where available.", "category": "hep-lat" }, { "text": "Curvature of the pseudocritical line in (2+1)-flavor QCD with HISQ\n fermions: We study QCD with (2+1)-HISQ fermions at nonzero temperature and nonzero\nimaginary baryon chemical potential. Monte Carlo simulations are performed\nusing the MILC code along the line of constant physics with a light to strange\nmass ratio of $m_l/m_s=1/20$ on lattices up to $48^3 \\times 12$ to check for\nfinite cutoff effects. We determine the curvature of the pseudocritical line\nextrapolated to the continuum limit.", "category": "hep-lat" }, { "text": "Bosonic color-flavor transformation for the special unitary group: We extend Zirnbauer's color-flavor transformation in the bosonic sector to\nthe color group SU(N_c). Because the flavor group U(N_b, N_b) is non-compact,\nthe algebraic method by which the original color-flavor transformation was\nderived leads to a useful result only for 2N_b \\le N_c. Using the character\nexpansion method, we obtain a different form of the transformation in the\nextended range N_b \\le N_c. This result can also be used for the color group\nU(N_c). The integrals to which the transformation can be applied are of\nrelevance for the recently proposed boson-induced lattice gauge theory.", "category": "hep-lat" }, { "text": "Charged Pion Polarizability from the Lattice: Direct evaluation of charged particle polarizabilities on the lattice is\nquite difficult. However, a short cut for charged pion polarizability - the\nDas, Mathur, Okubo Sum Rule - can readily be calculated using lattice\ntechniques. A phenomenological model has been developed to fit the time\nbehavior of the propagators in this expression. Numerical systematics are\ndiscussed and some preliminary results are presented.", "category": "hep-lat" }, { "text": "Chiral condensate from the Banks-Casher relation: We report on our ongoing project of determining the chiral condensate of\ntwo-flavor QCD from the Banks-Casher relation. We compute the mode number of\nthe O(a)-improved Wilson-Dirac operator for several values of \\Lambda, and we\ndiscuss different fitting strategies to extract the chiral condensate from its\nmass and \\Lambda dependence. Our preliminary results haven been obtained at two\ndifferent lattice spacings by using CLS-configurations.", "category": "hep-lat" }, { "text": "Thermal Correlators in the \u03c1 channel of two-flavor QCD: We present a lattice QCD calculation with two dynamical flavors of the\nisovector vector correlator in the high-temperature phase. We analyze the\ncorrelator in terms of the associated spectral function, for which we review\nthe theoretical expectations. In our main analysis, we perform a fit for the\ndifference of the thermal and vacuum spectral functions, and we use an exact\nsum rule that constrains this difference. We also perform a direct fit for the\nthermal spectral function, and obtain good agreement between the two analyses\nfor frequencies below the two-pion threshold. Under the assumption that the\nspectral function is smooth in that region, we give an estimate of the\nelectrical conductivity.", "category": "hep-lat" }, { "text": "Power corrections from decoupling of the charm quark: Decoupling of heavy quarks at low energies can be described by means of an\neffective theory as shown by S. Weinberg in Ref. [1]. We study the decoupling\nof the charm quark by lattice simulations. We simulate a model, QCD with two\ndegenerate charm quarks. In this case the leading order term in the effective\ntheory is a pure gauge theory. The higher order terms are proportional to\ninverse powers of the charm quark mass $M$ starting at $M^{-2}$. Ratios of\nhadronic scales are equal to their value in the pure gauge theory up to power\ncorrections. We show, by precise measurements of ratios of scales defined from\nthe Wilson flow, that these corrections are very small and that they can be\ndescribed by a term proportional to $M^{-2}$ down to masses in the region of\nthe charm quark mass.", "category": "hep-lat" }, { "text": "$d^\\ast (2380)$ dibaryon from lattice QCD: The $\\Delta\\Delta$ dibaryon resonance $d^\\ast (2380)$ with $(J^P, I)=(3^+,\n0)$ is studied theoretically on the basis of the 3-flavor lattice QCD\nsimulation with heavy pion masses ($m_\\pi =679, 841$ and $1018$ MeV). By using\nthe HAL QCD method, the central $\\Delta$-$\\Delta$ potential in the ${}^7S_3$\nchannel is obtained from the lattice data with the lattice spacing $a\\simeq\n0.121$ fm and the lattice size $L\\simeq 3.87$ fm. The resultant potential shows\na strong short-range attraction, so that a quasi-bound state corresponding to\n$d^\\ast (2380)$ is formed with the binding energy $25$-$40$ MeV below the\n$\\Delta\\Delta$ threshold for the heavy pion masses. The tensor part of the\ntransition potential from $\\Delta\\Delta$ to $NN$ is also extracted to\ninvestigate the coupling strength between the $S$-wave $\\Delta\\Delta$ system\nwith $J^P=3^+$ and the $D$-wave $NN$ system. Although the transition potential\nis strong at short distances, the decay width of $d^\\ast (2380)$ to $NN$ in the\n$D$-wave is kinematically suppressed, which justifies our single-channel\nanalysis at the range of the pion mass explored in this study.", "category": "hep-lat" }, { "text": "Dilaton EFT from p-regime to RMT in the $\u03b5$-regime: New results are reported from tests of a low-energy effective field theory\n(EFT) that includes a dilaton field to describe the emergent light scalar with\n${ 0^{++} }$ quantum numbers in the strongly coupled near-conformal gauge\ntheory with a massless fermion flavor doublet in the two-index symmetric\n(sextet) representation of the SU(3) color gauge group. In the parlor of\nwalking --- based on the observed light scalar, the small $\\beta$-function at\nstrong coupling, and the large anomalous scale dimension of the chiral\ncondensate --- the dilaton EFT hypothesis is introduced to test if it explains\nthe slowly changing nearly scale invariant physics that connects the\nasymptotically free UV fixed point and the far-infrared scale of chiral\nsymmetry breaking. The characteristic dilaton EFT signatures of scale symmetry\nbreaking are probed in this report in the small Compton wavelength limit of\nGoldstone bosons relative to the size of the lattice volume (p-regime) and in\nthe limit when the Goldstone wavelength exceeds the size of the volume\n($\\epsilon$-regime). Random matrix theory (RMT) analysis of the dilaton EFT is\napplied to the lowest part of the Dirac spectrum in the $\\epsilon$-regime to\ndirectly test predictions for the fundamental EFT parameters. The predictions,\nsensitive to the choice of the dilaton potential, were limited before to the\np-regime, using extrapolations from far above the chiral limit with untested\nuncertainties. The dilaton EFT analysis of the $\\epsilon$-regime was first\nsuggested in \\cite{Fodor:2019vmw}, with some results presented at this\nconference and with our continued post-conference analysis added to stimulate\ndiscussions.", "category": "hep-lat" }, { "text": "Quark propagator from an improved staggered action in Laplacian and\n Landau gauges: Studies of gauge dependent quantities are afflicted with Gribov copies, but\nLaplacian gauge fixing provides one possible solution to this problem. We\npresent results for the lattice quark propagator in both Landau and Laplacian\ngauges using standard and improved staggered quark actions. The standard\nKogut-Susskind action has errors of \\oa{2} while the improved ``Asqtad'' action\nhas \\oa{4}, \\oag{2}{2} errors and this improvement is seen in the quark\npropagator. We demonstrate the application of tree-level corrections to these\nactions and see that Landau and Laplacian gauges produce very similar results.\nIn addition, we test an ansatz for the quark mass function, with promising\nresults. In the chiral limit, the infrared quark mass, $M(q^2 = 0)$ is found to\nbe $260\\pm 20$ MeV.", "category": "hep-lat" }, { "text": "SPHERICALLY SYMMETRIC RANDOM WALKS III. POLYMER ADSORPTION AT A\n HYPERSPHERICAL BOUNDARY: A recently developed model of random walks on a $D$-dimensional\nhyperspherical lattice, where $D$ is {\\sl not} restricted to integer values, is\nused to study polymer growth near a $D$-dimensional attractive hyperspherical\nboundary. The model determines the fraction $P(\\kappa)$ of the polymer adsorbed\non this boundary as a function of the attractive potential $\\kappa$ for all\nvalues of $D$. The adsorption fraction $P(\\kappa)$ exhibits a second-order\nphase transition with a nontrivial scaling coefficient for $04$. At $D=4$ there is a\ntricritical point with logarithmic scaling. This model reproduces earlier\nresults for $D=1$ and $D=2$, where $P(\\kappa)$ scales linearly and\nexponentially, respectively. A crossover transition that depends on the radius\nof the adsorbing boundary is found.", "category": "hep-lat" }, { "text": "Some exact results on the QCD critical point: We show, in a model-independent manner, that the QCD critical point can\nappear only inside the pion condensation phase of the phase-quenched QCD as\nlong as the contribution of flavor-disconnected diagrams is negligible. The\nsign problem is known to be maximally severe in this region, implying that the\nQCD critical point is reachable by the present lattice QCD techniques only if\nthere is an enhancement of the flavor-disconnected contribution at finite\nbaryon chemical potential.", "category": "hep-lat" }, { "text": "Temperature dependence of shear viscosity of $SU(3)$--gluodynamics\n within lattice simulation: In this paper we study the shear viscosity temperature dependence of\n$SU(3)$--gluodynamics within lattice simulation. To do so, we measure the\ncorrelation functions of energy-momentum tensor in the range of temperatures\n$T/T_c\\in [0.9, 1.5]$. To extract the values of shear viscosity we used two\napproaches. The first one is to fit the lattice data with some physically\nmotivated ansatz for the spectral function with unknown parameters and then\ndetermine shear viscosity. The second approach is to apply the Backus-Gilbert\nmethod which allows to extract shear viscosity from the lattice data\nnonparametrically. The results obtained within both approaches agree with each\nother. Our results allow us to conclude that within the temperature range\n$T/T_c \\in [0.9, 1.5]$ SU(3)--gluodynamics reveals the properties of a strongly\ninteracting system, which cannot be described perturbatively, and has the ratio\n$\\eta/s$ close to the value ${1}/{4\\pi}$ in $N = 4$ Supersymmetric Yang-Mills\ntheory.", "category": "hep-lat" }, { "text": "Perturbative renormalization of moments of quark momentum, helicity and\n transversity distributions with overlap and Wilson fermions: Using overlap as well as Wilson fermions, we have computed the one-loop\nrenormalization factors of ten non-singlet operators which measure the third\nmoment of quark momentum and helicity distributions (the lowest two having been\ncomputed in a previous paper), as well as the lowest three moments of the $g_2$\nstructure function and the lowest two non-trivial moments of the $h_1$\ntransversity structure function (plus the tensor charge). These factors are\nneeded to extract physical observables from Monte Carlo simulations of the\ncorresponding matrix elements.\n An exact chiral symmetry is maintained in our calculations with overlap\nfermions, and its most important consequence here is that the operators\nmeasuring $g_2$ do not show any of the power-divergent mixings with operators\nof lower dimension which are present in the Wilson case. Many of our results\nfor Wilson fermions are also new; for the remaining ones, we agree with the\nliterature except in one case. The computations have been carried out using the\nsymbolic language FORM, in a general covariant gauge, which turns out also to\nbe useful in checking the gauge-invariance of the final results.", "category": "hep-lat" }, { "text": "Roper Resonance in 2+1 Flavor QCD: The low-lying even-parity states of the nucleon are explored in lattice QCD\nusing the PACS-CS collaboration 2+1-flavor dynamical-QCD gauge-field\nconfigurations made available through the International Lattice Datagrid\n(ILDG). The established correlation-matrix approach is used, in which various\nfermion source and sink smearings are utilized to provide an effective basis of\ninterpolating fields to span the space of low-lying energy eigenstates. Of\nparticular interest is the nature of the first excited state of the nucleon,\nthe $N{1/2}^{+}$ Roper resonance of $P_{11}$ pion-nucleon scattering. The Roper\nstate of the present analysis approaches the physical mass, displaying\nsignificant chiral curvature at the lightest quark mass. These full QCD\nresults, providing the world's first insight into the nucleon mass spectrum in\nthe light-quark regime, are significantly different from those of quenched QCD\nand provide interesting insights into the dynamics of QCD.", "category": "hep-lat" }, { "text": "P-wave heavy-light mesons using NRQCD and D234: The masses of S- and P-wave heavy-light mesons are computed in quenched QCD\nusing a classically and tadpole-improved action on anisotropic lattices. Of\nparticular interest are the splittings among P-wave states, which have not yet\nbeen resolved experimentally; even the ordering of these states continues to be\ndiscussed in the literature. The present work leads to upper bounds for these\nsplittings, and is suggestive, but not conclusive, about the ordering.", "category": "hep-lat" }, { "text": "Non-perturbative renormalization of left-left four-fermion operators in\n quenched lattice QCD: We define a family of Schroedinger Functional renormalization schemes for the\nfour-quark multiplicatively renormalizable operators of the $\\Delta F = 1$ and\n$\\Delta F = 2$ effective weak Hamiltonians. Using the lattice regularization\nwith quenched Wilson quarks, we compute non-perturbatively the renormalization\ngroup running of these operators in the continuum limit in a large range of\nrenormalization scales. Continuum limit extrapolations are well controlled\nthanks to the implementation of two fermionic actions (Wilson and Clover). The\nratio of the renormalization group invariant operator to its renormalized\ncounterpart at a low energy scale, as well as the renormalization constant at\nthis scale, is obtained for all schemes.", "category": "hep-lat" }, { "text": "Quark mass dependence of the low-lying charmed mesons at one loop in\n HH$\u03c7$PT: We study the light and heavy quark mass dependence of the low-lying charmed\nmesons in the framework of one-loop HH$\\chi$PT. The low energy constants are\ndetermined by analyzing the available lattice data from different LQCD\nsimulations. Model selection tools are implemented to determine the relevant\nparameters as required by data with a higher precision. Discretization and\nother effects due to the charm quark mass setting are discussed.", "category": "hep-lat" }, { "text": "Exact Chiral Fermions and Finite Density on Lattice: Any mu^2-divergence is shown analytically to be absent for a class of actions\nfor Overlap and Domain Wall Fermions with nonzero chemical potential. All such\nactions are, however, shown to violate the chiral invariance. While the\nparameter M of these actions can be shown to be irrelevant in the continuum\nlimit, as expected, it is shown numerically that the continuum limit can be\nreached with relatively coarser lattices for M in the range of 1.5-1.6.", "category": "hep-lat" }, { "text": "Antisymmetric and other subleading corrections to scaling in the local\n potential approximation: For systems in the universality class of the three-dimensional Ising model we\ncompute the critical exponents in the local potential approximation (LPA), that\nis, in the framework of the Wegner-Houghton equation. We are mostly interested\nin antisymmetric corrections to scaling, which are relatively poorly studied.\nWe find the exponent for the leading antisymmetric correction to scaling\n$\\omega_A \\approx 1.691$ in the LPA. This high value implies that such\ncorrections cannot explain asymmetries observed in some Monte Carlo\nsimulations.", "category": "hep-lat" }, { "text": "Lattice QCD investigation of a doubly-bottom $\\bar{b} \\bar{b} u d$\n tetraquark with quantum numbers $I(J^P) = 0(1^+)$: We use lattice QCD to investigate the spectrum of the $\\bar{b} \\bar{b} u d$\nfour-quark system with quantum numbers $I(J^P) = 0(1^+)$. We use five different\ngauge-link ensembles with $2+1$ flavors of domain-wall fermions, including one\nat the physical pion mass, and treat the heavy $\\bar{b}$ quark within the\nframework of lattice nonrelativistic QCD. Our work improves upon previous\nsimilar computations by considering in addition to local four-quark\ninterpolators also nonlocal two-meson interpolators and by performing a\nL\\\"uscher analysis to extrapolate our results to infinite volume. We obtain a\nbinding energy of $(-128 \\pm 24 \\pm 10) \\, \\textrm{MeV}$, corresponding to the\nmass $(10476 \\pm 24 \\pm 10) \\, \\textrm{MeV}$, which confirms the existence of a\n$\\bar{b} \\bar{b} u d$ tetraquark that is stable with respect to the strong and\nelectromagnetic interactions.", "category": "hep-lat" }, { "text": "Stable solvers for real-time Complex Langevin: This study explores the potential of modern implicit solvers for stochastic\npartial differential equations in the simulation of real-time complex Langevin\ndynamics. Not only do these methods offer asymptotic stability, rendering the\nissue of runaway solution moot, but they also allow us to simulate at\ncomparatively largeLangevin time steps, leading to lower computational cost. We\ncompare different ways of regularizing the underlying path integral and\nestimate the errors introduced due to the finite Langevin time. Based on that\ninsight, we implement benchmark (non-)thermal simulations of the quantum\nanharmonic oscillator on the canonical Schwinger-Keldysh contour of short\nreal-time extent.", "category": "hep-lat" }, { "text": "Note on the Lattice Fermion Chiral Symmetry Group: The group structure of the variant chiral symmetry discovered by Luscher in\nthe Ginsparg-Wilson description of lattice chiral fermions is analyzed. It is\nshown that the group contains an infinite number of linearly independent\nsymmetry generators, and the Lie algebra is given explicitly. CP is an\nautomorphism of the chiral group, and the CP transformation properties of the\nsymmetry generators is found. Features of the currents associated with these\nsymmetries are discussed, including the fact that some different, non-commuting\nsymmetry generators lead to the same Noether current. These strange features\noccur in all implementations of lattice fermions based on the Ginsparg-Wilson\nrelation, including overlap, domain-wall, and perfect-action chiral fermions.\nThe conclusions are illustrated in a solvable example, free overlap fermions.", "category": "hep-lat" }, { "text": "Intrinsic quark transverse momentum in the nucleon from lattice QCD: A better understanding of transverse momentum (k_T-) dependent quark\ndistributions in a hadron is needed to interpret several experimentally\nobserved large angular asymmetries and to clarify the fundamental role of gauge\nlinks in non-abelian gauge theories. Based on manifestly non-local gauge\ninvariant quark operators we introduce process-independent k_T-distributions\nand study their properties in lattice QCD. We find that the longitudinal and\ntransverse momentum dependence approximately factorizes, in contrast to the\nbehavior of generalized parton distributions. The resulting quark\nk_T-probability densities for the nucleon show characteristic dipole\ndeformations due to correlations between intrinsic k_T and the quark or nucleon\nspin. Our lattice calculations are based on N_f=2+1 mixed action propagators of\nthe LHP collaboration.", "category": "hep-lat" }, { "text": "Singularities of QCD in the complex chemical potential plane: We study the thermodynamic singularities of QCD in the complex chemical\npotential plane by a numerical simulation of lattice QCD, and discuss a method\nto understand the nature of the QCD phase transition at finite density from the\ninformation of the singularities. The existence of singular points at which the\npartition function (Z) vanishes is expected in the complex plane. These are\ncalled Lee-Yang zeros or Fisher zeros. We investigate the distribution of these\nsingular points using the data obtained by a simulation of two-flavor QCD with\np4-improved staggered quarks. The convergence radius of a Taylor expansion of\nln Z in terms of the chemical potential is also discussed.", "category": "hep-lat" }, { "text": "Longitudinal and transverse meson correlators in the deconfined phase\n from the lattice: It has long been known that QCD undergoes a deconfining phase transition at\nhigh temperature. One of the consequent features of this new, quark-gluon phase\nis that hadrons become unbounded. In this talk meson correlation functions at\nnon-zero momentum are studied in the deconfined phase using the Maximum Entropy\nMethod.", "category": "hep-lat" }, { "text": "A new lattice measurement for potentials between static SU(3) sources: In this article, a new calculation of static potentials between sources of\ndifferent representations in SU(3) gauge group is presented. The results of\nauthor's previous study \\cite{Deld00} at the smallest lattice spacing\n$a_{s}\\simeq0.11$~ fm are shown to have been affected by finite volume effects.\nWithin statistical errors, the new results obtained here are still in agreement\nwith both, Casimir scaling and flux tube counting. There is also no\ncontradiction to the results obtained in Ref.~ \\cite{Bali00} which however\nexclude flux counting.", "category": "hep-lat" }, { "text": "Magnetic properties of light nuclei from lattice QCD: After a short review of Lattice QCD methodology and techniques, I summarize\nrecent results of Lattice QCD calculations of the interactions of nucleons and\nlight nuclei with magnetic fields at pion masses of 805 MeV and 450 MeV.\nInterestingly, the magnetic moments are found to be consistent with the\nexperimental values when given in terms of natural nuclear magnetons. The very\nlow-energy cross section for $np\\rightarrow d\\gamma$ is calculated and found to\nagree with the experimental measurement. First calculations of the magnetic\npolarizabilities of light nuclei are presented, with a large isovector\npolarizability observed for the nucleon at these heavier pion masses.", "category": "hep-lat" }, { "text": "Reweighting Lefschetz Thimbles: We present a novel reweighting technique to calculate the relative weights in\nthe Lefschetz thimble decomposition of a path integral. Our method is put to\nwork using a $U(1)$ one-link model providing for a suitable testing ground and\nsharing many features with realistic gauge theories with fermions at finite\ndensity. We discuss prospects and future challenges to our method.", "category": "hep-lat" }, { "text": "Abelian Dyons in the Maximal Abelian Projection of SU(2) Gluodynamics: Correlations of the topological charge Q, the electric current J^e and the\nmagnetic current J^m in SU(2) lattice gauge theory in the Maximal Abelian\nprojection are investigated. It occurs that the correlator <> is\nnonzero for a wide range of values of the bare charge. It is shown that: (i)\nthe abelian monopoles in the Maximal Abelian projection are dyons which carry\nfluctuating electric charge; (ii) the sign of the electric charge e(x)\ncoincides with that of the product of the monopole charge m(x) and the\ntopological charge density Q(x).", "category": "hep-lat" }, { "text": "Extracting excited states from lattice QCD: the Roper resonance: We present a new method for extracting excited states from a single two-point\ncorrelation function calculated on the lattice. Our method simply combines the\ncorrelation function evaluated at different time slices so as to ``subtract''\nthe leading exponential decay (ground state) and to give access to the first\nexcited state. The method is applied to a quenched lattice study (volume = 24^3\nx 64, beta = 6.2, 1/a = 2.55 GeV) of the first excited state of the nucleon\nusing the local interpolating operator O = [uT C gamma5 d] u. The results are\nconsistent with the identification of our extracted excited state with the\nRoper resonance N'(1440). The switching of the level ordering with respect to\nthe negative-parity partner of the nucleon, N*(1535), is not seen at the\nsimulated quark masses and, basing on crude extrapolations, is tentatively\nexpected to occur close to the physical point.", "category": "hep-lat" }, { "text": "Electromagnetic properties of doubly charmed baryons in Lattice QCD: We compute the electromagnetic properties of \\Xi_cc baryons in 2+1 flavor\nLattice QCD. By measuring the electric charge and magnetic form factors of\n\\Xi_cc baryons, we extract the magnetic moments, charge and magnetic radii as\nwell as the \\Xi_cc \\Xi_cc \\rho coupling constant, which provide important\ninformation to understand the size, shape and couplings of the doubly charmed\nbaryons. We find that the two heavy charm quarks drive the charge radii and the\nmagnetic moment of \\Xi_cc to smaller values as compared to those of, e.g., the\nproton.", "category": "hep-lat" }, { "text": "B- and D-meson decay constants from three-flavor lattice QCD: We calculate the leptonic decay constants of B_{(s)} and D_{(s)} mesons in\nlattice QCD using staggered light quarks and Fermilab bottom and charm quarks.\nWe compute the heavy-light meson correlation functions on the MILC\nasqtad-improved staggered gauge configurations which include the effects of\nthree light dynamical sea quarks. We simulate with several values of the light\nvalence- and sea-quark masses (down to ~m_s/10) and at three lattice spacings\n(a ~ 0.15, 0.12, and 0.09 fm) and extrapolate to the physical up and down quark\nmasses and the continuum using expressions derived in heavy-light meson\nstaggered chiral perturbation theory. We renormalize the heavy-light axial\ncurrent using a mostly nonperturbative method such that only a small correction\nto unity must be computed in lattice perturbation theory and higher-order terms\nare expected to be small. We obtain f_{B^+} = 196.9(8.9) MeV, f_{B_s} =\n242.0(9.5) MeV, f_{D^+} = 218.9(11.3) MeV, f_{D_s} = 260.1(10.8) MeV, and the\nSU(3) flavor-breaking ratios f_{B_s}/f_{B} = 1.229(26) and f_{D_s}/f_{D} =\n1.188(25), where the numbers in parentheses are the total statistical and\nsystematic uncertainties added in quadrature.", "category": "hep-lat" }, { "text": "Quenched hadron spectroscopy with improved staggered quark action: We investigate light hadron spectroscopy with an improved quenched staggered\nquark action. We compare the results obtained with an improved gauge plus an\nimproved quark action, an improved gauge plus standard quark action, and the\nstandard gauge plus standard quark action. Most of the improvement in the\nspectroscopy results is due to the improved gauge sector. However, the improved\nquark action substantially reduces violations of Lorentz invariance, as\nevidenced by the meson dispersion relations.", "category": "hep-lat" }, { "text": "Non-perturbative improvement of bilinears in unquenched QCD: We describe how the improvement of quark bilinears generalizes from quenched\nto unquenched QCD, and discuss which of the additional improvement constants\ncan be determined using Ward Identities.", "category": "hep-lat" }, { "text": "In search of a scaling scalar glueball: Anisotropic lattices are an efficient means of studying the glueballs of QCD,\nhowever problems arise with simulations of the lightest, scalar state. The mass\nis strongly dependent on the lattice spacing, even when a mean-field improved\ngluon action is used. The nature and cause of these errors are discussed and\nthe scaling properties of the scalar from different lattice actions are\npresented.", "category": "hep-lat" }, { "text": "Finite size scaling in CP(N-1) models: Finite size effects in Euclidean ${\\rm CP}^{N-1}$ models with periodic\nboundary conditions are investigated by means of the $1/N$ expansion and by\nMonte Carlo simulations. Analytic and numerical results for magnetic\nsusceptibility and correlation length are compared and found to agree for small\nvolumes. For large volumes a discrepancy is found and explained as an effect of\nthe physical bound state extension. The leading order finite size effects on\nthe Abelian string tension are computed and compared with simulations finding\nagreement. Finite size dependence of topological quantities is also discussed.", "category": "hep-lat" }, { "text": "Determination of the mass anomalous dimension for $N_f=12$ and $N_f=9$\n SU($3$) gauge theories: We show the numerical simulation result for the mass anomalous dimension of\nthe SU($3$) gauge theory coupled to $N_f = 12$ fundamental fermions. We use two\nindependent methods, namely the step scaling method and the hyperscaling method\nof the Dirac mode number, to determine the anomalous dimension in the vicinity\nof the infrared fixed point of the theory. We show the continuum extrapolations\nkeeping the renormalized coupling constant as a reference in both analyses.\n Furthermore, some recent works seems to suggest the lower boundary of the\nconformal window of the SU($3$) gauge theory exists between $N_f=8$ and $10$.\nWe also briefly report our new project, in which the numerical simulation of\nthe SU($3$) gauge theory coupled to $N_f=9$ fundamental fermions has been\nperformed.", "category": "hep-lat" }, { "text": "Contribution of the charm quark to the \u0394I=1/2 rule: We report on the progress of our ongoing project to quantify the role of the\ncharm quark in the non-leptonic decay of a kaon into two pions. The effect of\nits associated mass scale in the dynamics underlying the \\Delta I = 1/2 rule\ncan be studied by monitoring the dependence of kaon decay amplitudes on the\ncharm quark mass using an effective \\Delta S = 1 weak Hamiltonian. In contrast\nto commonly used approaches the charm quark is kept as an active degree of\nfreedom. Quenched results in the GIM limit have shown that a significant part\nof the \\Delta I = 1/2 enhancement is purely due to low-energy QCD effects.\nMoving away from the GIM limit involves the computation of diagrams containing\nclosed quark loops which requires new variance reduction techniques in order to\ndetermine the relevant weak effective low-energy couplings. We employ a\ncombination of low-mode averaging and stochastic volume sources in order to\ncompute these diagrams and observe a significant improvement in the statistical\nsignal.", "category": "hep-lat" }, { "text": "Spectrum of Mesons and Baryons with $b$ Quarks: We present highlights of the spectrum of mesons and baryons calculated using\nNRQCD for heavy quarks and tadpole improved clover action for the light quarks.", "category": "hep-lat" }, { "text": "Instantaneous interquark potential in generalized Landau gauge in SU(3)\n lattice QCD: a possible gauge for the quark potential model: We investigate \"instantaneous interquark potential\", an interesting\ngauge-dependent quantity defined from the spatial correlator $<\\mathrm{Tr}\n[U_4^\\dagger(s)U_4(s')]>$ of the temporal link-variable $U_4$, in detail in\ngeneralized Landau gauge using SU(3) quenched lattice QCD. While the\ninstantaneous potential has no linear part in the Landau gauge, in the Coulomb\ngauge, it is expressed by the Coulomb plus linear potential, where the slope is\n2-3 times larger than the physical string tension, and the lowest energy state\nis considered to be a gluon-chain state. Using the generalized Landau gauge, we\nfind that the instantaneous potential can be continuously described between the\nLandau and the Coulomb gauges, and it approximately reproduces the physical\ninterquark potential in a specific intermediate gauge, which we call\n\"$\\lambda_C$-gauge\". This $\\lambda_C$-gauge is expected to provide a\nquark-potential-model picture, where dynamical gluons do not appear. We also\ninvestigate $T$-length terminated Polyakov-line correlator and its\ncorresponding \"finite-time potential\" in generalized Landau gauge.", "category": "hep-lat" }, { "text": "Vacuum alignment and lattice artifacts: When a subgroup of the flavor symmetry group of a gauge theory is weakly\ncoupled to additional gauge fields, the vacuum tends to align such that the\ngauged subgroup is unbroken. At the same time, the lattice discretization\ntypically breaks the flavor symmetry explicitly, and can give rise to new\nlattice-artifact phases with spontaneously broken symmetries. We discuss the\ninterplay of these two phenomena, using chiral lagrangian techniques. Our first\nexample is two-flavor Wilson QCD coupled to electromagnetism. We also consider\nexamples of theories with staggered fermions, and demonstrate that recent\nclaims in the literature based on the use of staggered fermions are incorrect.", "category": "hep-lat" }, { "text": "Broken Symmetries from Minimally Doubled Fermions: Novel chirally symmetric fermion actions containing the minimum amount of\nfermion doubling have been recently proposed in the literature. We study the\nsymmetries and renormalization of these actions and find that in each case,\ndiscrete symmetries, such as parity and time-reversal, are explicitly broken.\nConsequently, when the gauge interactions are included, these theories\nradiatively generate relevant and marginal operators. Thus the restoration of\nthese symmetries and the approach to the continuum limit require the\nfine-tuning of several parameters. With some assumptions, we show that this\nbehavior is unavoidable for actions displaying minimal fermion doubling.", "category": "hep-lat" }, { "text": "Proton and neutron electromagnetic form factors from lattice QCD: The electromagnetic form factors of the proton and the neutron are computed\nwithin lattice QCD using simulations with quarks masses fixed to their physical\nvalues. Both connected and disconnected contributions are computed. We analyze\ntwo new ensembles of $N_f = 2$ and $N_f = 2 + 1 + 1$ twisted mass\nclover-improved fermions and determine the proton and neutron form factors, the\nelectric and magnetic radii, and the magnetic moments. We use several values of\nthe sink-source time separation in the range of 1.0 fm to 1.6 fm to ensure\nground state identification. Disconnected contributions are calculated to an\nunprecedented accuracy at the physical point. Although they constitute a small\ncorrection, they are non-negligible and contribute up to 15% for the case of\nthe neutron electric charge radius.", "category": "hep-lat" }, { "text": "Remarks on abelian dominance: We used a renormalisation group based smoothing to address two questions\nrelated to abelian dominance. Smoothing drastically reduces short distance\nfluctuations but it preserves the long distance physical properties of the\nSU(2) configurations. This enabled us to extract the abelian heavy-quark\npotential from time-like Wilson loops on Polyakov gauge projected\nconfigurations. We obtained a very small string tension which is inconsistent\nwith the string tension extracted from Polyakov loop correlators. This shows\nthat the Polyakov gauge projected abelian configurations do not have a\nconsistent physical meaning. We also applied the smoothing on SU(2)\nconfigurations to test how sensitive abelian dominance in the maximal abelian\ngauge is to the short distance fluctuations. We found that on smoothed SU(2)\nconfigurations the abelian string tension was about 30% smaller than the SU(2)\nstring tension which was unaffected by smoothing. This suggests that the\napproximate abelian dominance found with the Wilson action is probably an\naccident and it has no fundamental physical relevance.", "category": "hep-lat" }, { "text": "Entanglement entropy of SU(3) Yang-Mills theory: We calculate the entanglement entropy using a SU(3) quenched lattice gauge\nsimulation. We find that the entanglement entropy scales as $1/l^2$ at small\n$l$ as in the conformal field theory. Here $l$ is the size of the system, whose\ndegrees of freedom is left after the other part are traced out. The derivative\nof the entanglement entropy with respect to $l$ hits zero at about $l^{\\ast} =\n0.6 \\sim 0.7$ [fm] and vanishes above the length. It may imply that the\nYang-Mills theory has the mass gap of the order of $1/l^{\\ast}$. Within our\nstatistical errors, no discontinuous change can be seen in the entanglement\nentropy. We discuss also a subtle point appearing in gauge systems when we\ndivide a system with cuts.", "category": "hep-lat" }, { "text": "'t Hooft loop and the phases of SU(2) LGT: We analyze the vacuum structure of SU(2) lattice gauge theories in D=2,3,4,\nconcentrating on the stability of 't Hooft loops. High precision calculations\nhave been performed in D=3; similar results hold also for D=4 and D=2. We\ndiscuss the impact of our findings on the continuum limit of Yang-Mills\ntheories.", "category": "hep-lat" }, { "text": "Real-Time-Evolution of Heavy Quarks in the Glasma: We introduce a novel real-time formulation of lattice NRQCD designed for\nsimulations in the background of an highly occupied gluon field. By evolving\nquarks in the background of a dynamically evolving gluon field we computed the\ntime-evolution of heavy-quarkonium spectral functions as well as the static and\nfor finitely heavy quarks generalised potential. We conclude that the back\nreaction of the quarks is necessary for any binding process. Here we discuss\nthe methodology, our results and the origin of the absence of a binding\nprocess.", "category": "hep-lat" }, { "text": "Decay constants of B and D mesons from improved relativistic lattice QCD\n with two flavours of sea quarks: We present a calculation of the B and D meson decay constants in lattice QCD\nwith two (Nf=2) flavours of light dynamical quarks, using an O(a)-improved\nWilson action for both light and heavy quarks and a renormalization-group\nimproved gauge action. Simulations are made at three values of lattice spacing\na=0.22, 0.16, 0.11 fm and four values of sea quark mass in the range m_PS/m_V\n\\~= 0.8-0.6. Our estimate for the continuum values of the decay constants are\nfBd = 208(10)(11) MeV, fBs = 250(10)(13)(^{+8}_{-0}) MeV, fDd = 225(14)(14)\nMeV, fDs = 267(13)(17)(^{+10}_{-0}) MeV for Nf=2 where the statistical and\nsystematic errors are separately listed, and the third error for fBs and fDs\nshow uncertainty of determination of strange quark mass. We also carry out a\nset of quenched simulations using the same action to make a direct examination\nof sea quark effects. Taking the ratio of results for Nf=2 and Nf=0, we obtain\nfb^{Nf=2}/fb^{Nf=0} = 1.11(6), fbs^{Nf=2}/fbs^{Nf=0} = 1.14(5),\nfd^{Nf=2}/\\fd^{Nf=0} = 1.03(6), fds^{Nf=2}/\\fds^{Nf=0} = 1.07(5). They show a\n10-15% increase in the Nf=2 results over those of Nf=0 for the B meson decay\nconstants, while evidence for such a trend is statistically less clear for the\nD meson decay constants.", "category": "hep-lat" }, { "text": "Lambda-parameter of lattice QCD with the overlap-Dirac operator: We compute the ratio $\\Lambda_L/\\Lambda_{\\bar{MS}}$ between the scale\nparameter $\\Lambda_L$, associated with a lattice formulation of QCD using the\noverlap-Dirac operator, and $\\Lambda_{\\bar{MS}}$ of the $\\bar{\\rm MS}$\nrenormalization scheme. To this end, the necessary one-loop relation between\nthe lattice coupling $g_0$ and the coupling renormalized in the $\\bar{{\\rm\nMS}}$ scheme is calculated, using the lattice background field technique.", "category": "hep-lat" }, { "text": "Behavior and finite-size effects of the sixth order cumulant in the\n three-dimensional Ising universality class: The high-order cumulants of conserved charges are suggested to be sensitive\nobservables to search for the critical point of Quantum Chromodynamics (QCD).\nThis has been calculated to the sixth order in experiments. Corresponding\ntheoretical studies on the sixth order cumulant are necessary. Based on the\nuniversality of the critical behavior, we study the temperature dependence of\nthe sixth order cumulant of the order parameter using the parametric\nrepresentation of the three-dimensional Ising model, which is expected to be in\nthe same universality class as QCD. The density plot of the sign of the sixth\norder cumulant is shown on the temperature and external magnetic field plane.\nWe found that at non-zero external magnetic field, when the critical point is\napproached from the crossover side, the sixth order cumulant has a negative\nvalley. The width of the negative valley narrows with decreasing external\nfield. Qualitatively, the trend is similar to the result of Monte Carlo\nsimulation on a finite-size system. Quantitatively, the temperature of the sign\nchange is different. Through Monte Carlo simulation of the Ising model, we\ncalculated the sixth order cumulant of different sizes of systems. We discuss\nthe finite-size effects on the temperature at which the cumulant changes sign.", "category": "hep-lat" }, { "text": "Simulating Yang-Mills theories with a complex coupling: We propose a novel simulation strategy for Yang-Mills theories with a complex\ncoupling, based on the Lefschetz thimble decomposition. We envisage, that the\napproach developed in the present work, can also be adapted to QCD at finite\ndensity, and real time simulations.\n Simulations with Lefschetz thimbles offer a potential solution to sign\nproblems in Monte Carlo calculations within many different models with complex\nactions. We discuss the structure of Generalized Lefschetz thimbles for pure\nYang-Mills theories with a complex gauge coupling $\\beta$ and show how to\nincorporate the gauge orbits. We propose to simulate such theories on the union\nof the tangential manifolds to the relevant Lefschetz thimbles attached to the\ncritical manifolds of the Yang-Mills action. We demonstrate our algorithm on a\n(1+1)-dimensional U(1) model and discuss how, starting from the main thimble\nresult, successive subleading thimbles can be taken into account via a\nreweighting approach. While we face a residual sign problem, our novel approach\nperforms exponentially better than the standard reweighting approach.", "category": "hep-lat" }, { "text": "D-branes, Wilson Bags, and Coherent Topological Charge Structure in QCD: Monte Carlo studies of pure glue SU(3) gauge theory using the overlap-based\ntopological charge operator have revealed a laminar structure in the QCD vacuum\nconsisting of extended, thin, coherent, locally 3-dimensional sheets of\ntopological charge embedded in 4D space, with opposite sign sheets interleaved.\nStudies of localization properties of Dirac eigenmodes have also shown evidence\nfor the delocalization of low-lying modes on effectively 3-dimensional\nsurfaces. In this talk, I review some theoretical ideas which suggest the\npossibility of 3-dimensionally coherent topological charge structure in\n4-dimensional gauge theory and provide a possible interpretation of the\nobserved structure. I begin with Luscher's ``Wilson bag'' integral over the\n3-index Chern-Simons tensor. The analogy with a Wilson loop as a charged world\nline in 2-dimensional $CP^{N-1}$ sigma models suggests that the Wilson bag\nsurface represents the world volume of a physical membrane. The large-N chiral\nLagrangian arguments of Witten also indicate the existence of multiple\n``k-vacuum'' states with discontinuous transitions between k-vacua at $\\theta=$\nodd multiples of $\\pi$. The domain walls between these vacua have the\nproperties of a Wilson bag surface. Finally, I review the AdS/CFT duality view\nof $\\theta$ dependence in QCD. The dual realtionship between topological charge\nin gauge theory and Ramond-Ramond charge in type IIA string theory suggests\nthat the coherent topological charge sheets observed on the lattice are the\nholographic image of wrapped D6 branes.", "category": "hep-lat" }, { "text": "Perfect discretizations of differential operators: We investigate an approach for the numerical solution of differential\nequations which is based on the perfect discretization of actions. Such perfect\ndiscretizations show up at the fixed points of renormalization group\ntransformations. This technique of integrating out the high momentum degrees of\nfreedom with a path integral has been mainly used in lattice field theory,\ntherefore our study of its application to PDE's explores new possibilities. We\ncalculate the perfect discretized Laplace operator for several non-trivial\nboundary conditions analytically and numerically. Then we construct a\nparametrization of the perfect Laplace operator and we show that with this\nparametrization discretization errors -- or computation time -- can be reduced\ndramatically compared to the standard discretization.", "category": "hep-lat" }, { "text": "Deconfinement Phase Transition in Bosonic BMN Model at General Coupling: We present our analysis of the deconfinement phase transition in the bosonic\nBMN matrix model. The model is investigated using a non-perturbative lattice\nframework. We used the Polyakov loop as the order parameter to monitor the\nphase transition, and the results were verified using the separatrix ratio. The\ncalculations are performed using a large number of colors and a broad range of\ntemperatures for all couplings. Our results indicate a first-order phase\ntransition in this theory for all the coupling values that connect the\nperturbative and non-perturbative regimes of the theory.", "category": "hep-lat" }, { "text": "Berry phase in lattice QCD: We propose the lattice QCD calculation of the Berry phase which is defined by\nthe ground state of a single fermion. We perform the ground-state projection of\na single-fermion propagator, construct the Berry link variable on a\nmomentum-space lattice, and calculate the Berry phase. As the first\napplication, the first Chern number of the (2+1)-dimensional Wilson fermion is\ncalculated by the Monte Carlo simulation.", "category": "hep-lat" }, { "text": "Minimally doubled fermions and their renormalization: Minimally doubled fermions have been proposed as a strictly local\ndiscretization of the QCD quark action, which also preserves chiral symmetry at\nfinite cut-off. We study the renormalization and mixing properties of two\nparticular realizations of minimally doubled fermions in lattice perturbation\ntheory at one loop, and we construct conserved axial currents which have a\nsimple form involving only nearest-neighbours sites. We also introduce a\nnotation which allows a unified description of the renormalization properties\nof both actions.", "category": "hep-lat" }, { "text": "Fast Partitioning of Pauli Strings into Commuting Families for\n Expectation Value Measurements of Dense Operators: The cost of measuring quantum expectation values of an operator can be\nreduced by grouping the Pauli string ($SU(2)$ tensor product) decomposition of\nthe operator into maximally commuting sets. We detail an algorithm, presented\nin [1], to partition the full set of $m$-qubit Pauli strings into the minimal\nnumber of commuting families, and benchmark the performance with dense\nHamiltonians on IBM hardware. Here we also compare how our method scales\ncompared to graph-theoretic techniques for the generally commuting case.", "category": "hep-lat" }, { "text": "The pion form factor on the lattice at zero and finite temperature: We calculate the electromagnetic form factor of the pion in quenched lattice\nQCD. The non-perturbatively improved Sheikoleslami-Wohlert lattice action is\nused together with the consistently O(a) improved current. We calculate the\npion form factor for masses down to m_pi = 360 MeV, extract the charge radius,\nand extrapolate toward the physical pion mass. In the second part, we discuss\nresults for the pion form factor and charge radius at 0.93 T_c and compare with\nzero temperature results.", "category": "hep-lat" }, { "text": "Semi-leptonic decays of heavy mesons and the Isgur-Wise function in\n quenched lattice QCD: The form factors for the semi-leptonic B->D and B->D* decays are evaluated in\nquenched lattice QCD at two different values of the coupling, beta=6.0 and 6.2.\nThe action and the operators are fully O(a) non-perturbatively improved. The\nslope of the Isgur-Wise function is evaluated, and found to be\nrho^2=0.83^{+15+24}_{-11-1} (quoted errors are statistical and systematic\nrespectively). Ratios of form factors are evaluated and compared to\nexperimental determinations.", "category": "hep-lat" }, { "text": "Thermodynamics of Two Flavor QCD to Sixth Order in Quark Chemical\n Potential: We present results of a simulation of 2-flavor QCD on a 4x16^3 lattice using\np4-improved staggered fermions with bare quark mass m/T=0.4. Derivatives of the\nthermodynamic grand canonical partition function Z(V,T,mu_u,mu_d) with respect\nto chemical potentials mu_(u,d) for different quark flavors are calculated up\nto sixth order, enabling estimates of the pressure and the quark number density\nas well as the chiral condensate and various susceptibilities as functions of\nmu_q = (mu_u + mu_d)/2 via Taylor series expansion. Furthermore, we analyze\nbaryon as well as isospin fluctuations and discuss the relation between the\nradius of convergence of the Taylor series and the chiral critical point in the\nQCD phase diagram. We argue that bulk thermodynamic observables do not, at\npresent, provide direct evidence for the existence of a chiral critical point\nin the QCD phase diagram. Results are compared to high temperature perturbation\ntheory as well as a hadron resonance gas model.", "category": "hep-lat" }, { "text": "Taste non-Goldstone, flavor-charged pseudo-Goldstone boson masses in\n staggered chiral perturbation theory: We calculate the masses of taste non-Goldstone pions and kaons in staggered\nchiral perturbation theory through next-to-leading order in the standard power\ncounting. The results can be used to quantitatively understand taste violations\nin existing lattice data generated with staggered fermions and to extract the\n$u$, $d$, and $s$ quark masses and Gasser-Leutwyler parameters from the\nexperimentally observed spectrum. The expressions for the non-Goldstone masses\ncontain low-energy couplings unique to the non-Goldstone sector. With two\nexceptions these enter as coefficients of analytic terms; all the new couplings\ncan be fixed by performing spectrum calculations. We report one-loop results\nfor the quenched case and the fully dynamical and partially quenched 1+1+1 and\n2+1 flavor cases in the chiral SU(3) and SU(2) theories.", "category": "hep-lat" }, { "text": "Comparison of different source calculations in two-nucleon channel at\n large quark mass: We investigate a systematic error coming from higher excited state\ncontributions in the energy shift of light nucleus in the two-nucleon channel\nby comparing two different source calculations with the exponential and wall\nsources. Since it is hard to obtain a clear signal of the wall source\ncorrelation function in a plateau region, we employ a large quark mass as the\npion mass is 0.8 GeV in quenched QCD. We discuss the systematic error in the\nspin-triplet channel of the two-nucleon system, and the volume dependence of\nthe energy shift.", "category": "hep-lat" }, { "text": "Moments of parton evolution probabilities on the lattice within the\n Schroedinger functional scheme: We define, within the Schroedinger functional scheme (SF), the matrix\nelements of the twist-2 operators corresponding to the first two moments of\nnon-singlet parton densities. We perform a lattice one-loop calculation that\nfixes the relation between the SF scheme and other common schemes and shows the\nmain source of lattice artefacts. This calculation sets the basis for a\nnumerical evaluation of the non-perturbative running of parton densities.", "category": "hep-lat" }, { "text": "O(4) scaling analysis in two-flavor QCD at finite temperature and\n density with improved Wilson quarks: We study the curvature of the chiral transition/crossover line between the\nlow-temperature hadronic phase and the high-temperature quark-gluon-plasma\nphase at low densities, performing simulations of two-flavor QCD with improved\nWilson quarks. After confirming that the chiral order parameter defined by a\nWard-Takahashi identity is consistent with the scaling of the O(4) universality\nclass at zero chemical potential, we extend the scaling analysis to finite\nchemical potential to determine the curvature of the chiral\ntransition/crossover line at low densities assuming the O(4) universality. To\nconvert the curvature in lattice units to that of the $T_c(\\mu_B)$ in physical\nunits, we evaluate the lattice scale applying a gradient flow method. We find\n$\\kappa=0.0006(1)$ in the chiral limit, which is much smaller than that\nobtained in (2+1)-flavor QCD with improved staggered quarks.", "category": "hep-lat" }, { "text": "Status of the MILC calculation of electromagnetic contributions to\n pseudoscalar masses: We calculate pseudoscalar masses on gauge configurations containing the\neffects of 2+1 flavors of dynamical asqtad quarks and quenched\nelectromagnetism. The lattice spacings vary from 0.12 to 0.06 fm. The masses\nare fit with staggered chiral perturbation theory including NLO electromagnetic\nterms. We attempt to extract the fit parameters for the electromagnetic\ncontributions, while taking into account the finite volume effects, and\nextrapolate them to the physical limit.", "category": "hep-lat" }, { "text": "Spectroscopy of two dimensional N=2 Super Yang Mills theory: Albeit the standard model is the most successful model of particles physics,\nit still has some theoretical shortcomings, for instance the hierarchy problem,\nthe absence of dark matter, etc. Supersymmetric extensions of the standard\nmodel could be a possible solution to these problems. One of the building\nblocks of these supersymmetric models are supersymmetric gauge theories. It is\nexpected that they exhibit interesting features like confinement, chiral\nsymmetry breaking, magnetic monopoles and the like. We present new results on\nN=2 Super Yang Mills theory in two dimensions. The lattice action is derived by\na dimensional reduction of the N=1 Super Yang Mills theory in four dimensions.\nBy preserving the R symmetry of the four dimensional model we can exploit Ward\nidentities to fine tune our parameters of the model to obtain the chiral and\nsupersymmetric continuum limit. This allows us to calculate the mass spectrum\nat the physical point and compare these results with effective field theories.", "category": "hep-lat" }, { "text": "Fast algorithms for simulating chiral fermions in U(1)lattice gauge\n theory: In order to develop fast inversion algorithms we have used overlap solvers in\ntwo dimensions. Lattice QED theory with U(1) group symmetry in two dimensional\nspace-times dimensions has always been a testing ground for algorithms. By the\nother side, motivated by our previews work that the two-grid algorithm converge\nfaster than the standard iterative methods for overlap inversion but not for\nall quark masses, we thought to test this idea in less dimensions such as U(1)\ngauge theory. Our main objective of this paper it is to implement and develop\nthe idea of a two level algorithm in a new algorithm coded in QCDLAB. This\nimplementation is presented in the preconditioned GMRESR algorithm, as our new\ncontribution in QCDLAB package. The preconditioned part of our algorithm,\ndifferent from the one of [18], is the approximation of the overlap operator\nwith the truncated overlap operator with finite N3 dimension. We have tested it\nfor 100 statistically independent configurations on 32 x 32 lattice background\nU(1) field at coupling constant \\b{eta}=1 and for different bare quark masses\nmq = [0.5, 0.45, 0.4, 0.35, 0.3, 0.25, 0.2, 0.15, 0.1]. We have compared the\nconvergence history of the preconditioned GMRESR residual norm with another\noverlap inverter of QCDLAB as an optimal one, such as SHUMR. We have shown that\nour algorithm converges faster than SHUMR for different quark masses. Also, we\nhave demonstrated that it saves more time for light quarks compared to SHUMR\nalgorithm. Our algorithm is approximately independent from the quark mass. This\nis a key result in simulations with chiral fermions in lattice theories. By the\nother side, if we compare the results of [18] for quark mass 0.1 in SU(3),\nresults that our chosen preconditioned saves a factor of 2 but in U(1). Our\nnext step is to test this algorithm in SU(3) and to adopt it in parallel.", "category": "hep-lat" }, { "text": "Lattice QCD and heavy ion collisions: a review of recent progress: In the last few years, numerical simulations of QCD on the lattice have\nreached a new level of accuracy. A wide range of thermodynamic quantities is\nnow available in the continuum limit and for physical quark masses. This allows\na comparison with measurements from heavy ion collisions for the first time.\nFurthermore, calculations of dynamical quantities are also becoming available.\nThe combined effort from first principles and experiment allows us to gain an\nunprecedented understanding of the properties of quark-gluon plasma. I will\nreview the state-of-the-art results from lattice simulations and connect them\nto the experimental information from RHIC and the LHC.", "category": "hep-lat" }, { "text": "Hyper-Systolic Parallel Computing: A new class of parallel algorithms is introduced that can achieve a\ncomplexity of O(n^3/2) with respect to the interprocessor communication, in the\nexact computation of systems with pairwise mutual interactions of all elements.\nHitherto, conventional methods exhibit a communicational complexity of O(n^2).\nThe amount of computation operations is not altered for the new algorithm which\ncan be formulated as a kind of h-range problem, known from the mathematical\nfield of Additive Number Theory. We will demonstrate the reduction in\ncommunicational expense by comparing the standard-systolic algorithm and the\nnew algorithm on the connection machine CM5 and the CRAY T3D. The parallel\nmethod can be useful in various scientific and engineering fields like exact\nn-body dynamics with long range forces, polymer chains, protein folding or\nsignal processing.", "category": "hep-lat" }, { "text": "Axial and tensor charge of the nucleon with dynamical fermions: We present preliminary results for the axial and tensor charge of the nucleon\nobtained from simulations with N_f=2 clover fermions. A comparison with chiral\nperturbation theory is attempted.", "category": "hep-lat" }, { "text": "Monte Carlo overrelaxation for SU(N) gauge theories: The standard approach to Monte Carlo simulations of SU(N) Yang-Mills theories\nupdates successive SU(2) subgroups of each SU(N) link. We follow up on an old\nproposal of Creutz, to perform overrelaxation in the full SU(N) group instead,\nand show that it is more efficient.", "category": "hep-lat" }, { "text": "Chromo-electric screening length in 2+1 flavor QCD: We study Polyakov loop as well as correlators of real and imaginary parts of\nthe Polyakov loop in 2+1 flavor QCD at finite temperature. We use hypercubic\n(HYP) smearing to improve the signal in the lattice calculations and to obtain\nreliable results for the correlators at large distances. From the large\ndistance behavior of the correlators we estimate the chromo-electric screening\nlength to be (0.38-44)/T. Furthermore, we show that the short distance\ndistortions due to HYP smearing do not affect the physics of interest", "category": "hep-lat" }, { "text": "A Critical Surface of Chiral-invariant System with Gauge Boson and\n Fermions: In the chirally-invariant context of the $U_{em}(1)$ gauge interaction and\nfour-fermion interactions for ordinary and mirror fermions, the Schwinger-Dyson\nequation for the fermion self-energy function is studied on a lattice. We find\nthat a sensible infrared limit can be defined on a critical surface, which is\nconsistent with the critical line found in the continuum theory.", "category": "hep-lat" }, { "text": "Predictions from Lattice QCD: In the past year, we calculated with lattice QCD three quantities that were\nunknown or poorly known. They are the $q^2$ dependence of the form factor in\nsemileptonic $D\\to Kl\\nu$ decay, the decay constant of the $D$ meson, and the\nmass of the $B_c$ meson. In this talk, we summarize these calculations, with\nemphasis on their (subsequent) confirmation by experiments.", "category": "hep-lat" }, { "text": "Flavor symmetry breaking in lattice QCD with a mixed action: We study the phase structure of mixed-action QCD with two Wilson sea quarks\nand any number of chiral valence quarks (and ghosts), starting from the chiral\nlagrangian. A priori, the effective theory allows for a rich phase structure,\nincluding a phase with a condensate made of sea and valence quarks. In such a\nphase, mass eigenstates would become admixtures of sea and valence fields, and\npure-sea correlation functions would depend on the parameters of the valence\nsector, in contradiction with the actual setup of mixed-action simulations.\nUsing that the spectrum of the chiral Dirac operator has a gap for nonzero\nquark mass we prove that spontaneous symmetry breaking of the flavor symmetries\ncan only occur within the sea sector. This rules out a mixed condensate, and\nimplies restrictions on the low-energy constants of the effective theory.", "category": "hep-lat" }, { "text": "Semileptonic B to D decays at nonzero recoil with 2+1 flavors of\n improved staggered quarks: The Fermilab Lattice-MILC collaboration is completing a comprehensive program\nof heavy-light physics on the MILC (2+1)-flavor asqtad ensembles with lattice\nspacings as small as 0.045 fm and light-to-strange-quark mass ratios as low as\n1/20. We use the Fermilab interpretation of the clover action for heavy valence\nquarks and the asqtad action for light valence quarks. The central goal of the\nprogram is to provide ever more exacting tests of the unitarity of the CKM\nmatrix. We give a progress report on one part of the program, namely the\nanalysis of the semileptonic decay B to D at both zero and nonzero recoil.\nAlthough final results are not presented, we discuss improvements in the\nanalysis methods, the statistical errors, and the parameter coverage that we\nexpect will lead to a significant reduction in the final error for |V_cb| from\nthis decay channel.", "category": "hep-lat" }, { "text": "Detecting Dual Superconductivity in the Ground State of Gauge Theories -\n II: A monopole creation operator is constructed: its vacuum expectation value is\nan order parameter for dual superconductivity in that, if different from zero\nit signals spontaneous breaking of the U(1) symmetry corresponding to monopole\ncharge conservation. The operator is tested on compact U(1) gauge theory on\nlattice. For SU(2) gauge theory it clearly demonstrates that confinement is\nproduced by dual superconductivity.", "category": "hep-lat" }, { "text": "Pion Distribution Amplitudes in the Continuum Limit: We present a lattice-QCD calculation of the pion distribution amplitudes\nusing large-momentum effective theory (LaMET). Our calculation is carried out\nusing five ensembles with 2+1+1 flavors of highly improved staggered quarks\n(HISQ), generated by MILC collaboration, at 310 MeV and 220 MeV pion mass with\n0.06, 0.09, 0.12 and 0.15 fm lattice spacings. We use clover fermion action for\nthe valence quarks and tune the quark mass to match the lightest light and\nstrange masses in the sea. The resulting lattice matrix elements are\nnonperturbatively renormalized in regularization-independent\nmomentum-subtraction (RI/MOM) scheme and extrapolated to the continuum. We\ncompare different approaches to extract the x-dependence of the pion\ndistribution amplitudes.", "category": "hep-lat" }, { "text": "On the lattice construction of electroweak gauge theory: Based on the Ginsparg-Wilson relation, a gauge invariant formulation of\nelectroweak SU(2)xU(1) gauge theory on the lattice is considered. If the\nhypercharge gauge coupling is turned off in the vacuum sector of the U(1) gauge\nfields, the theory consists of four left-handed SU(2) doublets and it is\npossible, as in vector-like theories, to make the fermion measure defined\nglobally in all topological sectors of SU(2). We then try to incorporate U(1)\ngauge field, following L\\\"uscher's reconstruction theorem. The global\nintegrability condition is proved for ``gauge loops'' in the space of the U(1)\ngauge fields with arbitrary SU(2) gauge field fixed in the background. For\n``non-gauge loops'', however, the proof is given so far only for the classical\nSU(2) instanton backgrounds.", "category": "hep-lat" }, { "text": "A quadrature-based eigensolver with a Krylov subspace method for shifted\n linear systems for Hermitian eigenproblems in lattice QCD: We consider a quadrature-based eigensolver to find eigenpairs of Hermitian\nmatrices arising in lattice quantum chromodynamics. To reduce the computational\ncost for finding eigenpairs of such Hermitian matrices, we propose a new\ntechnique for solving shifted linear systems with complex shifts by means of\nthe shifted CG method. Furthermore using integration paths along horizontal\nlines corresponding to the real axis of the complex plane, the number of\niterations for the shifted CG method is also reduced. Some numerical\nexperiments illustrate the accuracy and efficiency of the proposed method by\ncomparison with a conventional method.", "category": "hep-lat" }, { "text": "Towards Radiative Transitions in Charmonium: We present preliminary calculations towards radiative transitions in\ncharmonium using anisotropic $N_f = 2 + 1$ dynamical ensembles generated by the\nHadron Spectrum Collaboration. With the use of newer technologies we aim to\ninvestigate transitions between states, including potential exotic charmonium\nstates, lying higher in the spectrum than in previous studies. A crucial\ningredient in this work is the use of variationally optimised interpolating\noperators which allow for a reliable determination of the three-point\ncorrelation functions needed. Using these operators, we perform first\ncalculations of relevant three-point correlation functions before discussing\nfuture directions.", "category": "hep-lat" }, { "text": "Implementation of C* boundary conditions in the Hybrid Monte Carlo\n algorithm: In the study of QCD dynamics, C* boundary conditions are physically relevant\nin certain cases. In this paper we study the implementation of these boundary\nconditions in the lattice formulation of full QCD with staggered fermions. In\nparticular, we show that the usual even-odd partition trick to avoid the\nredoubling of the fermion matrix is still valid in this case. We give an\nexplicit implementation of these boundary conditions for the Hybrid Monte Carlo\nalgorithm.", "category": "hep-lat" }, { "text": "Mass estimates of the SU(2) $0^{++}$ glueball from spectral methods: The estimation of the K\\\"all\\'en-Lehmann spectral density from gauge\ninvariant lattice QCD two point correlation functions is proposed, and explored\nvia an inversion strategy based on Tikhonov regularisation. We test the method\non a mesonic toy model, showing that our methodology is competitive with the\ntraditional Maximum Entropy Method. As proof of concept the SU(2) glueball\nspectrum for the quantum numbers $J^{PC}=0^{++}$ is investigated, for various\nvalues of the lattice spacing, using the published data of arXiv:1910.07756.\nOur estimates for the ground state mass are in good agreement with the\ntraditional approach, which is based on the large time exponential behaviour of\nthe correlation functions. Furthermore, the spectral density also contains\nhints of excites states in the spectrum. Spectroscopic analysis of glueball\ntwo-point functions therefore provides a straightforward and insightful\nalternative to the traditional method based on the large time exponential\nbehaviour of the correlation functions.", "category": "hep-lat" }, { "text": "Present and future prospects for lattice QCD calculations of matrix\n elements for nEDM: A status report on the calculations of the contribution of four CP violating\noperators, the $\\Theta$-term, the quark EDM, the chromo EDM and the Weinberg\noperator to the neutron EDM are presented. At this time, there exit precise\nphysical results only for the quark EDM operator by the PNDME collaboration.\nFirst results showing signal in the contributions of the $\\Theta$-term and the\nconnected part of the chromo EDM operator have been presented. The challenge of\ndivergent mixing in the chromo EDM and Weinberg operators has motivated\ncalculations in the gradient flow scheme. While there has been steady progress,\nthe challenges remaining are large. Results with $O(50\\%)$ uncertainty with\ncontrol over all systematic errors can be expected for the $\\Theta$-term over\nthe next five years. Prediction of a timeline for progress on the chromo EDM\nand the Weinberg operators will depend on when the renormalization and\ndivergent mixing of these operators is brought under control. The most\noptimistic scenario is that the gradient flow scheme provides a solution to the\nnumerical signal and mixing problems for both the gluonic and quark operators.", "category": "hep-lat" }, { "text": "Glueballs on the three-sphere: We study the non-perturbative effects of the global features of the\nconfiguration space for SU(2) gauge theory on the three-sphere. The strategy is\nto reduce the full problem to an effective theory for the dynamics of the\nlow-energy modes. By explicitly integrating out the high-energy modes, the\none-loop correction to the effective hamiltonian is obtained. Imposing the\n$\\theta$ dependence through boundary conditions in configuration space\nincorporates the non-perturbative effects of the non-contractable loops in the\nfull configuration space. After this we obtain the glueball spectrum of the\neffective theory with a variational method.", "category": "hep-lat" }, { "text": "Discrete Symmetry Enhancement in Nonabelian Models and the Existence of\n Asymptotic Freedom: We study the universality between a discrete spin model with icosahedral\nsymmetry and the O(3) model in two dimensions. For this purpose we study\nnumerically the renormalized two-point functions of the spin field and the four\npoint coupling constant. We find that those quantities seem to have the same\ncontinuum limits in the two models. This has far reaching consequences, because\nthe icosahedron model is not asymptotically free in the sense that the coupling\nconstant proposed by L\"uscher, Weisz and Wolff [1] does not approach zero in\nthe short distance limit. By universality this then also applies to the O(3)\nmodel, contrary to the predictions of perturbation theory.", "category": "hep-lat" }, { "text": "Physical and unphysical effects in the mixed SU(2)/SO(3) gauge theory: We investigate possible problems with universality in lattice gauge theory\nwhere a mixed fundamental SU(2) and SO(3)-invariant gauge group is used: the\n(second order) finite temperature phase transition becomes involved with first\norder effects with increased SO(3) coupling, and this first order effect has a\nnoticeable coupling dependence for small lattices. We produce evidence that the\nfirst order transition is essentially bulk in nature as generally believed, and\nthat the finite temperature effects start to separate out from the lower end of\nthe bulk effects for a lattice of 8 sites in the finite temperature direction.\nWe strengthen our picture of the first order effects as artefacts by using an\nimproved action: this shifts the end point of the first order line away from\nthe fundamental SU(2) axis.", "category": "hep-lat" }, { "text": "Scaling behavior at the tricritical point in the fermion-gauge-scalar\n model: We investigate a strongly coupled U(1) gauge theory with fermions and scalars\non the lattice and analyze whether the continuum limit might be a\nrenormalizable theory with dynamical mass generation. Most attention is paid to\nthe phase with broken chiral symmetry in the vicinity of the tricritical point\nfound in the model. There we investigate the scaling of the masses of the\ncomposite fermion and of some bosonic bound states. As a by-product we confirm\nthe mean-field exponents at the endpoint in the U(1)-Higgs model, by analyzing\nthe scaling of the Fisher zeros.", "category": "hep-lat" }, { "text": "Thermal mass and dispersion relations of quarks in the deconfined phase\n of quenched QCD: Temporal quark correlation functions are analyzed in quenched lattice QCD for\ntwo values of temperature above the critical temperature (Tc) for\ndeconfinement, T=1.5Tc and 3Tc. A two-pole ansatz for the quark spectral\nfunction is used to determine the bare quark mass and the momentum dependence\nof excitation spectra on large lattices of size up to 128^3x16. The dependence\nof the quark correlator on these parameters as well as the finite volume\ndependence of the excitation energies are analyzed in detail in order to\nexamine the reliability of our analysis. Our results suggest the existence of\nquasi-particle peaks in the quark spectrum. We furthermore find evidence that\nthe dispersion relation of the plasmino mode has a minimum at non-zero momentum\neven in the non-perturbative region near Tc. We also elaborate on the\nenhancement of the quark correlator near the chiral limit which is observed at\nT=1.5Tc on about half of the gauge configurations. We attribute this to the\npresence of near zero-modes of the fermion matrix that are associated with\nnon-trivial topology of the gauge configurations.", "category": "hep-lat" }, { "text": "Chiral transition and monopole percolation in lattice scalar QED with\n quenched fermions: We study the interplay between topological observables and chiral and Higgs\ntransitions in lattice scalar QED with quenched fermions. Emphasis is put on\nthe chiral transition line and magnetic monopole percolation at strong gauge\ncoupling. We confirm that at infinite gauge coupling the chiral transition is\ndescribed by mean field exponents. We find a rich and complicated behaviour at\nthe endpoint of the Higgs transition line which hampers a satisfactory analysis\nof the chiral transition. We study in detail an intermediate coupling, where\nthe data are consistent both with a trivial chiral transition clearly separated\nfrom monopole percolation and with a chiral transition coincident with monopole\npercolation, and characterized by the same critical exponent $\\nu \\simeq 0.65$.\nWe discuss the relevance (or lack thereof) of these quenched results to our\nunderstanding of the \\chupiv\\ model. We comment on the interplay of magnetic\nmonopoles and fermion dynamics in more general contexts.", "category": "hep-lat" }, { "text": "Attractive $N$-$\u03c6$ Interaction and Two-Pion Tail from Lattice QCD\n near Physical Point: First results on the interaction between the $\\phi$-meson and the nucleon\n($N$) are presented based on the ($2+1$)-flavor lattice QCD simulations with\nnearly physical quark masses. Using the HAL QCD method, the spacetime\ncorrelation of the $N$-$\\phi$ system in the spin 3/2 channel is converted into\nthe $N$-$\\phi$ scattering phase shift through the interaction potential. The\n$N$-$\\phi$ potential appears to be a combination of a short-range attractive\ncore and a long-range attractive tail. The latter is found to be consistent\nwith the two-pion exchange (TPE) obtained from the interaction between a\ncolor-dipole and the nucleon. The resultant scattering length and effective\nrange for $m_{\\pi}=$ 146.4 MeV are $ a^{(3/2)}_0=-1.43(23)_{\\rm\nstat.}\\left(^{+36}_{-06}\\right)_{\\rm syst.} {\\rm fm}$ and $ r^{(3/2)}_{\\rm\neff}=2.36(10)_{\\rm stat.}\\left(^{+02}_{-48}\\right)_{\\rm syst.} {\\rm fm}$,\nrespectively. The magnitude of the scattering length is shown to have\nnontrivial dependence of $m_{\\pi}$ and is sensitive to the existence of the\nlong-range tail from TPE.", "category": "hep-lat" }, { "text": "Gluons in Two-Color QCD at High Baryon Density: Landau gauge longitudinal and transverse gluon propagators are studied in\nlattice QCD with gauge group $SU(2)$ at varying temperature and quark density.\nIn particular, it is found that the longitudinal propagator decreases with\nincreasing quark chemical potential at all temperatures under study, whereas\nthe transverse propagator increases with increasing quark chemical potential at\n$T<200$ MeV and does not depend on it at higher temperatures. The relative\nstrength of chromoelectric and chromomagnetic interactions is also discussed.", "category": "hep-lat" }, { "text": "Remark on the energy-momentum tensor in the lattice formulation of 4D\n $\\mathcal{N}=1$ SYM: In a recent paper, arXiv:1209.2473 \\cite{Suzuki:2012gi}, we presented a\npossible definition of the energy-momentum tensor in the lattice formulation of\nthe four-dimensional $\\mathcal{N}=1$ supersymmetric Yang--Mills theory, that is\nconserved in the quantum continuum limit. In the present Letter, we propose a\nquite similar but somewhat different definition of the energy-momentum tensor\n(that is also conserved in the continuum limit) which is superior in several\naspects: In the continuum limit, the origin of the energy automatically becomes\nconsistent with the supersymmetry and the number of renormalization constants\nthat require a (non-perturbative) determination is reduced to two from four,\nthe number of renormalization constants appearing in the construction in Ref.\n\\cite{Suzuki:2012gi}.", "category": "hep-lat" }, { "text": "Nature of the $a_1$ meson in lattice quantum chromodynamics studied with\n chiral fermions: We study the $a_1$ meson using a quenched lattice quantum chromodynamics\nsimulation with the truncated overlap fermions formalism based on the domain\nwall fermions. The obtained lightest mass of the $a_1$ meson, 1272(45) MeV, is\nconsistent with the experimental value for $a_1$(1260). Thus, $a_1$(1260) can\nbe identified to have a simple two-body constituent-quark structure. Our\nquenched simulation result of $a_1$(1420) can not explain the experimental mass\nvalue, which suggests $a_1$(1420) is not a simple $q\\bar{q}$ two quark state.", "category": "hep-lat" }, { "text": "Lattice investigations of the chimera baryon spectrum in the Sp(4) gauge\n theory: We report the results of lattice numerical studies of the Sp(4) gauge theory\ncoupled to fermions (hyperquarks) transforming in the fundamental and two-index\nantisymmetric representations of the gauge group. This strongly-coupled theory\nis the minimal candidate for the ultraviolet completion of composite Higgs\nmodels that facilitate the mechanism of partial compositeness for generating\nthe top-quark mass. We measure the spectrum of the low-lying, half-integer\nspin, bound states composed of two fundamental and one antisymmetric\nhyperquarks, dubbed chimera baryons, in the quenched approximation. In this\nfirst systematic, non-perturbative study, we focus on the three lightest\nparity-even chimera-baryon states, in analogy with QCD, denoted as\n$\\Lambda_{\\rm CB}$, $\\Sigma_{\\rm CB}$ (both with spin 1/2), and $\\Sigma_{\\rm\nCB}^\\ast$(with spin 3/2). The spin-1/2 such states are candidates of the top\npartners. The extrapolation of our results to the continuum and\nmassless-hyperquark limit is performed using formulae inspired by QCD\nheavy-baryon Wilson chiral perturbation theory. Within the range of hyperquark\nmasses in our simulations, we find that $\\Sigma_{\\mathrm{CB}}$ is not heavier\nthan $\\Lambda_{\\mathrm{CB}}$.", "category": "hep-lat" }, { "text": "A Study of Charmonium Systems across the Deconfinement Transition: We present results from lattice studies of charmonium systems near the\ndeconfinement transition temperature. On quenched isotropic lattices with\nlattice spacings between 0.02 and 0.05 fm, bar{q} q systems with quark masses\nclose to the charm mass and with different spin-parity quantum numbers are\nstudied in the temperature range 0.9 Tc - 3 Tc. Results for temporal\ncorrelators of local operators, and the spectral functions constructed from\nthem, are discussed. For the pseudoscalar and vector channels, the correlators\nare observed to change very little across the deconfinement transition, unlike\nin the case of the light quarks.", "category": "hep-lat" }, { "text": "Theoretical Developments in Lattice Gauge Theory for Applications in\n Double-beta Decay Processes and Quantum Simulation: Double beta decays are rare nuclear processes that can occur in two modes:\ntwo-neutrino double beta decay, observed in the Standard Model, and\nneutrinoless double beta decay, a hypothetical process with profound\nimplications for Particle Physics. To draw reliable conclusions from their\nexperimental constraints, it is necessary to have accurate predictions of the\nunderlying hadronic interactions described by quantum chromodynamics (QCD), a\nnon-Abelian gauge theory with the symmetry group SU(3). QCD predictions require\nnon-perturbative methods for calculating observables, and lattice QCD (LQCD), a\nnumerical method based on QCD formulated on a finite space-time grid, is the\nonly reliable first-principles technique for obtaining quantitative results.\nHowever, LQCD needs formal prescriptions to match numerical results with\nobservables. This thesis provides such prescriptions for double beta decays\nusing the finite volume effects in the LQCD framework. Matching relations that\nconnect two-nucleon double beta decay amplitudes to quantities accessible via\nLQCD calculations, namely the nuclear matrix elements and two-nucleon energy\nspectra in a finite volume are provided. The impact of uncertainties is\nexamined on the precision with which low-energy constants of the corresponding\neffective field theories can be determined from future LQCD calculations.\n Hamiltonian simulation of QCD is another non-perturbative method of solving\nQCD which can be more suitable in some cases than the conventional LQCD. The\nrise of tensor network methods and quantum simulation has made Hamiltonian\nsimulation of lattice gauge theories (LGTs) a reality. Towards the goal of\nsimulating QCD, a loop-string-hadron (LSH) formulation of an SU(3) LGT with\nmatter in 1+1 dimensions is developed in this thesis, motivated by recent\nstudies that showed the LSH formulation of an SU(2) LGT to be advantageous over\nother formulations.", "category": "hep-lat" }, { "text": "Canonical Demon Monte Carlo Renormalization Group: We describe a new method to compute renormalized coupling constants in a\nMonte Carlo renormalization group calculation. The method can be used for a\ngeneral class of models, e.g., lattice spin or gauge models. The basic idea is\nto simulate a joint system of block spins and canonical demons. In contrast to\nthe Microcanonical Renormalization Group invented by Creutz et al. our method\ndoes not suffer from systematical errors stemming from a simultaneous use of\ntwo different ensembles. We present numerical results for the $O(3)$ nonlinear\n$\\sigma$-model.", "category": "hep-lat" }, { "text": "Equation of state for pure SU(3) gauge theory with renormalization group\n improved action: A lattice study of the equation of state for pure SU(3) gauge theory using a\nrenormalization-group (RG) improved action is presented. The energy density and\npressure are calculated on a $16^3\\times 4$ and a $32^3\\times 8$ lattice\nemploying the integral method. Extrapolating the results to the continuum\nlimit, we find the energy density and pressure to be in good agreement with\nthose obtained with the standard plaquette action within the error of 3-4%.", "category": "hep-lat" }, { "text": "A Study of Meson Correlators at Finite Temperature: We present results for mesonic propagators in temporal and spatial directions\nat T below and above the deconfining transition in quenched QCD. Anisotropic\nlattices are used to get enough information in the temporal direction. We use\nthe Wilson fermion action for light quarks and Fermilab action for heavy\nquarks.", "category": "hep-lat" }, { "text": "Mean-Field Gauge Interactions in Five Dimensions II. The Orbifold: We study Gauge-Higgs Unification in five dimensions on the lattice by means\nof the mean-field expansion. We formulate it for the case of an SU(2) pure\ngauge theory and orbifold boundary conditions along the extra dimension, which\nexplicitly break the gauge symmetry to U(1) on the boundaries. Our main result\nis that the gauge boson mass computed from the static potential along\nfour-dimensional hyperplanes is nonzero implying spontaneous symmetry breaking.\nThis observation supports earlier data from Monte Carlo simulations [12].", "category": "hep-lat" }, { "text": "Central Dominance and the Confinement Mechanism in Gluodynamics: New topological objects, which we call center monopoles, naturally arise in\nthe Maximal Center Projection of SU(3) gluodynamics. The condensate of the\ncenter monopoles is the order parameter of the theory.", "category": "hep-lat" }, { "text": "Exploring the QCD phase diagram with three flavors of M\u00f6bius domain\n wall fermions: We present an update on the study of the QCD phase transition with 3 flavors\nof M\\\"obius domain wall fermions at zero baryon density. We performed\nsimulations on lattices of size $36^3\\times12\\times16$ and\n$24^3\\times12\\times32$ with a variety of quark masses at a fixed lattice\nspacing $a=0.1361(20)$ fm, which correspond to a temperature 121(2) MeV. By\nanalyzing the chiral condensate, chiral susceptibilitities and Binder cumulant\non $36^3\\times12\\times16$ lattices together with the result obtained from our\nprevious study on $24^3\\times12\\times16$ lattices, we identified a crossover\noccurring at quark mass around $m_q^{\\mathrm{\\overline {MS}}}(2\\, \\mathrm{GeV})\n\\sim 3-4$ MeV for this temperature. Besides, we show the effects of residual\nchiral symmetry breaking on chiral condensate and chiral susceptibilities\nbetween $L_s=16$ and 32.", "category": "hep-lat" }, { "text": "Rediscovery of Numerical L\u00fcscher's Formula from the Neural Network: We present that by predicting the spectrum in discrete space from the phase\nshift in continuous space, the neural network can remarkably reproduce the\nnumerical L\\\"uscher's formula to a high precision. The model-independent\nproperty of the L\\\"uscher's formula is naturally realized by the\ngeneralizability of the neural network. This exhibits the great potential of\nthe neural network to extract model-independent relation between\nmodel-dependent quantities, and this data-driven approach could greatly\nfacilitate the discovery of the physical principles underneath the intricate\ndata.", "category": "hep-lat" }, { "text": "Thermodynamics of heavy-light hadrons: Ratios of cumulants of conserved net charge fluctuations are sensitive to the\ndegrees of freedom that are carriers of the corresponding quantum numbers in\ndifferent phases of strong interaction matter. We calculate second and fourth\norder cumulants of net charm and strange fluctuations and their correlations\nwith other conserved charges such as net baryon number and electric charge.\nSimulation are performed on $N_\\tau$=6 and 8 lattices using the Highly Improved\nStaggered Quark (HISQ) action with a light to strange quark mass ratio of 1/20\nand having charm quarks treated in the quenched approximation. Analysing\nappropriate ratios of these cumulants we observe that both open strange and\ncharm hadrons start to get dissociated in the chiral crossover region. We\nprovide indirect evidence for the existence of additional, experimentally yet\nunobserved open charm and strange hadrons from QCD thermodynamics. This is done\nby comparing lattice QCD results to Hadron Resonance Gas (HRG) model\ncalculations performed with a hadron spectrum as listed in the Particle Data\nTables as well as with a spectrum predicted in the relativistic quark model and\nobserved in lattice QCD calculations. We also discuss the influence of these\nexperimentally yet unobserved states on the determination of freeze-out\ntemperature and chemical potentials from heavy ion collision experiments. We\nfound that including these additional states in the HRG model leads to a\nsystematic 5-8 MeV decrease in the freeze-out temperature of strange hadrons.", "category": "hep-lat" }, { "text": "Two-nucleon scattering in multiple partial waves: We determine scattering phase shifts for S,P,D, and F partial wave channels\nin two-nucleon systems using lattice QCD methods. We use a generalization of\nLuscher's finite volume method to determine infinite volume phase shifts from a\nset of finite volume ground- and excited-state energy levels on two volumes,\nV=(3.4 fm)^3 and V=(4.5 fm)^3. The calculations are performed in the\nSU(3)-flavor limit, corresponding to a pion mass of approximately 800 MeV. From\nthe energy dependence of the phase shifts we are able to extract scattering\nparameters corresponding to an effective range expansion.", "category": "hep-lat" }, { "text": "Determinant of a new fermionic action on a lattice - (I): We investigate, analytically and numerically, the fermion determinant of a\nnew action on a (1+1)-dimensional Euclidean lattice. In this formulation the\ndiscrete chiral symmetry is preserved and the number of fermion components is a\nhalf of that of Kogut-Susskind. In particular, we show that our fermion\ndeterminant is real and positive for U(1) gauge group under specific\nconditions, which correspond to gauge conditions on the infinite lattice. It is\nalso shown that the determinant is real and positive for SU(N) gauge group\nwithout any condition.", "category": "hep-lat" }, { "text": "Estimating the Unquenched Strange Quark Mass from the Lattice Axial Ward\n Identity: We present a determination of the strange quark mass for two flavours (nf=2)\nof light dynamical quarks using the axial Ward identity. The calculations are\nperformed on the lattice using O(a) improved Wilson fermions and include a\nfully non-perturbative determination of the renormalisation constant. In the\ncontinuum limit we find in the MSbar scheme at 2GeV, ms = 111(6)(4)(6)MeV using\nthe force scale r0 = 0.467fm, where the first error is statistical, the second\nand third are systematic due to the fit and scale uncertainties respectively.\nResults are also presented for the light quark mass and the chiral condensate.\nThe corresponding results are also given for r0=0.5fm.", "category": "hep-lat" }, { "text": "SU(N) polynomial integrals and some applications: We use the method of the Weingarten functions to evaluate SU(N) integrals of\nthe polynomial type. As an application we calculate various one-link integrals\nfor lattice gauge and spin SU(N) theories.", "category": "hep-lat" }, { "text": "High-loop perturbative renormalization constants for Lattice QCD (I):\n finite constants for Wilson quark currents: We present a high order perturbative computation of the renormalization\nconstants Z_V, Z_A and of the ratio Z_P/Z_S for Wilson fermions. The\ncomputational setup is the one provided by the RI'-MOM scheme. Three- and\nfour-loop expansions are made possible by Numerical Stochastic Perturbation\nTheory. Results are given for various numbers of flavours and/or (within a\nfinite accuracy) for generic n_f up to three loops. For the case n_f=2 we also\npresent four-loop results. Finite size effects are well under control and the\ncontinuum limit is taken by means of hypercubic symmetric Taylor expansions.\nThe main indetermination comes from truncation errors, which should be assessed\nin connection with convergence properties of the series. The latter is best\ndiscussed in the framework of Boosted Perturbation Theory, whose impact we try\nto assess carefully. Final results and their uncertainties show that high-loop\nperturbative computations of Lattice QCD RC's are feasible and should not be\nviewed as a second choice. As a by-product, we discuss the perturbative\nexpansion for the critical mass, also for which results are for generic n_f up\nto three loops, while a four-loop result is obtained for n_f=2.", "category": "hep-lat" }, { "text": "Multicanonical Spin Glass Simulations: We report a Monte Carlo simulation of the $2D$ Edwards-Anderson spin glass\nmodel within the recently introduced multicanonical ensemble. Replica on\nlattices of size $L^2$ up to $L=48$ are investigated. Once a true groundstate\nis found, we are able to give a lower bound on the number of statistically\nindependent groundstates sampled. Temperature dependence of the energy, entropy\nand other quantities of interest are easily calculable. In particular we report\nthe groundstate results. Computations involving the spin glass order parameter\nare more tedious. Our data indicate that the large $L$ increase of the\nergodicity time is reduced to an approximately $V^3$ power law. Altogether the\nresults suggest that the multicanonical ensemble improves the situation of\nsimulations for spin glasses and other systems which have to cope with similar\nproblems of conflicting constraints.", "category": "hep-lat" }, { "text": "B Meson Semileptonic Form Factors from Unquenched Lattice QCD: The semileptonic process, B --> \\pi l \\nu, is studied via full QCD Lattice\nsimulations. We use unquenched gauge configurations generated by the MILC\ncollaboration. These include the effect of vacuum polarization from three quark\nflavors: the $s$ quark and two very light flavors ($u/d$) of variable mass\nallowing extrapolations to the physical chiral limit. We employ Nonrelativistic\nQCD to simulate the $b$ quark and a highly improved staggered quark action for\nthe light sea and valence quarks. We calculate the form factors $f_+(q^2)$ and\n$f_0(q^2)$ in the chiral limit for the range 16 GeV$^2 \\leq q^2 < q^2_{max}$\nand obtain $\\int^{q^2_{max}}_{16 GeV^2} [d\\Gamma/dq^2] dq^2 / |v_{ub}|^2 =\n1.46(35) ps^{-1}$. Combining this with a preliminary average by the Heavy\nFlavor Averaging Group (HFAG'05) of recent branching fraction data for\nexclusive B semileptonic decays from the BaBar, Belle and CLEO collaborations,\nleads to $|V_{ub}| = 4.22(30)(51) \\times 10^{-3}$. PLEASE NOTE APPENDIX B with\nan ERRATUM, to appear in Physical Review D, to the published version of this\ne-print (Phys.Rev.D 73, 074502 (2006)). Results for the form factor $f_+(q^2)$\nin the chiral limit have changed significantly. The last two sentences in this\nabstract should now read; \"We calculate the form factor $f_+(q^2)$ and\n$f_0(q^2)$ in the chiral limit for the range 16 Gev$^2 \\leq q^2 < q^2_{max}$\nand obtain $\\int^{q^2_{max}}_{16 GeV^2} [d\\Gamma/dq^2] dq^2 / |V_{ub}|^2 =\n2.07(57)ps^{-1}$. Combining this with a preliminary average by the Heavy Flavor\nAveragibg Group (HFAG'05) of recent branching fraction data for exclusive B\nsemileptonic decays from the BaBar, Belle and CLEO collaborations, leads to\n$|V_{ub}| = 3.55(25)(50) \\times 10^{-3}$.\"", "category": "hep-lat" }, { "text": "Compact Gauge Fields on Causal Dynamical Triangulations: a 2D case study: We discuss the discretization of Yang-Mills theories on Dynamical\nTriangulations in the compact formulation, with gauge fields living on the\nlinks of the dual graph associated with the triangulation, and the numerical\ninvestigation of the minimally coupled system by Monte Carlo simulations. We\nprovide, in particular, an explicit construction and implementation of the\nMarkov chain moves for 2D Causal Dynamical Triangulations coupled to either\n$U(1)$ or $SU(2)$ gauge fields; the results of exploratory numerical\nsimulations on a toroidal geometry are also presented for both cases. We study\nthe critical behavior of gravity related observables, determining the\nassociated critical indices, which turn out to be independent of the bare gauge\ncoupling: we obtain in particular $\\nu = 0.496(7)$ for the critical index\nregulating the divergence of the correlation length of the volume profiles.\nGauge observables are also investigated, including holonomies (torelons) and,\nfor the $U(1)$ gauge theory, the winding number and the topological\nsusceptibility. An interesting result is that the critical slowing down of the\ntopological charge, which affects various lattice field theories in the\ncontinuum limit, seems to be strongly suppressed (i.e., by orders of magnitude)\nby the presence of a locally variable geometry: that may suggest possible ways\nfor improvement also in other contexts.", "category": "hep-lat" }, { "text": "Approximate forms of the density of states: We compare MC calculations of the density of states in SU(2) pure gauge\ntheory with the weak and strong coupling expansions. Surprisingly, the range of\nvalidity of the two approximations overlap significantly, however the large\norder behavior of both expansions appear to be similar to the corresponding\nexpansions of the plaquette. We discuss the implications for the calculation of\nthe Fisher's zeros of the partition function.", "category": "hep-lat" }, { "text": "$\u03c7_{\\textrm{top}}(T \\gg T_{\\textrm{c}})$ in pure-glue QCD through\n reweighting: We calculate the topological susceptibility at 2.5 Tc and 4.1 Tc in SU(3)\npure Yang-Mills theory. We define topology with the help of gradient flow and\nwe largely overcome the problem of poor statistics at high temperatures by\napplying a reweighting technique in terms of the topological charge, measured\nafter a specific small amount of gradient flow. This allows us to obtain a\nsample of configurations which compares topological sectors with good\nstatistics, with enhanced tunneling between topologies. We quote continuum\nextrapolated results at these two temperatures and conclude that our method is\nviable and can be extended without new conceptual problems to the case of full\nQCD with fermions.", "category": "hep-lat" }, { "text": "Deconfinement transition and dimensional cross-over in the 3D gauge\n Ising model: We present a high precision Monte Carlo study of the finite temperature $Z_2$\ngauge theory in 2+1 dimensions. The duality with the 3D Ising spin model allows\nus to use powerful cluster algorithms for the simulations. For temporal\nextensions up to $N_t=16$ we obtain the inverse critical temperature with a\nstatistical accuracy comparable with the most accurate results for the bulk\nphase transition of the 3D Ising model. We discuss the predictions of T. W.\nCapehart and M.E. Fisher for the dimensional crossover from 2 to 3 dimensions.\nOur precise data for the critical exponents and critical amplitudes confirm the\nSvetitsky-Yaffe conjecture. We find deviations from Olesen's prediction for the\ncritical temperature of about 20%.", "category": "hep-lat" }, { "text": "Dirac-mode analysis for quark number density and its application for\n deconfinement transition: The quark number density at finite imaginary chemical potential is\ninvestigated in the lattice QCD using the Dirac-mode expansion. We find the\nanalytical formula of the quark number density in terms of the Polyakov loop in\nthe large quark mass regime. On the other hand, in the small quark mass region,\nthe quark number density is investigated by using the quenched lattice QCD\nsimulation. The quark number density is found to strongly depend on the\nlow-lying Dirac modes while its sign does not change. This result leads to that\nthe quark number holonomy is not sensitive to the low-lying Dirac modes. We\ndiscuss the confinement-deconfinement transition from the property of the quark\nnumber density and the quark number holonomy.", "category": "hep-lat" }, { "text": "Recent Developments of Muon g-2 from Lattice QCD: One of the most promising quantities for the search of signatures of physics\nbeyond the Standard Model is the anomalous magnetic moment $g-2$ of the muon,\nwhere a comparison of the experimental result with the Standard Model estimate\nyields a deviation of about $3.5~\\sigma$. On the theory side, the largest\nuncertainty arises from the hadronic sector, namely the hadronic vacuum\npolarisation and the hadronic light-by-light scattering. I review recent\nprogress in calculating the hadronic contributions to the muon $g-2$ from the\nlattice and discuss the prospects and challenges to match the precision of the\nupcoming experiments.", "category": "hep-lat" }, { "text": "Towards corrections to the strong coupling limit of staggered lattice\n QCD: We report on the first steps of an ongoing project to add gauge observables\nand gauge corrections to the well-studied strong coupling limit of staggered\nlattice QCD, which has been shown earlier to be amenable to numerical\nsimulations by the worm algorithm in the chiral limit and at finite density.\nHere we show how to evaluate the expectation value of the Polyakov loop in the\nframework of the strong coupling limit at finite temperature, allowing to study\nconfinement properties along with those of chiral symmetry breaking. We find\nthe Polyakov loop to rise smoothly, thus signalling deconfinement. The\nnon-analytic nature of the chiral phase transition is reflected in the\nderivative of the Polyakov loop. We also discuss how to construct an effective\ntheory for non-zero lattice coupling, which is valid to $O(\\beta)$.", "category": "hep-lat" }, { "text": "Impact of Dynamical Fermions on the Centre Vortex Gluon Propagator: The impact of $SU(3)$ centre vortices on the Landau-gauge gluon propagator is\ncalculated in the presence of dynamical fermions and compared to the pure\nYang-Mills case. The presence of dynamical fermions is found to alter the\nbehaviour of the centre vortex propagator when compared to the established\npure-gauge result. The gluon spectral representation is also explored from the\ncentre vortex perspective, where centre vortices are shown to exhibit clear\nsigns of positivity violation, which is an indicator of confinement. Vortex\nremoval subsequently restores positivity, demonstrating the crucial role centre\nvortices play in the confinement of gluons.", "category": "hep-lat" }, { "text": "Enumerating Copies in the First Gribov Region on the Lattice in up to\n four Dimensions: The covariant gauges are known to suffer from the Gribov problem: even after\nfixing a gauge non-perturbatively, there may still exist residual copies which\nare physically equivalent to each other, called Gribov copies. While the\ninfluence of Gribov copies in the relevant quantities such as gluon propagators\nhas been heavily debated in recent studies, the significance of the role they\nplay in the Faddeev--Popov procedure is hardly doubted. We concentrate on\nGribov copies in the first Gribov region, i.e., the space of Gribov copies at\nwhich the Faddeev--Popov operator is strictly positive (semi)definite. We\ninvestigate compact U($1$) as the prototypical model of the more complicated\nstandard model group SU($N_{c}$). With our Graphical Processing Unit (GPU)\nimplementation of the relaxation method we collect up to a few million Gribov\ncopies per orbit. We show that the numbers of Gribov copies even in the first\nGribov region increase exponentially in two, three and four dimensions.\nFurthermore, we provide strong indication that the number of Gribov copies is\ngauge orbit dependent.", "category": "hep-lat" }, { "text": "Finite-volume effects in long-distance processes with massless leptonic\n propagators: In Ref. [1], a method was proposed to calculate QED corrections to hadronic\nself energies from lattice QCD without power-law finite-volume errors. In this\npaper, we extend the method to processes which occur at second-order in the\nweak interaction and in which there is a massless (or almost massless) leptonic\npropagator. We demonstrate that, in spite of the presence of the propagator of\nan almost massless electron, such an infinite-volume reconstruction procedure\ncan be used to obtain the amplitude for the rare kaon decay\n$K^+\\to\\pi^+\\nu\\bar\\nu$ from a lattice quantum chromodynamics computation with\nonly exponentially small finite-volume corrections.", "category": "hep-lat" }, { "text": "Phase diagram of two-dimensional SU($N$) super-Yang--Mills theory with\n four supercharges: We non-perturbatively study two-dimensional SU($N$) supersymmetric\nYang--Mills theory with four supercharges and large $12 \\leq N \\leq 20$.\nAlthough this theory has no known holographic dual, we conduct numerical\ninvestigations to check for features similar to the sixteen-supercharge theory,\nwhich has a well-defined gravity dual. We carry out lattice field theory\ncalculations to determine the phase diagram, observing a spatial deconfinement\ntransition, similar to the maximally supersymmetric case. However, the\ntransition does not continue to strong couplings, implying the absence of a\nholographic interpretation for this four-supercharge theory.", "category": "hep-lat" }, { "text": "Lattice QCD Study of the Pentaquark Baryons: We study the spin $\\frac12$ hadronic state in quenched lattice QCD to search\nfor a possible $S=+1$ pentaquark resonance. Simulations are carried out on\n$8^3\\times 24$, $10^3\\times 24$, $12^3\\times 24$ and $16^3\\times 24$ lattices\nat $\\beta$=5.7 at the quenched level with the standard plaquette gauge action\nand Wilson quark action. We adopt two independent operators with I=0 and\n$J^P=\\frac12$ to construct a $2\\times 2$ correlation matrix. After the\ndiagonalization of the correlation matrix, we successfully obtain the energies\nof the ground-state and the 1st excited-state in this channel. The volume\ndependence of the energies suggests the existence of a possible resonance state\nslightly above the NK threshold in I=0 and $J^P=\\frac12^-$ channel.", "category": "hep-lat" }, { "text": "Charmonium spectral functions from 2+1 flavour lattice QCD: Finite temperature charmonium spectral functions in the pseudoscalar and\nvector channels are studied in lattice QCD with 2+1 flavours of dynamical\nWilson quarks, on fine isotropic lattices (with a lattice spacing of 0.057 fm),\nwith a non-physical pion mass of $m_{\\pi} \\approx$ 545 MeV. The highest\ntemperature studied is approximately $1.4 T_c$. Up to this temperature no\nsignificant variation of the spectral function is seen in the pseudoscalar\nchannel. The vector channel shows some temperature dependence, which seems to\nbe consistent with a temperature dependent low frequency peak related to heavy\nquark transport, plus a temperature independent term at \\omega>0. These results\nare in accord with previous calculations using the quenched approximation.", "category": "hep-lat" }, { "text": "Lattice QCD results at finite T and \u03bc: We propose a method to study lattice QCD at finite temperature (T) and\nchemical potential (\\mu). We test the method and compare it with the Glasgow\nmethod using n_f=4 staggered QCD with imaginary \\mu. The critical endpoint (E)\nof QCD on the Re(\\mu)-T plane is located. We use n_f=2+1 dynamical staggered\nquarks with semi-realistic masses on L_t=4 lattices. Our results are based on\n{\\cal{O}}(10^3-10^4) configurations.", "category": "hep-lat" }, { "text": "Complex spacing ratios of the non-Hermitian Dirac operator in\n universality classes AI$^\\dagger$ and AII$^\\dagger$: We consider non-Hermitian Dirac operators in QCD-like theories coupled to a\nchiral U(1) potential or an imaginary chiral chemical potential. We show that\nin the continuum they fall into the recently discovered universality classes\nAI$^\\dagger$ or AII$^\\dagger$ of random matrix theory if the fermions transform\nin pseudoreal or real representations of the gauge group, respectively. For\nstaggered fermions on the lattice this correspondence is reversed. We verify\nour predictions by computing spacing ratios of complex eigenvalues, whose\ndistribution is universal without the need for unfolding.", "category": "hep-lat" }, { "text": "Light Hadron Masses from Lattice QCD: This article reviews lattice QCD results for the light hadron spectrum. We\ngive an overview of different formulations of lattice QCD, with discussions on\nthe fermion doubling problem and improvement programs. We summarize recent\ndevelopments in algorithms and analysis techniques, that render calculations\nwith light, dynamical quarks feasible on present day computer resources.\nFinally, we summarize spectrum results for ground state hadrons and resonances\nusing various actions.", "category": "hep-lat" }, { "text": "Hopping Parameter Analysis of Leptonic and Semi-Leptonic Heavy-Light\n Decays: We study leptonic and semi-leptonic decays of D and B mesons. Use of the\nHopping Parameter Expansion (HPE) for two-point functions allows us\ncontinuously to vary the pseudoscalar mass from below m_D up towards m_B. We\ncompute the pseudoscalar decay constants f_D and f_B, and observe consistency\nwith the value calculated in the static limit. {}From the measurement of\nthree-point functions we compute the matrix element relevant to the decay \\bar\nB -> D l \\bar nu_l and extract the Isgur-Wise function xi(v.v'). The HPE\nenables us freely to vary the initial state pseudoscalar mass at constant v.v',\nand we investigate the 1/m_Q corrections to the heavy-quark limit.", "category": "hep-lat" }, { "text": "Hadron correlators with improved fermions: We investigate point-to-point correlation functions for various mesonic and\nbaryonic channels using the ${\\cal O}(a)$-improved Wilson action due to\nSheikholeslami and Wohlert. We consider propagators to both time slices 0 and\n1. We find that discretisation effects are more pronounced than those reported\nwith unimproved Wilson fermions, but that the same procedure for removing\nfinite size effects is successful. Extrapolating to the chiral limit, we see\nthe notable features predicted phenomenologically: the ratio of interacting to\nfree correlators in the vector channel is roughly constant to about 1 fm, while\nin the pseudoscalar channel the ratio increases markedly due to the strong\nbinding.", "category": "hep-lat" }, { "text": "Practical methods for a direct calculation of $\u0394I=1/2$ $K$ to\n $\u03c0\u03c0$ Decay: A direct calculation of the complex $\\Delta I=1/2$ kaon decay amplitude is\nnotoriously difficult because of the presence of disconnected graphs. Here we\ndescribe and demonstrate two practical methods to defeat this problem: the\nEigCG algorithm and the use of time-separated $\\pi-\\pi$ sources. With a fine\ntuned EigCG implementation for domain wall fermions, the calculation of light\nquark propagators is accelerated by a factor of 5-10 on a variety of lattices\nfrom small ($16^3\\times32\\times16$) to large ($32^3\\times64\\times32$). In\naddition, a substantial reduction in noise is achieved by separating each of\nthe sources for the two pions in the time direction by 2-5 lattice spacings.\nThese methods are combined in a calculation of $K$ to $\\pi\\pi$ threshold decay\nusing a $24^3\\times64\\times16$ volume and 329 MeV pions. These methods result\nin non-zero signals for both Re($A_0$) and Im($A_0$) from 138 gauge\nconfigurations.", "category": "hep-lat" }, { "text": "The Mellin moments $\\langle x \\rangle$ and $\\langle x^2 \\rangle$ for the\n pion and kaon from lattice QCD: We present a calculation of the pion quark momentum fraction, $\\langle x\n\\rangle$, and its third Mellin moment $\\langle x^2 \\rangle$. We also obtain\ndirectly, for the first time, $\\langle x \\rangle$ and $\\langle x^2 \\rangle$ for\nthe kaon using local operators. We use an ensemble of two degenerate light, a\nstrange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with\nclover improvement. The quark masses are chosen so that they reproduce a pion\nmass of about 260 MeV, and a kaon mass of 530 MeV. The lattice spacing of the\nensemble is 0.093 fm and the lattice has a spatial extent of 3 fm. We analyze\nseveral values of the source-sink time separation within the range of\n$1.12-2.23$ fm to study and eliminate excited-states contributions. The\nnecessary renormalization functions are calculated non-perturbatively in the\nRI$'$ scheme, and are converted to the $\\overline{\\rm MS}$ scheme at a scale of\n2 GeV. The final values for the momentum fraction are $\\langle x\n\\rangle^\\pi_{u^+}=0.261(3)_{\\rm stat}(6)_{\\rm syst}$, $\\langle x\n\\rangle^K_{u^+}=0.246(2)_{\\rm stat}(2)_{\\rm syst}$, and $\\langle x\n\\rangle^K_{s^+}=0.317(2)_{\\rm stat}(1)_{\\rm syst}$. For the third Mellin\nmoments we find $\\langle x^2 \\rangle^\\pi_{u^+}=0.082(21)_{\\rm stat}(17)_{\\rm\nsyst}$, $\\langle x^2 \\rangle^K_{u^+}=0.093(5)_{\\rm stat}(3)_{\\rm syst}$, and\n$\\langle x^2 \\rangle^K_{s^+}=0.134(5)_{\\rm stat}(2)_{\\rm syst}$. The reported\nsystematic uncertainties are due to excited-state contamination. We also give\nthe ratio $\\langle x^2 \\rangle/\\langle x \\rangle$ which is an indication of how\nquickly the PDFs lose support at large $x$.", "category": "hep-lat" }, { "text": "Chiral Limit of Staggered Fermions at Strong Couplings: A Loop\n Representation: The partition function of two dimensional massless staggered fermions\ninteracting with U(N) gauge fields is rewritten in terms of loop variables in\nthe strong coupling limit. We use this representation of the theory to devise a\nnon-local Metropolis algorithm to calculate the chiral susceptibility. For\nsmall lattices our algorithm reproduces exact results quite accurately.\nApplying this algorithm to large volumes yields rather surprising results. In\nparticular we find $m_\\pi \\neq 0$ for all $N$ and it increases with $N$. Since\nthe talk was presented we have found reasons to believe that our algorithm\nbreaks down for large volumes questioning the validity of our results.", "category": "hep-lat" }, { "text": "Extending the eigCG algorithm to nonsymmetric Lanczos for linear systems\n with multiple right-hand sides: The technique that was used to build the EigCG algorithm for sparse symmetric\nlinear systems is extended to the nonsymmetric case using the BiCG algorithm.\nWe show that, similarly to the symmetric case, we can build an algorithm that\nis capable of computing a few smallest magnitude eigenvalues and their\ncorresponding left and right eigenvectors of a nonsymmetric matrix using only a\nsmall window of the BiCG residuals while simultaneously solving a linear system\nwith that matrix. For a system with multiple right-hand sides, we give an\nalgorithm that computes incrementally more eigenvalues while solving the first\nfew systems and then uses the computed eigenvectors to deflate BiCGStab for the\nremaining systems. Our experiments on various test problems, including Lattice\nQCD, show the remarkable ability of EigBiCG to compute spectral approximations\nwith accuracy comparable to that of the unrestarted, nonsymmetric Lanczos.\nFurthermore, our incremental EigBiCG followed by appropriately restarted and\ndeflated BiCGStab provides a competitive method for systems with multiple\nright-hand sides.", "category": "hep-lat" }, { "text": "Status of Lattice QCD Determination of Nucleon Form Factors and their\n Relevance for the Few-GeV Neutrino Program: Calculations of neutrino-nucleus cross sections begin with the\nneutrino-nucleon interaction, making the latter critically important to\nflagship neutrino oscillation experiments, despite limited measurements with\npoor statistics. Alternatively, lattice QCD (LQCD) can be used to determine\nthese interactions from the Standard Model with quantifiable theoretical\nuncertainties. Recent LQCD results of $g_{\\mathrm{A}}$ are in excellent\nagreement with data, and results for the (quasi-)elastic nucleon form factors\nwith full uncertainty budgets are expected within a few years. We review the\nstatus of the field and LQCD results for the nucleon axial form factor,\n$F_{\\mathrm{A}}(Q^2)$, a major source of uncertainty in modeling sub-GeV\nneutrino-nucleon interactions. Results from different LQCD calculations are\nconsistent, but collectively disagree with existing models, with potential\nimplications for current and future neutrino oscillation experiments. We\ndescribe a road map to solidify confidence in the LQCD results and discuss\nfuture calculations of more complicated processes, important to few-GeV\nneutrino oscillation experiments.", "category": "hep-lat" }, { "text": "String breaking mechanisms induced by magnetic and electric condensates: The normal confining phase of gauge theories is characterised by the\ncondensation of magnetic monopoles and center vortices. Sometimes in coupled\ngauge system one finds another phase with simultaneous condensation of electric\nand magnetic charges. In both phases the confining string breaks down at a\ngiven scale because of pair creation, however the mechanism is different. In\nthe former case the string breaking is a mixing phenomenon which is invisible\nin the Wilson loop. On the contrary, in presence of both electric and magnetic\ncondensates the string breaking can be observed even in the Wilson loops.\nNumerical experiments on a 3D $Z_2$ gauge-Higgs system neatly show this new\nphenomenon.", "category": "hep-lat" }, { "text": "Finite-size scaling for the left-current correlator with non-degenerate\n quark masses: We study the volume dependence of the left-current correlator with\nnon-degenerate quark masses to next-to-leading order in the chiral expansion.\nWe consider three possible regimes: all quark masses are in the\n$\\epsilon$-regime, all are in the $p$-regime and a mixed-regime where the\nlighest quark masses satisfy $m_v \\Sigma V \\leq 1$ while the heavier $m_s\n\\Sigma V \\gg 1$. These results can be used to match lattice QCD and the Chiral\nEffective Theory in a large but finite box in which the Compton wavelength of\nthe lightest pions is of the order of the box size. We consider both the full\nand partially-quenched results.", "category": "hep-lat" }, { "text": "Four-loop logarithms in 3d gauge + Higgs theory: We discuss the logarithmic contributions to the vacuum energy density of the\nthree-dimensional SU(3) + adjoint Higgs theory in its symmetric phase, and\nrelate them to numerical Monte Carlo simulations. We also comment on the\nimplications of these results for perturbative and non-perturbative\ndeterminations of the pressure of finite-temperature QCD.", "category": "hep-lat" }, { "text": "Monopoles and hadron spectrum in quenched QCD: We report the preliminary results of the studies of hadron spectrum under the\nbackground of abelian and monopole gauge fields in quenched Wilson SU(3) QCD.\nAbelian gauge fields alone reproduce the same chiral limit as in the full case.\nCritical hopping parameter $\\kappa_c$ and $m_{\\rho}$ are the same in both\ncases. We need more time to get a definite result in the case of monopole\nbackground. The photon contribution do not produce any mass gap in the chiral\nlimit ($\\kappa=\\kappa_c\\sim 0.17$). The behavior is similar to those in the\nfree photon case for $\\kappa_c= 0.125$.", "category": "hep-lat" }, { "text": "Nucleon to $\u0394$ and $\u0394$ form factors in Lattice QCD: We present recent lattice QCD results on the electroweak nucleon to $\\Delta$\ntransition and $\\Delta$ form factors using dynamical fermion gauge\nconfigurations with a lowest pion mass of about 300 MeV, with special emphasis\nin the determination of the sub-dominant quadrupole $N\\gamma^*\\rightarrow\n\\Delta$ and $\\Delta$ electromagnetic form factors.", "category": "hep-lat" }, { "text": "Hadron-Hadron Interactions from Imaginary-time Nambu-Bethe-Salpeter Wave\n Function on the Lattice: Imaginary-time Nambu-Bethe-Salpeter (NBS) wave function is introduced to\nextend our previous approach for hadron-hadron interactions on the lattice.\nScattering states of hadrons with different energies encoded in the NBS\nwave-function are utilized to extract non-local hadron-hadron potential. \"The\nground state saturation\", which is commonly used in lattice QCD but is hard to\nbe achieved for multi-baryons, is not required. We demonstrate that the present\nmethod works efficiently for the nucleon-nucleon interaction (the potential and\nthe phase shift) in the 1S_0 channel.", "category": "hep-lat" }, { "text": "Higgs and W boson spectrum from lattice simulations: The spectrum of energy levels is computed for all available angular momentum\nand parity quantum numbers in the SU(2)-Higgs model, with parameters chosen to\nmatch experimental data from the Higgs-W boson sector of the standard model.\nSeveral multi-boson states are observed, with and without linear momentum, and\nall are consistent with weakly-interacting Higgs and W bosons. The creation\noperators used in this study are gauge-invariant so, for example, the Higgs\noperator is quadratic rather than linear in the Lagrangian's scalar field.", "category": "hep-lat" }, { "text": "Systematics of the HAL QCD Potential at Low Energies in Lattice QCD: The $\\Xi\\Xi$ interaction in the $^1$S$_0$ channel is studied to examine the\nconvergence of the derivative expansion of the non-local HAL QCD potential at\nthe next-to-next-to-leading order (N$^2$LO). We find that (i) the leading order\npotential from the N$^2$LO analysis gives the scattering phase shifts\naccurately at low energies, (ii) the full N$^2$LO potential gives only small\ncorrection to the phase shifts even at higher energies below the inelastic\nthreshold, and (iii) the potential determined from the wall quark source at the\nleading order analysis agrees with the one at the N$^2$LO analysis except at\nshort distances, and thus, it gives correct phase shifts at low energies. We\nalso study the possible systematic uncertainties in the HAL QCD potential such\nas the inelastic state contaminations and the finite volume artifact for the\npotential and find that they are well under control for this particular system.", "category": "hep-lat" }, { "text": "Distributing the chiral and flavour components of Dirac-Kahler fermions\n across multiple lattices: We use a specific implementation of discrete differential geometry to\ndescribe Dirac-Kahler fermions in such a way that we can separate their chiral\nand flavour components. The formulation introduces additional lattices so that\non each lattice there is a single field of definate chirality. Within this\nframework, we define an non-compact Abelian gauge theory.", "category": "hep-lat" }, { "text": "Correlation functions in lattice formulations of quantum gravity: We compare different models of a quantum theory of four-dimensional lattice\ngravity based on Regge's original proposal. From Monte Carlo simulations we\ncalculate two-point functions between geometrical quantities and estimate the\nmasses of the corresponding interaction particles.", "category": "hep-lat" }, { "text": "Lattice QCD study of baryon-baryon interactions in the (S,I)=(-2,0)\n system using the coupled-channel formalism: We investigate baryon-baryon interactions with strangeness $S=-2$ and isospin\nI=0 system from Lattice QCD. In order to solve this system, we prepare three\ntypes of baryon-baryon operators ($\\Lambda-\\Lambda$, $N-\\Xi$ and\n$\\Sigma-\\Sigma$) for the sink and construct three source operators\ndiagonalizing the $3\\times3$ correlation matrix. Combining of the prepared sink\noperators with the diagonalized source operators, we obtain nine effective\nNambu-Bethe-Salpeter (NBS) wave functions. The $3\\times3$ potential matrix is\ncalculated by solving the coupled-channel Schr\\\"odinger equation. The flavor\nSU(3) breaking effects of the potential matrix are also discussed by comparing\nwith the results of the SU(3) limit calculation. Our numerical results are\nobtained from three sets of 2+1 flavor QCD gauge configurations provided by the\nCP-PACS/JLQCD Collaborations.", "category": "hep-lat" }, { "text": "Chiral Phase Transition in Lattice QCD with Wilson Quarks: The nature of the chiral phase transition in lattice QCD is studied for the\ncases of 2, 3 and 6 flavors with degenerate Wilson quarks, mainly on a lattice\nwith the temporal direction extension $N_t=4$. We find that the chiral phase\ntransition is continuous for the case of 2 flavors, while it is of first order\nfor 3 and 6 flavors.", "category": "hep-lat" }, { "text": "New Algorithm of the Finite Lattice Method for the High-temperature\n Expansion of the Ising Model in Three Dimensions: We propose a new algorithm of the finite lattice method to generate the\nhigh-temperature series for the Ising model in three dimensions. It enables us\nto extend the series for the free energy of the simple cubic lattice from the\nprevious series of 26th order to 46th order in the inverse temperature. The\nobtained series give the estimate of the critical exponent for the specific\nheat in high precision.", "category": "hep-lat" }, { "text": "Chebyshev and Backus-Gilbert reconstruction for inclusive semileptonic\n $B_{(s)}$-meson decays from Lattice QCD: We present a study on the nonperturbative calculation of observables for\ninclusive semileptonic decays of $B_{(s)}$ mesons using lattice QCD. We focus\non the comparison of two different methods to analyse the lattice data of\nEuclidean correlation functions, specifically Chebyshev and Backus-Gilbert\napproaches. This type of computation may eventually provide new insight into\nthe long-standing tension between the inclusive and exclusive determinations of\nthe Cabibbo-Kobayashi-Maskawa (CKM) matrix elements $|V_{cb}|$ and $|V_{ub}|$.\nWe report the results from a pilot lattice computation for the decay $B_s\n\\rightarrow X_c \\, l\\nu_l$, where the valence quark masses are approximately\ntuned to their physical values using the relativistic-heavy quark action for\nthe $b$ quark and the domain-wall formalism for the other valence quarks. We\naddress the computation of the total decay rate as well as leptonic and\nhadronic moments, discussing similarities and differences between the two\nanalysis techniques.", "category": "hep-lat" }, { "text": "Numerical tests of the electroweak phase transition and thermodynamics\n of the electroweak plasma: The finite temperature phase transition in the SU(2) Higgs model at a Higgs\nboson mass $M_H \\simeq 34$ GeV is studied in numerical simulations on\nfour-dimensional lattices with time-like extensions up to $L_t=5$. The effects\nof the finite volume and finite lattice spacing on masses and couplings are\nstudied in detail. The errors due to uncertainties in the critical hopping\nparameter are estimated. The thermodynamics of the electroweak plasma near the\nphase transition is investigated by determining the relation between energy\ndensity and pressure.", "category": "hep-lat" }, { "text": "Systematics of the HAL QCD Potential at Low Energies in Lattice QCD: The $\\Xi\\Xi$ interaction in the $^1$S$_0$ channel is studied to examine the\nconvergence of the derivative expansion of the non-local HAL QCD potential at\nthe next-to-next-to-leading order (N$^2$LO). We find that (i) the leading order\npotential from the N$^2$LO analysis gives the scattering phase shifts\naccurately at low energies, (ii) the full N$^2$LO potential gives only small\ncorrection to the phase shifts even at higher energies below the inelastic\nthreshold, and (iii) the potential determined from the wall quark source at the\nleading order analysis agrees with the one at the N$^2$LO analysis except at\nshort distances, and thus, it gives correct phase shifts at low energies. We\nalso study the possible systematic uncertainties in the HAL QCD potential such\nas the inelastic state contaminations and the finite volume artifact for the\npotential and find that they are well under control for this particular system.", "category": "hep-lat" }, { "text": "Absolute X-distribution and self-duality: Various models of QCD vacuum predict that it is dominated by excitations that\nare predominantly self-dual or anti-self-dual. In this work we look at the\ntendency for self-duality in the case of pure-glue SU(3) gauge theory using the\noverlap-based definition of the field-strength tensor. To gauge this property,\nwe use the absolute X-distribution method which is designed to quantify the\ndynamical tendency for polarization for arbitrary random variables that can be\ndecomposed in a pair of orthogonal subspaces.", "category": "hep-lat" }, { "text": "Center Projection With and Without Gauge Fixing: We consider projections of SU(2) lattice link variables onto Z(2) center and\nU(1) subgroups, with and without gauge-fixing. It is shown that in the absence\nof gauge-fixing, and up to an additive constant, the static quark potential\nextracted from projected variables agrees exactly with the static quark\npotential taken from the full link variables; this is an extension of recent\narguments by Ambjorn and Greensite, and by Ogilvie. Abelian and center\ndominance is essentially trivial in this case, and seems of no physical\nrelevance. The situation changes drastically upon gauge fixing. In the case of\ncenter projection, there are a series of tests one can carry out, to check if\nvortices identified in the projected configurations are physical objects. All\nthese criteria are satisfied in maximal center gauge, and we show here that\nthey all fail in the absence of gauge fixing. The non-triviality of center\nprojection is due entirely to the maximal center gauge-fixing, which pumps\ninformation about the location of extended physical objects into local Z(2)\nobservables.", "category": "hep-lat" }, { "text": "Lattice gauge-fixing for generic covariant gauges: We propose a method which allows the generalization of the Landau lattice\ngauge-fixing procedure to generic covariant gauges. We report preliminary\nnumerical results showing how the procedure works for $SU(2)$ and $SU(3)$. We\nalso report numerical results showing that the contribution of finite\nlattice-spacing effects and/or spurious copies are relevant in the lattice\ngauge-fixing procedure.", "category": "hep-lat" }, { "text": "Twisted mass ensemble generation on GPU machines: We present how we ported the Hybrid Monte Carlo implementation in the tmLQCD\nsoftware suite to GPUs through offloading its most expensive parts to the QUDA\nlibrary. We discuss our motivations and some of the technical challenges that\nwe encountered as we added the required functionality to both tmLQCD and QUDA.\nWe further present some performance details, focussing in particular on the\nusage of QUDA's multigrid solver for poorly conditioned light quark monomials\nas well as the multi-shift solver for the non-degenerate strange and charm\nsector in $N_f=2+1+1$ simulations using twisted mass clover fermions, comparing\nthe efficiency of state-of-the-art simulations on CPU and GPU machines. We also\ntake a look at the performance-portability question through preliminary tests\nof our HMC on a machine based on AMD's MI250 GPU, finding good performance\nafter a very minor additional porting effort. Finally, we conclude that we\nshould be able to achieve GPU utilisation factors acceptable for the current\ngeneration of (pre-)exascale supercomputers with subtantial efficiency\nimprovements and real time speedups compared to just running on CPUs. At the\nsame time, we find that future challenges will require different approaches\nand, most importantly, a very significant investment of personnel for software\ndevelopment.", "category": "hep-lat" }, { "text": "Evidence for fine tuning of fermionic modes in lattice gluodynamics: We consider properties of zero and near-zero fermionic modes in lattice\ngluodynamics. The modes are known to be sensitive to the topology of the\nunderlying gluonic fields in the quantum vacuum state of the gluodynamics. We\nfind evidence that these modes are fine tuned, that is exhibit sensitivity to\nboth physical (one can say, hadronic) scale and to the ultraviolet cutoff.\nNamely, the density of the states is in physical units while the localization\nvolume of the modes tends to zero in physical units with the lattice spacing\ntending to zero. We discuss briefly possible theoretical implications and also\ninclude some general, review-type remarks.", "category": "hep-lat" }, { "text": "Towards the continuum limit of nucleon form factors at the physical\n point using lattice QCD: We present results for the axial charge and root-mean-square (RMS) radii of\nthe nucleon obtained from 2+1 flavor lattice QCD at the physical point with a\nlarge spatial extent of about 10 fm. Our calculations are performed with the\nPACS10 gauge configurations generated by the PACS Collaboration with the six\nstout-smeared $O(a)$ improved Wilson-clover quark action and Iwasaki gauge\naction at $\\beta$ = 1.82 and 2.00 corresponding to lattice spacings of 0.085 fm\nand 0.063 fm respectively. We first evaluate the value of $g_A/g_V$ , which is\nnot renormalized in the continuum limit and thus ends up with the renormalized\naxial charge. Moreover, we also calculate the nucleon elastic form factors and\ndetermine three kinds of isovector RMS radii such as electric, magnetic and\naxial ones at the two lattice spacings. We finally discuss the discretization\nuncertainties on renormalized axial charge and isovector RMS radii towards the\ncontinuum limit.", "category": "hep-lat" }, { "text": "Non-perturbative renormalization of quark mass in Nf=2+1 QCD with the\n Schroedinger functional scheme: We present an evaluation of the quark mass renormalization factor for Nf=2+1\nQCD. The Schroedinger functional scheme is employed as the intermediate scheme\nto carry out non-perturbative running from the low energy to deep in the high\nenergy perturbative region. The regularization independent step scaling\nfunction of the quark mass is obtained in the continuum limit. Renormalization\nfactors for the pseudo scalar density and the axial vector current are also\nevaluated for the same action and the bare couplings as two recent large scale\nNf=2+1 simulations; previous work of the CP-PACS/JLQCD collaboration, which\ncovered the up-down quark mass range heavier than m_pi=500 MeV and that of\nPACS-CS collaboration on the physical point using the reweighting technique.", "category": "hep-lat" }, { "text": "The Status of D-Theory: Field theories are usually quantized by performing a path integral over\nconfigurations of classical fields. This is the case both in perturbation\ntheory and in Wilson's nonperturbative lattice field theory. D-theory is an\nalternative nonperturbative formulation of field theory in which classical\nfields emerge from the low-energy collective dynamics of discrete quantum\nvariables (quantum spins and their gauge analogs -- quantum links) which\nundergo dimensional reduction. D-theory was developed some time ago as a\ndiscrete approach to U(1) and SU(2) pure gauge theories, extended to SU(N)\ngauge theories and full QCD, and also applied to a variety of other models. On\nthe practical side, D-theory provides a framework for the development of\nefficient numerical methods, such as cluster algorithms. For example, in the\nD-theory formulation of CP(N-1) models one can simulate efficiently at non-zero\nchemical potential or at non-zero vacuum angle theta. On the conceptual side,\nD-theory offers a natural solution for the nonperturbative hierarchy problem of\nchiral symmetry in QCD. We also take a broader nonperturbative view on\nfundamental physics and speculate that D-theory variables -- i.e. quantum spins\nand quantum links -- may be promising candidates for the physical degrees of\nfreedom that Nature has chosen to regularize the standard model physics at\nultra-short distances.", "category": "hep-lat" }, { "text": "On-shell representations of two-body transition amplitudes: single\n external current: This work explores scattering amplitudes that couple two-particle systems via\na single external current insertion, $2+\\mathcal{J}\\to 2$. Such amplitudes can\nprovide structural information about the excited QCD spectrum. We derive an\nexact analytic representation for these reactions. From these amplitudes, we\nshow how to rigorously define resonance and bound-state form-factors.\nFurthermore, we explore the consequences of the narrow-width limit of the\namplitudes as well as the role of the Ward-Takahashi identity for conserved\nvector currents. These results hold for any number of two-body channels with no\nintrinsic spin, and a current with arbitrary Lorentz structure and quantum\nnumbers. This work and the existing finite-volume formalism provide a complete\nframework for determining this class of amplitudes from lattice QCD.", "category": "hep-lat" }, { "text": "Quenched charmonium near the continuum limit: We study relativistic charmonium on very fine quenched lattices (beta=6.4 and\n6.6). We concentrate on the calculation of the hyperfine splitting between\neta_c and J/psi, aiming for a controlled continuum extrapolation of this\nquantity. Results for the eta_c and J/psi wave functions are also presented.", "category": "hep-lat" }, { "text": "Lattice QCD Study for Confinement and Hadrons: Using SU(3) lattice QCD, we perform the detailed studies of the three-quark\nand the multi-quark potentials. From the accurate calculation for more than 300\ndifferent patterns of 3Q systems, the static ground-state 3Q potential $V_{\\rm\n3Q}^{\\rm g.s.}$ is found to be well described by the Coulomb plus Y-type linear\npotential (Y-Ansatz) within 1%-level deviation. As a clear evidence for\nY-Ansatz, Y-type flux-tube formation is actually observed on the lattice in\nmaximally-Abelian projected QCD. For about 100 patterns of 3Q systems, we\nperform the accurate calculation for the 1st excited-state 3Q potential $V_{\\rm\n3Q}^{\\rm e.s.}$ by diagonalizing the QCD Hamiltonian in the presence of three\nquarks, and find a large gluonic-excitation energy $\\Delta E_{\\rm 3Q} \\equiv\nV_{\\rm 3Q}^{\\rm e.s.}-V_{\\rm 3Q}^{\\rm g.s.}$ of about 1 GeV, which gives a\nphysical reason of the success of the quark model. $\\Delta E_{\\rm 3Q}$ is found\nto be reproduced by the ``inverse Mercedes Ansatz'', which indicates a\ncomplicated bulk excitation for the gluonic-excitation mode. We study also the\ntetra-quark and the penta-quark potentials in lattice QCD, and find that they\nare well described by the OGE Coulomb plus multi-Y type linear potential, which\nsupports the flux-tube picture even for the multi-quarks.", "category": "hep-lat" }, { "text": "Lattice QCD study of a five-quark hadronic molecule: We compute the ground-state energies of a heavy-light K-Lambda like system as\na function of the relative distance r of the hadrons. The heavy quarks, one in\neach hadron, are treated as static. Then, the energies give rise to an\nadiabatic potential Va(r) which we use to study the structure of the five-quark\nsystem. The simulation is based on an anisotropic and asymmetric lattice with\nWilson fermions. Energies are extracted from spectral density functions\nobtained with the maximum entropy method. Our results are meant to give\nqualitative insight: Using the resulting adiabatic potential in a Schroedinger\nequation produces bound state wave functions which indicate that the ground\nstate of the five-quark system resembles a hadronic molecule, whereas the first\nexcited state, having a very small rms radius, is probably better described as\na five-quark cluster, or a pentaquark. We hypothesize that an all light-quark\npentaquark may not exist, but in the heavy-quark sector it might, albeit only\nas an excited state.", "category": "hep-lat" }, { "text": "Weak universality induced by $Q=\\pm 2e$ charges at the deconfinement\n transition of a (2+1)-d $U(1)$ lattice gauge theory: Matter-free lattice gauge theories (LGTs) provide an ideal setting to\nunderstand confinement to deconfinement transitions at finite temperatures,\nwhich is typically due to the spontaneous breakdown (at large temperatures) of\nthe centre symmetry associated with the gauge group. Close to the transition,\nthe relevant degrees of freedom (Polyakov loop) transform under these centre\nsymmetries, and the effective theory only depends on the Polyakov loop and its\nfluctuations. As shown first by Svetitsky and Yaffe, and subsequently verified\nnumerically, for the $U(1)$ LGT in $(2+1)$-d the transition is in the 2-d XY\nuniversality class, while for the $Z_2$ LGT, it is in the 2-d Ising\nuniversality class. We extend this classic scenario by adding higher charged\nmatter fields, and show that the notion of universality is generalized such\nthat the critical exponents $\\gamma, \\nu$ can change continuously as a coupling\nis varied, while their ratio is fixed to the 2-d Ising value. While such weak\nuniversality is well-known for spin models, we demonstrate this for LGTs for\nthe first time. Using an efficient cluster algorithm, we show that the finite\ntemperature phase transition of the $U(1)$ quantum link LGT in the spin\n$S=\\frac{1}{2}$ representation is in the 2-d XY universality class, as\nexpected. On the addition of $Q = \\pm 2e$ charges distributed thermally, we\ndemonstrate the occurrence of weak universality.", "category": "hep-lat" }, { "text": "A quark action for very coarse lattices: We investigate a tree-level O(a^3)-accurate action, D234c, on coarse\nlattices. For the improvement terms we use tadpole-improved coefficients, with\nthe tadpole contribution measured by the mean link in Landau gauge.\n We measure the hadron spectrum for quark masses near that of the strange\nquark. We find that D234c shows much better rotational invariance than the\nSheikholeslami-Wohlert action, and that mean-link tadpole improvement leads to\nsmaller finite-lattice-spacing errors than plaquette tadpole improvement. We\nobtain accurate ratios of lattice spacings using a convenient ``Galilean\nquarkonium'' method.\n We explore the effects of possible O(alpha_s) changes to the improvement\ncoefficients, and find that the two leading coefficients can be independently\ntuned: hadron masses are most sensitive to the clover coefficient, while hadron\ndispersion relations are most sensitive to the third derivative coefficient\nC_3. Preliminary non-perturbative tuning of these coefficients yields values\nthat are consistent with the expected size of perturbative corrections.", "category": "hep-lat" }, { "text": "Controlling sign problems in spin models using tensor renormalization: We consider the sign problem for classical spin models at complex $\\beta\n=1/g_0^2$ on $L\\times L$ lattices. We show that the tensor renormalization\ngroup method allows reliable calculations for larger Im$\\beta$ than the\nreweighting Monte Carlo method. For the Ising model with complex $\\beta$ we\ncompare our results with the exact Onsager-Kaufman solution at finite volume.\nThe Fisher zeros can be determined precisely with the TRG method. We check the\nconvergence of the TRG method for the O(2) model on $L\\times L$ lattices when\nthe number of states $D_s$ increases. We show that the finite size scaling of\nthe calculated Fisher zeros agrees very well with the Kosterlitz-Thouless\ntransition assumption and predict the locations for larger volume. The location\nof these zeros agree with Monte Carlo reweighting calculation for small volume.\nThe application of the method for the O(2) model with a chemical potential is\nbriefly discussed.", "category": "hep-lat" }, { "text": "Lee-Yang zeroes in the one flavour massive lattice Schwinger model: We study the partition function of the model formulated with Wilson fermions\nwith only one species, both analytically and numerically. At strong coupling we\nconstruct the solution for lattice size up to $8\\times 8$, a polynomial in the\nhopping parameter up to $O(\\ka^{128})$. At $\\be>0$ we evaluate the expectation\nvalue of the fermion determinant for complex values of $\\ka$. From the Lee-Yang\nzeroes we find support for the existence of a line of phase transitions from\n$(\\be=0, \\ka\\simeq 0.38)$ up to $(\\be=\\infty, \\ka=1/4)$.", "category": "hep-lat" }, { "text": "Order a improved renormalization constants: We present non-perturbative results for the constants needed for on-shell\n$O(a)$ improvement of bilinear operators composed of Wilson fermions. We work\nat $\\beta=6.0$ and 6.2 in the quenched approximation. The calculation is done\nby imposing axial and vector Ward identities on correlators similar to those\nused in standard hadron mass calculations. A crucial feature of the calculation\nis the use of non-degenerate quarks. We also obtain results for the constants\nneeded for off-shell $O(a)$ improvement of bilinears, and for the scale and\nscheme independent renormalization constants, (Z_A), (Z_V) and (Z_S/Z_P).\nSeveral of the constants are determined using a variety of different Ward\nidentities, and we compare their relative efficacies. In this way, we find a\nmethod for calculating $c_V$ that gives smaller errors than that used\npreviously. Wherever possible, we compare our results with those of the ALPHA\ncollaboration (who use the Schr\\\"odinger functional) and with 1-loop\ntadpole-improved perturbation theory.", "category": "hep-lat" }, { "text": "B, Bs, K and pi weak matrix elements with physical light quarks: Calculations of pseudoscalar decay constants of B, Bs, K and pi mesons with\nphysical light quarks are presented. We use HISQ ensembles that include u,d,s\nand c sea quarks at three lattice spacings. HISQ is used for the valence light\nquarks and a radiatively improved NRQCD action for the heavy quarks. The key\nresults are f_{B^+}=0.184(4)$ GeV, f_{B_s}=0.224(4) GeV,\nf_{B_s}/f_{B^+}=1.217(8), f_{K^+}/f_{pi^+}=1.1916(21), f_{K^+}=155.37(34) MeV,\ngiving a significant improvement over previous results that required chiral\nextrapolation. We also calculate the Wilson flow scale w_0, finding\nw_0=0.1715(9) fm.", "category": "hep-lat" }, { "text": "Phase structure of two-color QCD at real and imaginary chemical\n potentials; lattice simulations and model analyses: We investigate the phase structure of two-color QCD at both real and\nimaginary chemical potentials mu, performing lattice simulations and analyzing\nthe data with the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model.\nLattice QCD simulations are done on an 8^3 times 4 lattice with the\nclover-improved two-flavor Wilson fermion action and the renormalization-group\nimproved Iwasaki gauge action. We test the analytic continuation of physical\nquantities from imaginary mu to real mu by comparing lattice QCD results\ncalculated at real mu with the result of analytic function the coefficients of\nwhich are determined from lattice QCD results at imaginary mu. We also test the\nvalidity of the PNJL model by comparing model results with lattice QCD ones.\nThe PNJL model is good in the deconfinement region, but less accurate in the\ntransition and confinement regions. This problem is improved by introducing the\nbaryon degree of freedom to the model. It is also found that the vector-type\nfour-quark interaction is necessary to explain lattice data on the quark number\ndensity.", "category": "hep-lat" }, { "text": "Monopoles and Spatial String Tension in the High Temperature Phase of\n SU(2) QCD: We studied a behavior of monopole currents in the high temperature\n(deconfinement) phase of abelian projected finite temperature SU(2) QCD in\nmaximally abelian gauge. Wrapped monopole currents closed by periodic boundary\nplay an important role for the spatial string tension which is a\nnon-perturbative quantity in the deconfinement phase. The wrapped monopole\ncurrent density seems to be non-vanishing in the continuum limit. These results\nmay be related to Polyakov's analysis of the confinement mechanism using\nmonopole gas in 3-dimensional SU(2) gauge theory with Higgs fields.", "category": "hep-lat" }, { "text": "The QCD equation of state in background magnetic fields: We determine the equation of state of 2+1-flavor QCD with physical quark\nmasses, in the presence of a constant (electro)magnetic background field on the\nlattice. To determine the free energy at nonzero magnetic fields we develop a\nnew method, which is based on an integral over the quark masses up to\nasymptotically large values where the effect of the magnetic field can be\nneglected. The method is compared to other approaches in the literature and\nfound to be advantageous for the determination of the equation of state up to\nlarge magnetic fields. Thermodynamic observables including the longitudinal and\ntransverse pressure, magnetization, energy density, entropy density and\ninteraction measure are presented for a wide range of temperatures and magnetic\nfields, and provided in ancillary files. The behavior of these observables\nconfirms our previous result that the transition temperature is reduced by the\nmagnetic field. We calculate the magnetic susceptibility and permeability,\nverifying that the thermal QCD medium is paramagnetic around and above the\ntransition temperature, while we also find evidence for weak diamagnetism at\nlow temperatures.", "category": "hep-lat" }, { "text": "Landau gauge gluon and ghost propagators from two-flavor lattice QCD at\n T > 0: In this contribution we extend our unquenched computation of the Landau gauge\ngluon and ghost propagators in lattice QCD at non-zero temperature. The study\nwas aimed at providing input for investigations employing continuum functional\nmethods. We show data which correspond to pion mass values between 300 and 500\nMeV and are obtained for a lattice size 32**3 x 12. The longitudinal and\ntransversal components of the gluon propagator turn out to change smoothly\nthrough the crossover region, while the ghost propagator exhibits only a very\nweak temperature dependence. For a pion mass of around 400 MeV and the\nintermediate temperature value of approx. 240 MeV we compare our results with\nadditional data obtained on a lattice with smaller Euclidean time extent N_t =\n8, 10 and find a reasonable scaling behavior.", "category": "hep-lat" }, { "text": "Fermionic observables in Numerical Stochastic Perturbation Theory: We present technical details of fermionic observables computations in NSPT.\nIn particular we discuss the construction of composite operators starting from\nthe inverse Dirac operator building block, the subtraction of UV divergences\nand the treatment of irrelevant contributions in extracting the continuum\nlimit.", "category": "hep-lat" }, { "text": "Lattice calculation of SU(3) flavor breaking ratios in B - anti-B mixing: We present an unquenched lattice calculation for the SU(3) flavor breaking\nratios of the heavy-light decay constants and the $\\Delta B = 2$ matrix\nelements. The calculation was performed on $16^3 \\times 32$ lattices with two\ndynamical flavors of domain-wall quarks and inverse lattice spacing $1/a =\n1.69(5)$ GeV. Heavy quarks were implemented using an improved lattice\nformulation of the static approximation. In the infinite heavy-quark mass limit\nwe obtain $f_{B_s}/f_{B_d} = 1.29(4)(6)$, $B_{B_s}/B_{B_d} = 1.06(6)(4)$, $\\xi\n= 1.33(8)(8)$ where the first error is statistical and the second systematic.", "category": "hep-lat" }, { "text": "Duality and scaling in 3-dimensional scalar electrodynamics: Three-dimensional scalar electrodynamics, with a local U(1) gauge symmetry,\nis believed to be dual to a scalar theory with a global U(1) symmetry, near the\nphase transition point. The conjectured duality leads to definite predictions\nfor the scaling exponents of the gauge theory transition in the type II region,\nand allows thus to be scrutinized empirically. We review these predictions, and\ncarry out numerical lattice Monte Carlo measurements to test them: a number of\nexponents, characterising the two phases as well as the transition point, are\nfound to agree with expectations, supporting the conjecture. We explain why\nsome others, like the exponent characterising the photon correlation length,\nappear to disagree with expectations, unless very large system sizes and the\nextreme vicinity of the transition point are considered. Finally, we remark\nthat in the type I region the duality implies an interesting quantitative\nrelationship between a magnetic flux tube and a 2-dimensional non-topological\nsoliton.", "category": "hep-lat" }, { "text": "Correlation Functions of Hadron Currents in the QCD Vacuum Calculated in\n Lattice QCD: Point-to-point vacuum correlation functions for spatially separated hadron\ncurrents are calculated in quenched lattice QCD on a $16^3\\times 24$ lattice\nwith $6/g^2=5.7$. The lattice data are analyzed in terms of dispersion\nrelations, which enable us to extract physical information from small distances\nwhere asymptotic freedom is apparent to large distances where the hadronic\nresonances dominate. In the pseudoscalar, vector, and axial vector channels\nwhere experimental data or phenomenological information are available,\nsemi-quantitative agreement is obtained. In the nucleon and delta channels,\nwhere no experimental data exist, our lattice data complement experiments.\nComparison with approximations based on sum rules and interacting instantons\nare made, and technical details of the lattice calculation are described.", "category": "hep-lat" }, { "text": "Delta I = 3/2, K to Pi Pi Decays with a Nearly Physical Pion Mass: The Delta I = 3/2 K to Pi Pi decay amplitude is calculated on RBC/UKQCD 32^3\nx 64, L_s=32 dynamical lattices with 2+1 flavors of domain wall fermions using\nthe DSDR and Iwasaki gauge action. The calculation is performed with a single\npion mass (m_pi=141.9(2.3) MeV, partially quenched) and kaon mass\n(m_K=507.4(8.5) MeV) which are nearly physical, and with nearly energy\nconserving kinematics. Antiperiodic boundary conditions in two spatial\ndirections are used to give the two pions non-zero ground state momentum.\nResults for time separations of 20, 24, 28 and 32 between the kaon and two-pion\nsources are computed and an error weighted average is performed to reduce the\nerror. We find prelimenary results for Re(A_2)=1.396(081)_stat(160)_sys x\n10^(-8) GeV and Im(A_2) = -8.46(45)_stat(1.95)_sys x 10^(-13) GeV.", "category": "hep-lat" }, { "text": "Simulating lattice QCD at finite temperature and zero quark mass: We simulate lattice QCD with an irrelevant chiral 4-fermion interaction which\nallows us to simulate at zero quark mass. This enables us to study the\nfinite-temperature chiral-symmetry-restoring phase transition for 2 massless\nquark flavours, which is believed to be second order. In particular, it enables\nus to estimate the critical exponents which characterize the universality class\nof this transition. Our earlier simulations on $N_t=4$ and $N_t=6$ lattices\nrevealed that finite lattice-spacing artifacts on such coarse lattices affect\nthe nature of the transition. We are now simulating on $N_t=8$ lattices ($12^3\n\\times 8$, $16^3 \\times 8$ and $24^3 \\times 8$ lattices) where we expect to\nexpose the continuum behaviour of this transition.", "category": "hep-lat" }, { "text": "Spectroscopy in finite density lattice field theory: An exploratory\n study in the relativistic Bose gas: We analyze 2-point functions in the relativistic Bose gas on the lattice,\ni.e., a charged scalar phi-4 field with chemical potential mu. Using a\ngeneralized worm algorithm we perform a Monte Carlo simulation in a dual\nrepresentation in terms of fluxes where the complex action problem is overcome.\nWe explore various aspects of lattice spectroscopy at finite density and zero\ntemperature, such as the asymmetry of forward and backward propagation in time\nand the transition into the condensed phase. It is shown that after a suitable\nsubtraction the exponents for forward and backward propagation are independent\nof mu and agree with the mass obtained from the propagator at mu = 0. This\nholds for mu < mu_c and shows that below the condensation transition the mass\nis independent of mu as expected from the Silver Blaze scenario.", "category": "hep-lat" }, { "text": "A computational system for lattice QCD with overlap Dirac quarks: We outline the essential features of a Linux PC cluster which is now being\ndeveloped at National Taiwan University, and discuss how to optimize its\nhardware and software for lattice QCD with overlap Dirac quarks. At present,\nthe cluster constitutes of 30 nodes, with each node consisting of one Pentium 4\nprocessor (1.6/2.0 GHz), one Gbyte of PC800 RDRAM, one 40/80 Gbyte hard disk,\nand a network card. The speed of this system is estimated to be 30 Gflops, and\nits price/performance ratio is better than $1.0/Mflops for 64-bit (double\nprecision) computations in quenched lattice QCD with overlap Dirac quarks.", "category": "hep-lat" }, { "text": "Infrared fixed point in SU(2) gauge theory with adjoint fermions: We apply Schrodinger-functional techniques to the SU(2) lattice gauge theory\nwith N_f=2 flavors of fermions in the adjoint representation. Our use of\nhypercubic smearing enables us to work at stronger couplings than did previous\nstudies, before encountering a critical point and a bulk phase boundary.\nMeasurement of the running coupling constant gives evidence of an infrared\nfixed point g* where 1/g*^2 = 0.20(4)(3). At the fixed point, we find a mass\nanomalous dimension gamma_m(g*) = 0.31(6).", "category": "hep-lat" }, { "text": "A new strategy for evaluating the LO HVP contribution to $(g-2)_\u03bc$ on\n the lattice: A highly physical model of the subtracted $I=1$ vector polarization, obtained\nusing a dispersive representation with precise hadronic $\\tau$ decay data as\ninput, is used to investigate systematic issues in the lattice evaluation of\nthe leading order hadronic vacuum polarization contribution to the anomalous\nmagnetic moment of the muon. The model is also employed to study possible\nresolutions of these problems. A hybrid approach to analyzing lattice data,\ninvolving low-order Pad\\'e, low-degree conformal-variable polynomial, or\nsupplemented NNLO ChPT fits for $Q^2$ below $\\sim 0.1-0.2$ GeV$^2$ and direct\nnumerical integration of lattice data above this point, is shown to bring the\nsystematic issues identified under control at the sub-$1\\%$ level.", "category": "hep-lat" }, { "text": "Atomic Bose Condensation and the Lattice: I show how interaction corrections to the Bose condensation temperature of an\natomic gas can be computed using a combination of perturbative effective field\ntheory and lattice techniques.", "category": "hep-lat" }, { "text": "The Landshoff-Nachtmann Pomeron on the Lattice: We investigate the Landshoff-Nachtmann two-gluon-exchange model of the\nPomeron using gluon propagators computed in the Landau gauge within quenched\nlattice QCD calculations. We first determine an effective gluon-quark coupling\nby constraining the Pomeron-quark coupling to its phenomenological value\n$\\beta_0 = 2\\, \\gev^{-1}$. We then provide predictions for a variety of\ndiffractive processes. As the propagators have been evaluated entirely from QCD\nfirst principles (although in the quenched approximation), our results provide\na consistency check of the Landshoff-Nachtmann model. We address the issue of\nthe possible gauge-dependence of our results, which will be the object of a\nfuture study.", "category": "hep-lat" }, { "text": "Display of probability densities for data from a continuous distribution: Based on cumulative distribution functions, Fourier series expansion and\nKolmogorov tests, we present a simple method to display probability densities\nfor data drawn from a continuous distribution. It is often more efficient than\nusing histograms.", "category": "hep-lat" }, { "text": "The vector and axial vector current in Wilson ChPT: We construct the vector and axial vector currents in Wilson Chiral\nPerturbation Theory (WChPT), the low-energy effective theory for lattice QCD\nwith Wilson fermions.\n Our construction is slightly different compared to ChPT in continuum QCD,\nwhere the currents are essentially the (partially) conserved currents\nassociated with the chiral symmetries. In WChPT, due to explicit chiral\nsymmetry breaking at non-zero lattice spacing, there appear O(a) terms in the\nexpressions for the currents which do not stem from the effective action. In\naddition, the finite renormalization of the currents needs to be taken into\naccount in order to properly match the currents of the effective theory.\n As an illustration we compute f_pi to one loop with the renormalized axial\nvector current for a particular renormalization condition. It turns out that\nfor this particular condition some of the O(a) corrections are taken care of by\nthe renormalization.", "category": "hep-lat" }, { "text": "Glueball matrix elements: a lattice calculation and applications: We compute the matrix elements of the energy-momentum tensor between glueball\nstates and the vacuum in SU(3) lattice gauge theory and extrapolate them to the\ncontinuum. These matrix elements may play an important phenomenological role in\nidentifying glue-rich mesons. Based on a relation derived long ago by the ITEP\ngroup for J/psi radiative decays, the scalar matrix element leads to a\nbranching ratio for the glueball that is at least three times larger than the\nexperimentally observed branching ratio for the f_0 mesons above 1GeV. This\nsuggests that the glueball component must be diluted quite strongly among the\nknown scalar mesons. Finally we review the current best continuum determination\nof the scalar and tensor glueball masses, the deconfining temperature, the\nstring tension and the Lambda parameter, all in units of the Sommer reference\nscale, using calculations based on the Wilson action.", "category": "hep-lat" }, { "text": "Lattice Simulations using OpenACC compilers: OpenACC compilers allow one to use Graphics Processing Units without having\nto write explicit CUDA codes. Programs can be modified incrementally using\nOpenMP like directives which causes the compiler to generate CUDA kernels to be\nrun on the GPUs. In this article we look at the performance gain in lattice\nsimulations with dynamical fermions using OpenACC compilers.", "category": "hep-lat" }, { "text": "Approaching the chiral point in two-flavour lattice simulations: We investigate the behaviour of the pion decay constant and the pion mass in\ntwo-flavour lattice QCD, with the physical and chiral points as ultimate goal.\nMeasurements come from the ensembles generated by the CLS initiative using the\nO(a)-improved Wilson formulation, with lattice spacing down to about 0.05 fermi\nand pion masses as low as 190 MeV. The applicability of SU(2) chiral\nperturbation theory is investigated, and various functional forms, and their\nrange of validity, are compared. The physical scale is set through the kaon\ndecay constant, whose measurement is enabled by inserting a third, heavier\nvalence strange quark.", "category": "hep-lat" }, { "text": "Critical exponents of a three dimensional O(4) spin model: By Monte Carlo simulation we study the critical exponents governing the\ntransition of the three-dimensional classical O(4) Heisenberg model, which is\nconsidered to be in the same universality class as the finite-temperature QCD\nwith massless two flavors. We use the single cluster algorithm and the\nhistogram reweighting technique to obtain observables at the critical\ntemperature. After estimating an accurate value of the inverse critical\ntemperature $\\Kc=0.9360(1)$, we make non-perturbative estimates for various\ncritical exponents by finite-size scaling analysis. They are in excellent\nagreement with those obtained with the $4-\\epsilon$ expansion method with\nerrors reduced to about halves of them.", "category": "hep-lat" }, { "text": "(1+1)-dimensional Baryons from the SU(N) Color-Flavor Transformation: The color-flavor transformation, an identity that connects two integrals,\neach of which is over one of a dual pair of Lie groups acting in the fermionic\nFock space, is extended to the case of the special unitary group. Using this\nextension, a toy model of lattice QCD is studied: N_f species of spinless\nfermions interacting with strongly coupled SU(N_c) lattice gauge fields in 1+1\ndimensions. The color-flavor transformed theory is expressed in terms of gauge\nsinglets, the meson fields, organized into sectors distinguished by the\ndistribution of baryonic flux. A comprehensive analytical and numerical search\nis made for saddle-point configurations of the meson fields, with various\ntopological charges, in the vacuum and single-baryon sectors. Two definitions\nof the static baryon on the square lattice, straight and zigzag, are\ninvestigated. The masses of the baryonic states are estimated using the\nsaddle-point approximation for large N_c.", "category": "hep-lat" }, { "text": "JLQCD IroIro++ lattice code on BG/Q: We describe our experience on the multipurpose C++ code IroIro++ designed for\nJLQCD to run on the BG/Q installation at KEK. We discuss some details on the\nperformance improvements specific for the IBM Blue Gene Q.", "category": "hep-lat" }, { "text": "The spin content of the proton in quenched QCD: We present preliminary results on the proton spin structure function at zero\nmomentum, in the quenched approximation. Our calculation makes use of a\nnonperturbative means of determining the multiplicative renormalization of the\ntopological charge density.", "category": "hep-lat" }, { "text": "Degeneracy of vector-channel spatial correlators in high temperature QCD: We study spatial isovector meson correlators in $N_f=2$ QCD with dynamical\ndomain-wall fermions on $32^3\\times 8$ lattices at temperatures up to 380 MeV\nwith various quark masses. We measure the correlators of spin-one isovector\noperators including vector, axial-vector, tensor and axial-tensor. At\ntemperatures above $T_c$ we observe an approximate degeneracy of the\ncorrelators in these channels, which is unexpected because some of them are not\nrelated under $SU(2)_L \\times SU(2)_R$ nor $U(1)_A$ symmetries. The observed\napproximate degeneracy suggests emergent $SU(2)_{CS}$ (chiral-spin) and $SU(4)$\nsymmetries at high $T$.", "category": "hep-lat" }, { "text": "Testing universality and the fractional power prescription for the\n staggered fermion determinant: In [Phys.Rev.Lett.92:162002 (2004), hep-lat/0312025] expressions for the\ncontinuous Euclidean time limits of various lattice fermion determinants were\nderived and compared in order to test universality expectations in Lattice QCD.\nHere we review that work with emphasis on its relevance for assessing the\nfractional power prescription for the determinant in dynamical staggered\nfermion simulations. Some new supplementary material is presented; in\nparticular the status of the \"universality anomaly\" is clarified: it is shown\nto be gauge field-independent and therefore physically inconsequential.", "category": "hep-lat" }, { "text": "A multigrid accelerated eigensolver for the Hermitian Wilson-Dirac\n operator in lattice QCD: Eigenvalues of the Hermitian Wilson-Dirac operator are of special interest in\nseveral lattice QCD simulations, e.g., for noise reduction when evaluating\nall-to-all propagators. In this paper we present a Davidson-type eigensolver\nthat utilizes the structural properties of the Hermitian Wilson-Dirac operator\n$Q$ to compute eigenpairs of this operator corresponding to small eigenvalues.\nThe main idea is to exploit a synergy between the (outer) eigensolver and its\n(inner) iterative scheme which solves shifted linear systems. This is achieved\nby adapting the multigrid DD-$\\alpha$AMG algorithm to a solver for shifted\nsystems involving the Hermitian Wilson-Dirac operator. We demonstrate that\nupdating the coarse grid operator using eigenvector information obtained in the\ncourse of the generalized Davidson method is crucial to achieve good\nperformance when calculating many eigenpairs, as our study of the local\ncoherence shows. We compare our method with the commonly used software-packages\nPARPACK and PRIMME in numerical tests, where we are able to achieve significant\nimprovements, with speed-ups of up to one order of magnitude and a near-linear\nscaling with respect to the number of eigenvalues. For illustration we compare\nthe distribution of the small eigenvalues of $Q$ on a $64\\times 32^3$ lattice\nwith what is predicted by the Banks-Casher relation in the infinite volume\nlimit.", "category": "hep-lat" }, { "text": "Investigating the critical properties of beyond-QCD theories using Monte\n Carlo Renormalization Group matching: Monte Carlo Renormalization Group (MCRG) methods were designed to study the\nnon-perturbative phase structure and critical behavior of statistical systems\nand quantum field theories. I adopt the 2-lattice matching method used\nextensively in the 1980's and show how it can be used to predict the existence\nof non-perturbative fixed points and their related critical exponents in many\nflavor SU(3) gauge theories. This work serves to test the method and I study\nrelatively well understood systems: the $N_f=0$, 4 and 16 flavor models. The\npure gauge and $N_f=4$ systems are confining and chirally broken and the MCRG\nmethod can predict their bare step scaling functions. Results for the $N_f=16$\nmodel indicate the existence of an infrared fixed point with nearly marginal\ngauge coupling. I present preliminary results for the scaling dimension of the\nmass at this new fixed point.", "category": "hep-lat" }, { "text": "Progress on the QCD deconfinement critical point for $N_\\text{f}=2$\n staggered fermions: The global center symmetry of quenched QCD at zero baryonic chemical\npotential is broken spontaneously at a critical temperature $T_c$ leading to a\nfirst-order phase transition. Including heavy dynamical quarks breaks the\ncenter symmetry explicitly and weakens the first-order phase transition for\ndecreasing quark masses until it turns into a smooth crossover at a\n$Z(2)$-critical point. We investigate the $Z(2)$-critical quark mass value\ntowards the continuum limit for $N_\\text{f}=2$ flavors using lattice QCD in the\nstaggered formulation. As part of a continued study, we present results from\nMonte-Carlo simulations on $N_\\tau=8,10$ lattices. Several aspect ratios and\nquark mass values were simulated in order to obtain the critical mass from a\nfit of the Polyakov loop to a kurtosis finite size scaling formula. Moreover,\nthe possibility to develop a Ginzburg-Landau effective theory around the\n$Z(2)$-critical point is explored.", "category": "hep-lat" }, { "text": "QCD Thermodynamics: Recent results on QCD thermodynamics are presented. The nature of the T>0\ntransition is determined, which turns out to be an analytic cross-over. The\nabsolute scale for this transition is calculated. The temperature dependent\nstatic potential is given. The results were obtained by using a Symanzik\nimproved gauge and stout-link improved fermionic action. In order to approach\nthe continuum limit four different sets of lattice spacings were used with\ntemporal extensions N_t=4, 6, 8 and 10 (they correspond to lattice spacings a\n\\sim 0.3, 0.2, 0.15 and 0.12 fm). A new technique is presented, which --in\ncontrast to earlier methods-- enables one to determine the equation of state at\nvery large temperatures.", "category": "hep-lat" }, { "text": "A Wilson-Majorana Regularization for Lattice Chiral Gauge Theories: We discuss the regularization of chiral gauge theories on the lattice\nintroducing only physical degrees of freedom. This is obtained by writing the\nWilson term in a Majorana form, at the expense of the U(1) symmetry related to\nfermion number conservation. The idea of restoring chiral invariance in the\ncontinuum by introducing a properly chosen set of counterterms to be added to\nthe tree level action is checked against one-loop perturbative calculations.", "category": "hep-lat" }, { "text": "Fighting topological freezing in the two-dimensional CP$^{N-1}$ model: We perform Monte Carlo simulations of the CP$^{N-1}$ model on the square\nlattice for $N=10$, $21$, and $41$. Our focus is on the severe slowing down\nrelated to instantons. To fight this problem we employ open boundary conditions\nas proposed by L\\\"uscher and Schaefer for lattice QCD. Furthermore we test the\nefficiency of parallel tempering in a line defect. Our results for open\nboundary conditions are consistent with the expectation that topological\nfreezing is avoided, while autocorrelation times are still large. The results\nobtained with parallel tempering are encouraging.", "category": "hep-lat" }, { "text": "Numerical study of lattice index theorem usingimproved cooling and\n overlap fermions: We investigate topological charge and the index theorem on finite lattices\nnumerically. Using mean field improved gauge field configurations we calculate\nthe topological charge Q using the gluon field definition with ${\\cal\nO}(a^4)$-improved cooling and an ${\\cal O}(a^4)$-improved field strength tensor\n$F_{\\mu\\nu}$. We also calculate the index of the massless overlap fermion\noperator by directly measuring the differences of the numbers of zero modes\nwith left- and right--handed chiralities. For sufficiently smooth field\nconfigurations we find that the gluon field definition of the topological\ncharge is integer to better than 1% and furthermore that this agrees with the\nindex of the overlap Dirac operator, i.e., the Atiyah-Singer index theorem is\nsatisfied. This establishes a benchmark for reliability when calculating\nlattice quantities which are very sensitive to topology.", "category": "hep-lat" }, { "text": "The pi-N Sigma term - an evaluation using staggered fermions: A lattice calculation of the pi-N sigma term is described using dynamical\nstaggered fermions. Preliminary results give a sea term comparable in magnitude\nto the valence term.", "category": "hep-lat" }, { "text": "CP violation and Kaon weak matrix elements from Lattice QCD: In this short review, I present the recent lattice computations of kaon weak\nmatrix elements relevant to $K \\to \\pi\\pi$ decays and neutral kaon mixing.\nThese matrix elements are key to the theoretical determination of the CP\nviolation parameters $\\epsilon$ and $\\epsilon'$ . Impressive progress have been\nachieved recently, in particular the first realistic computation of\n$\\epsilon'/\\epsilon$ with physical kinematics has been reported in [1]. The\nnovelty is the $\\Delta I = 1/2$ channel, whereas the $\\Delta I = 3/2$\ncontribution is now computed at several values of the lattice spacing and\nextrapolated to the continuum limit. I will also present the status of $B_K$\nand discuss its error budget, with a particular emphasis on the perturbative\nerror. Finally I will review the matrix elements of neutral kaon mixing beyond\nthe standard model and will argue that the discrepancy observed by different\ncollaborations could be explained by the renormalisation procedure of the\nrelevant four-quark operators.", "category": "hep-lat" }, { "text": "Anatomy of the sign-problem in heavy-dense QCD: QCD at finite densities of heavy quarks is investigated using the\ndensity-of-states method. The phase factor expectation value of the quark\ndeterminant is calculated to unprecedented precision as a function of the\nchemical potential. Results are validated using those from a reweighting\napproach where the latter can produce a significant signal-to-noise ratio. We\nconfirm the particle-hole symmetry at low temperatures, find a strong sign\nproblem at intermediate values of the chemical potential, and an inverse Silver\nBlaze feature for chemical potentials close to the onset value: here, the phase\nquenched theory underestimates the density of the full theory.", "category": "hep-lat" }, { "text": "Finite-Size Scaling at Phase Coexistence: {}From a finite-size scaling (FSS) theory of cumulants of the order parameter\nat phase coexistence points, we reconstruct the scaling of the moments.\nAssuming that the cumulants allow a reconstruction of the free energy density\nno better than as an asymptotic expansion, we find that FSS for moments of low\norder is still complete. We suggest ways of using this theory for the analysis\nof numerical simulations. We test these methods numerically through the scaling\nof cumulants and moments of the magnetization in the low-temperature phase of\nthe two-dimensional Ising model. (LaTeX file; ps figures included as shar file)", "category": "hep-lat" }, { "text": "Correlation Function in Ising Models: We simulated the fourier transform of the correlation function of the Ising\nmodel in two and three dimensions using a single cluster algorithm with\nimproved estimators. The simulations are in agreement with series expansion and\nthe available exact results in $d=2$, which shows, that the cluster algorithm\ncan succesfully be applied for correlations. We show as a further result that\nour data do not support a hypothesis of Fisher that in any $d=2$ lattice the\nfourier transform of the correlation function depends on the lattice generating\nfunction only. In $d=3$ our simulation are again in agreement with the results\nfrom the series expansion, except for the amplitudes $f_{\\pm}$, where we find\n$f_+/f_-=2.06(1)$.", "category": "hep-lat" }, { "text": "Quark orbital dynamics in the proton from Lattice QCD -- from Ji to\n Jaffe-Manohar orbital angular momentum: Given a Wigner distribution simultaneously characterizing quark transverse\npositions and momenta in a proton, one can directly evaluate their\ncross-product, i.e., quark orbital angular momentum. The aforementioned\ndistribution can be obtained by generalizing the proton matrix elements of\nquark bilocal operators which define transverse momentum-dependent parton\ndistributions (TMDs); the transverse momentum information is supplemented with\ntransverse position information by introducing an additional nonzero momentum\ntransfer. A gauge connection between the quarks must be specified in the quark\nbilocal operators; the staple-shaped gauge link path used in TMD calculations\nyields the Jaffe-Manohar definition of orbital angular momentum, whereas a\nstraight path yields the Ji definition. An exploratory lattice calculation,\nperformed at the pion mass m_pi = 518 MeV, is presented which\nquasi-continuously interpolates between the two definitions and demonstrates\nthat their difference can be clearly resolved. The resulting Ji orbital angular\nmomentum is confronted with traditional evaluations based on Ji's sum rule.\nJaffe-Manohar orbital angular momentum is enhanced in magnitude compared to its\nJi counterpart.", "category": "hep-lat" }, { "text": "The topological structures in strongly coupled QGP with chiral fermions\n on the lattice: The nature of chiral phase transition for two flavor QCD is an interesting\nbut unresolved problem. One of the most intriguing issues is whether or not the\nanomalous U(1) symmetry in the flavor sector is effectively restored along with\nthe chiral symmetry. This may determine the universality class of the chiral\nphase transition. Since the physics near the chiral phase transition is\nessentially non-perturbative, we employ first principles lattice techniques to\naddress this issue. We use overlap fermions, which have exact chiral symmetry\non the lattice, to probe the anomalous U(1) symmetry violation of 2+1 flavor\ndynamical QCD configurations with domain wall fermions. The latter also\noptimally preserves chiral and flavor symmetries on the lattice, since it is\nknown that the remnant chiral symmetry of the light quarks influences the\nscaling of the chiral condensate in the crossover transition region. We observe\nthat the anomalous U(1) is not effectively restored in the chiral crossover\nregion. We perform a systematic study of the finite size and cut-off effects\nsince the signals of U(1) violation are sensitive to it. We also provide a\nglimpse of the microscopic topological structures of the QCD medium that are\nresponsible for the strongly interacting nature of the quark gluon plasma\nphase. We study the effect of these microscopic constituents through our first\ncalculations for the topological susceptibility of QCD at finite temperature,\nwhich could be a crucial input for the equation of state for anomalous\nhydrodynamics.", "category": "hep-lat" }, { "text": "High performance Beowulf computer for lattice QCD: We describe the construction of a high performance parallel computer composed\nof PC components, as well as the performance test in lattice QCD.", "category": "hep-lat" }, { "text": "The Standard Model and the Lattice: The $SU(3)\\otimes SU(2) \\otimes U(1)$ standard model maps smoothly onto a\nconventional lattice gauge formulation, including the parity violation of the\nweak interactions. The formulation makes use of the pseudo-reality of the weak\ngroup and requires the inclusion a full generation of both leptons and quarks.\nAs in continuum discussions, chiral eigenstates of the Dirac operator generate\nknown anomalies, although with rough gauge configurations these are no longer\nexact zero modes of the Dirac operator.", "category": "hep-lat" }, { "text": "Reducing cutoff effects in maximally twisted lattice QCD close to the\n chiral limit: When analyzed in terms of the Symanzik expansion, lattice correlators of\nmulti-local (gauge-invariant) operators with non-trivial continuum limit\nexhibit in maximally twisted lattice QCD ``infrared divergent'' cutoff effects\nof the type a^{2k}/(m_\\pi^2)^{h}, 2k\\geq h\\geq 1 (k,h integers), which tend to\nbecome numerically large when the pion mass gets small. We prove that, if the\naction is O(a) improved a` la Symanzik or, alternatively, the critical mass\ncounter-term is chosen in some ``optimal'' way, these lattice artifacts are\nreduced to terms that are at worst of the order a^{2}(a^2/m_\\pi^2)^{k-1}, k\\geq\n1. This implies that the continuum extrapolation of lattice results is smooth\nat least down to values of the quark mass, m_q, satisfying the order of\nmagnitude inequality m_q >a^2\\Lambda^3_{\\rm QCD}.", "category": "hep-lat" }, { "text": "The Phase Diagram of 2 flavour QCD with improved Actions: It has been proposed, that the chiral continuum limit of 2-flavour QCD with\nWilson fermions is brought about by a phase in which flavour and parity\nsymmetry are broken spontaneously at finite lattice spacing. At finite\ntemperature this phase should retract from the weak coupling limit to form 5\ncusps. This scenario is studied with tree level Symanzik improved actions for\nboth gauge and fermion fields on lattices of size $8^3\\times 4$ and $12^2\\times\n24\\times 4$.", "category": "hep-lat" }, { "text": "Renormalization of the effective theory for heavy quarks at small\n velocity: The slope of the Isgur-Wise function at the normalization point,\n$\\xi^{(1)}(1)$,is one of the basic parameters for the extraction of the $CKM$\nmatrix element $V_{cb}$ from exclusive semileptonic decay data. A method for\nmeasuring this parameter on the lattice is the effective theory for heavy\nquarks at small velocity $v$. This theory is a variant of the heavy quark\neffective theory in which the motion of the quark is treated as a perturbation.\nIn this work we study the lattice renormalization of the slow heavy quark\neffective theory. We show that the renormalization of $\\xi^{(1)}(1)$ is not\naffected by ultraviolet power divergences, implying no need of difficult\nnon-perturbative subtractions. A lattice computation of $\\xi^{(1)}(1)$ with\nthis method is therefore feasible in principle. The one-loop renormalization\nconstants of the effective theory for slow heavy quarks are computed to order\n$v^2$ together with the lattice-continuum renormalization constant of\n$\\xi^{(1)}(1)$ . We demonstrate that the expansion in the heavy-quark velocity\nreproduces correctly the infrared structure of the original (non-expanded)\ntheory to every order. We compute also the one-loop renormalization constants\nof the slow heavy quark effective theory to higher orders in $v^2$ and the\nlattice-continuum renormalization constants of the higher derivatives of the\n$\\xi$ function. Unfortunately, the renormalization constants of the higher\nderivatives are affected by ultraviolet power divergences, implying the\nnecessity of numerical non-perturbative subtractions. The lattice computation\nof higher derivatives of the Isgur-Wise function seems therefore problematic.", "category": "hep-lat" }, { "text": "A new framework to tune an improved relativistic heavy-quark action: We introduce a new non-perturbative method to tune the parameters of the\nColumbia formulation of an anisotropic, clover-improved relativistic\nheavy-quark (RHQ) action. By making use of suitable observables which can be\ncomputed at a sequence of heavy-quark mass values, employing an $O(a)$-improved\ndiscretized action with domain-wall chiral fermion, and safely interpolated\nbetween the accessible heavy-quark mass region and the static point predicted\nby heavy-quark effective theory, we are able to precisely determine the unknown\ncoefficients of the RHQ action. In this proof-of-principle study we benefit\nfrom the RBC/UKQCD Iwasaki gauge configurations with $2+1$ flavors of dynamical\nquarks, at three values of the lattice spacing varying from $0.11$ to $0.062$\nfm. Preliminary results and applications to bottom spectroscopy are also\npresented.", "category": "hep-lat" }, { "text": "Update on onium masses with three flavors of dynamical quarks: We update results presented at Lattice 2005 on charmonium masses. New\nensembles of gauge configurations with 2+1 flavors of improved staggered quarks\nhave been analyzed. Statistics have been increased for other ensembles. New\nresults are also available for P-wave mesons and for bottomonium on selected\nensembles.", "category": "hep-lat" }, { "text": "Chiral logs in twisted mass lattice QCD with large isospin breaking: The pion masses and the pion decay constant are calculated to 1-loop order in\ntwisted mass Wilson chiral perturbation theory, assuming a large pion mass\nsplitting and tuning to maximal twist. Taking the large mass splitting at\nleading order in the chiral expansion leads to significant modifications in the\nchiral logarithms. For example, the result for the charged pion mass contains a\nchiral logarithm that involves the neutral pion mass instead of the charged\none. Similar modifications appear in the results for the neutral pion mass and\nthe decay constant. These new results are used in fits to lattice data obtained\nrecently by the European twisted mass collaboration. The data can be fitted\nwell, in general better than with the standard chiral perturbation theory\nexpressions that ignore the mass splitting. The impact on the extraction of\nlow-energy couplings is briefly discussed.", "category": "hep-lat" }, { "text": "Improving center vortex detection by usage of center regions as guidance\n for the direct maximal center gauge: The center vortex model of quantum chromodynamic states that vortices, closed\ncolor-magnetic flux, percolate the vacuum. Vortices are seen as the relevant\nexcitations of the vacuum, causing confinement and dynamical chiral symmetry\nbreaking. In an appropriate gauge, as \\textit{direct maximal center gauge},\nvortices are detected by projecting onto the center degrees of freedom. Such\ngauges suffer from Gribov copy problems: different local maxima of the\ncorresponding gauge functional can result in different predictions of the\nstring tension. By using non-trivial center regions, that is, regions whose\nboundary evaluates to a non-trivial center element, a resolution of this issue\nseems possible. We use such non-trivial center regions to guide simulated\nannealing procedures, preventing an underestimation of the string tension in\norder to resolve the Gribov copy problem.", "category": "hep-lat" }, { "text": "Quenched charmonium near the continuum limit: We study relativistic charmonium on very fine quenched lattices (beta=6.4 and\n6.6). We concentrate on the calculation of the hyperfine splitting between\neta_c and J/psi, aiming for a controlled continuum extrapolation of this\nquantity. Results for the eta_c and J/psi wave functions are also presented.", "category": "hep-lat" }, { "text": "Non-Gaussian fixed point in four-dimensional pure compact U(1) gauge\n theory on the lattice: The line of phase transitions, separating the confinement and the Coulomb\nphases in the four-dimensional pure compact U(1) gauge theory with extended\nWilson action, is reconsidered. We present new numerical evidence that a part\nof this line, including the original Wilson action, is of second order. By\nmeans of a high precision simulation on homogeneous lattices on a sphere we\nfind that along this line the scaling behavior is determined by one fixed point\nwith distinctly non-Gaussian critical exponent nu = 0.365(8). This makes the\nexistence of a nontrivial and nonasymptotically free four-dimensional pure U(1)\ngauge theory in the continuum very probable. The universality and duality\narguments suggest that this conclusion holds also for the monopole loop gas,\nfor the noncompact abelian Higgs model at large negative squared bare mass, and\nfor the corresponding effective string theory.", "category": "hep-lat" }, { "text": "Particle Projection Using a Complex Langevin Method: Using complex stochastic quantization, we implement a particle-number\nprojection technique on the partition function of spin-1/2 fermions at finite\ntemperature on the lattice. We discuss the method, its application towards\nobtaining the thermal properties of finite Fermi systems in three spatial\ndimensions, and results for the first five virial coefficients of\none-dimensional, attractively interacting fermions.", "category": "hep-lat" }, { "text": "Chiral phase transition in a random matrix model with three flavors: The chiral phase transition in the conventional random matrix model is the\nsecond order in the chiral limit, irrespective of the number of flavors N_f,\nbecause it lacks the U_A(1)-breaking determinant interaction term. Furthermore,\nit predicts an unphysical value of zero for the topological susceptibility at\nfinite temperatures. We propose a new chiral random matrix model which resolves\nthese difficulties by incorporating the determinant interaction term within the\ninstanton gas picture. The model produces a second-order transition for N_f=2\nand a first-order transition for N_f=3, and recovers a physical temperature\ndependence of the topological susceptibility.", "category": "hep-lat" }, { "text": "$B_s$-$\\bar{B_s}$ mixing from lattice QCD: We study the $B^0_s-\\bar{B^0_s}$ mixing amplitude in Standard Model by\ncomputing the relevant hadronic matrix element in the static limit of lattice\nHQET with the Neuberger light quark action. In the quenched approximation, and\nafter matching to the $\\bar{\\rm MS}$ scheme in QCD, we obtain\n$\\hat{B}^{\\bar{\\rm MS},{\\rm NLO}}_{B_s}(m_b)=0.940(16)(22)$.", "category": "hep-lat" }, { "text": "Domain wall fermion zero modes on classical topological backgrounds: The domain wall approach to lattice fermions employs an additional dimension,\nin which gauge fields are merely replicated, to separate the chiral components\nof a Dirac fermion. It is known that in the limit of infinite separation in\nthis new dimension, domain wall fermions have exact zero modes, even for gauge\nfields which are not smooth. We explore the effects of finite extent in the\nfifth dimension on the zero modes for both smooth and non-smooth topological\nconfigurations and find that a fifth dimension of around ten sites is\nsufficient to clearly show zero mode effects. This small value for the extent\nof the fifth dimension indicates the practical utility of this technique for\nnumerical simulations of QCD.", "category": "hep-lat" }, { "text": "Exploring the Spectrum of QCD using the Lattice: The calculation of the spectrum of QCD is key to an understanding of the\nstrong interactions, and vital if we are to capitalize on the experimental\nstudy of the spectrum. In this paper, we describe progress towards\nunderstanding the spectrum of resonances of both mesons and baryons from\nlattice QCD, focusing in particular on the resonances of the $I=1/2$ nucleon\nstates, and of charmonium mesons composed of the heavy charmed quarks.", "category": "hep-lat" }, { "text": "Locality of staggered overlap operators: We give an explicit proof for the locality of staggered overlap operators.\nThe proof covers the original two flavor construction by Adams as well as a\nsingle flavor version. As in the case of Neuberger's operator, an admissibility\ncondition for the gauge fields is required.", "category": "hep-lat" }, { "text": "Gradient flow step-scaling function for SU(3) with ten fundamental\n flavors: We calculate the step scaling function, the lattice analog of the\nrenormalization group $\\beta$-function, for an SU(3) gauge theory with ten\nfundamental flavors. We present a detailed analysis including the study of\nsystematic effects of our extensive data set generated with ten dynamical\nflavors using the Symanzik gauge action and three times stout smeared M\\\"obius\ndomain wall fermions. Using up to $32^4$ volumes, we calculate renormalized\ncouplings for different gradient flow schemes and determine the step-scaling\n$\\beta$ function for a scale change $s=2$ on up to five different lattice\nvolume pairs. In an accompanying paper we discuss that gradient flow can\npromote lattice dislocations to instanton-like objects, introducing\nnonperturbative lattice artifacts to the step scaling function. Motivated by\nthe observation that Wilson flow sufficiently suppresses these artifacts, we\nchoose Wilson flow with the Symanzik operator as our preferred analysis. We\nstudy systematic effects by calculating the step-scaling function based on\nalternative flows (Zeuthen or Symanzik), alternative operators (Wilson\nplaquette, clover), and also explore the effects of the perturbative tree-level\nimprovement. Further we investigate the effects due to the finite value of\n$L_s$.", "category": "hep-lat" }, { "text": "High-degree Polynomial Noise Subtraction: In lattice QCD, the calculation of physical quantities from disconnected\nquark loop calculations have large variance due to the use of Monte Carlo\nmethods for the estimation of the trace of the inverse lattice Dirac operator.\nIn this work, we build upon our POLY and HFPOLY variance reduction methods by\nusing high-degree polynomials. Previously, the GMRES polynomials used were only\nstable for low-degree polynomials, but through application of a new, stable\nform of the GMRES polynomial, we have achieved higher polynomial degrees than\npreviously used. While the variance is not dependent on the trace correction\nterm within the methods, the evaluation of this term will be necessary for\nforming the vacuum expectation value estimates. This requires computing the\ntrace of high-degree polynomials, which can be evaluated stochastically through\nour new Multipolynomial Monte Carlo method. With these new high-degree noise\nsubtraction polynomials, we obtained a variance reduction for the scalar\noperator of nearly an order of magnitude over that of no subtraction on a $24^3\n\\times 32$ quenched lattice at $\\beta = 6.0$ and $\\kappa = 0.1570 \\approx\n\\kappa_{crit}$. Additionally, we observe that for sufficiently high polynomial\ndegrees, POLY and HFPOLY approach the same level of effectiveness. We also\nexplore the viability of using double polynomials for variance reduction as a\nmeans of reducing the required orthogonalization and memory costs associated\nwith forming high-degree GMRES polynomials.", "category": "hep-lat" }, { "text": "Critical Behaviour in the Single Flavor Thirring Model in 2+1d: Results of a lattice field theory simulation of the single-flavor Thirring\nmodel in 2+1 spacetime dimensions are presented. The lattice model is\nformulated using domain wall fermions as a means to recover the correct U(2)\nsymmetries of the continuum model in the limit where wall separation\n$L_s\\to\\infty$. Simulations on $12^3, 16^3\\times L_s$, varying self-interaction\nstrength $g^2$ and bare mass $m$ are performed with $L_s = 8, \\ldots 48$, and\nthe results for the bilinear condensate $\\langle\\bar\\psi\\psi\\rangle$ fitted to\na model equation of state assuming a U(2)$\\to$U(1)$\\otimes$U(1)\nsymmetry-breaking phase transition at a critical $g_c^2$. First estimates for\n$g^{-2}a$ and critical exponents are presented, showing small but significant\ndepartures from mean-field values. The results confirm that a symmetry-breaking\ntransition does exist and therefore the critical number of flavors for the\nThirring model $N_c > 1$. Results for both condensate and associated\nsusceptibility are also obtained in the broken phase on $16^3\\times48$,\nsuggesting that here the $L_s\\to\\infty$ extrapolation is not yet under control.\nWe also present results obtained with the associated 2+1$d$ truncated overlap\noperator DOL demonstrating exponential localisation, a necessary condition for\nthe recovery of U(2) global symmetry, but that recovery of the Ginsparg-Wilson\ncondition as $L_s\\to\\infty$ is extremely slow in the broken phase.", "category": "hep-lat" }, { "text": "SU(3) Deconfinement in (2+1)d from Twisted Boundary Conditions and\n Self-Duality: We study the pure SU(3) gauge theory in 2+1 dimensions on the lattice using\n't Hooft's twisted boundary conditions to force non-vanishing center flux\nthrough the finite volume. In this way we measure the free energy of spacelike\ncenter vortices as an order parameter for the deconfinement transition. The\ntransition is of 2nd order in the universality class of the 2d 3-state Potts\nmodel, which is self-dual. This self-duality can be observed directly in the\nSU(3) gauge theory, and it can be exploited to extract critical couplings with\nhigh precision in rather small volumes. We furthermore obtain estimates for\ncritical exponents and the critical temperature in units of the dimensionful\ncontinuum coupling. Finally, we also apply our methods to the (2+1)d SU(4)\ngauge theory which was previously found to have a weak 1st order transition. We\nnevertheless observe at least approximate q = 4 Potts scaling at length scales\ncorresponding to the lattice sizes used in our simulations.", "category": "hep-lat" }, { "text": "Delta expansion and Wilson fermion in the Gross-Neveu model:\n Compatibility with linear divergence and continuum limit from inverse-mass\n expansion: We apply the $\\delta$-expansion to the Gross-Neveu model in the large $N$\nlimit with Wilson fermion and investigate dynamical mass generation from\ninverse-mass expansion. The dimensionless mass $M$ defined via the effective\npotential is employed as the expansion parameter of the bare coupling constant\n$\\beta$ which is partially renormalized by the subtraction of linear\ndivergence. We show that $\\delta$-expansion of the $1/M$ series of $\\beta$ is\ncompatible with the mass renormalization. After the confirmation of the\ncontinuum scaling of the bare coupling without fermion doubling, we attempt to\nestimate dynamical mass in the continuum limit and obtain the results\nconverging to the exact value for values of Wilson parameter $r\\in (0.8,1.0)$.", "category": "hep-lat" }, { "text": "(2+1)-flavor QCD Thermodynamics from the Gradient Flow: Recently, we proposed a novel method to define and calculate the\nenergy-momentum tensor (EMT) in lattice gauge theory on the basis of the\nYang-Mills gradient flow [1]. In this proceedings, we summarize the basic idea\nand technical steps to obtain the bulk thermodynamic quantities in lattice\ngauge theory using this method for the quenched and $(2+1)$-flavor QCD. The\nrevised results of integration measure (trace anomaly) and entropy density of\nthe quenched QCD with corrected coefficients are shown. Furthermore, we also\nshow the flow time dependence of the parts of EMT including the dynamical\nfermions. This work is based on a joint-collaboration between FlowQCD and WHOT\nQCD.", "category": "hep-lat" }, { "text": "Twist-3 partonic distributions from lattice QCD: Twist-3 partonic distributions contain important information that\ncharacterizes nucleon's structure. In this work, we show our lattice\nexploration of the twist-3 PDFs $g_T(x)$, and $h_L(x)$. We also present our\npreliminary results on the twist-3 GPD $\\tilde{G}_2(x)$. We use the\nquasi-distribution approach to connect the lattice-extracted matrix elements,\nrenormalized in the RI/MOM scheme, to light-cone distributions, applying the\nmatching procedure that we developed in parallel. We also calculate the twist-2\ncounterparts of $g_T(x)$ and $h_L(x)$, i.e. $g_1(x)$, and $h_1(x)$, and test\nthe Wandzura-Wilczek approximation.", "category": "hep-lat" }, { "text": "Light meson masses and decay constants in 2+1 flavour domain wall QCD: We present results for light meson masses and psedoscalar meson decay\nconstants in 2+1 flavour domain wall QCD with the DBW2 and Iwasaki gauge\nactions, using lattices with linear sizes in the range 1.6 to 2.2fm and $u$ and\n$d$ quark masses as low as one quarter of the strange quark mass. All data were\ngenerated on the QCDOC machines at the University of Edinburgh and Brookhaven\nNational Laboratory. Despite large residual masses and a limited number of sea\nquark mass values with which to perform chiral extrapolations, our results\nagree with experiment and scale within errors.", "category": "hep-lat" }, { "text": "Hopping Parameter Expansion for Heavy-Light Systems: We present a technique which permits the calculation of two-point functions\nof operators containing one heavy quark and an arbitrary number of light quarks\nas analytic functions of the heavy-quark mass. It is based on the standard\nJacobi linear solver used for the calculation of quark propagators. Results for\nthe heavy-light pseudoscalar and vector meson masses are obtained on 16^3x48\nlattices at beta = 6.2 using the Wilson fermion action, and agree with\npublished data. The incorporation of smeared operators and $O(a)$-improved\nactions presents no problems.", "category": "hep-lat" }, { "text": "Can Sigma Models Describe Finite Temperature Chiral Transitions?: Large-N expansions and computer simulations indicate that the universality\nclass of the finite temperature chiral symmetry restoration transition in the\n3D Gross-Neveu model is mean field theory. This is a counterexample to the\nstandard 'sigma model' scenario which predicts the 2D Ising model universality\nclass. We trace the breakdown of the standard scenario (dimensional reduction\nand universality) to the absence of canonical scalar fields in the model. We\npoint out that our results could be generic for theories with dynamical\nsymmetry breaking, such as Quantum Chromodynamics.", "category": "hep-lat" }, { "text": "The non-perturbative part of the plaquette in quenched QCD: We define the non-perturbative part of a quantity as the difference between\nits numerical value and the perturbative series truncated by dropping the order\nof minimal contribution and the higher orders. For the anharmonic oscillator,\nthe double-well potential and the single plaquette gauge theory, the\nnon-perturbative part can be parametrized as A (lambda)^B exp{-C/lambda} and\nthe coefficients can be calculated analytically. For lattice QCD in the\nquenched approximation, the perturbative series for the average plaquette is\ndominated at low order by a singularity in the complex coupling plane and the\nasymptotic behavior can only be reached by using extrapolations of the existing\nseries. We discuss two extrapolations that provide a consistent description of\nthe series up to order 20-25. These extrapolations favor the idea that the\nnon-perturbative part scales like (a/r_0)^4 with a/r_0 defined with the force\nmethod. We discuss the large uncertainties associated with this statement. We\npropose a parametrization of ln((a/r_0)) as the two-loop universal terms plus a\nconstant and exponential corrections. These corrections are consistent with\na_{1-loop}^2 and play an important role when beta<6. We briefly discuss the\npossibility of calculating them semi-classically at large beta.", "category": "hep-lat" }, { "text": "Study of SU(2) gauge theories with multiple Higgs fields in different\n representations: We study two different SU(2) gauge-scalar theories in 3 and 4 spacetime\ndimensions. Firstly, we focus on the 3 dimensional SU(2) theory with multiple\nHiggs fields in the adjoint representation, that can be mapped to cuprate\nsystems in condensed matter physics which host a rich phase diagram including\nhigh-Tc superconductivity. It has been proposed that the theory with 4 adjoint\nHiggs fields can be used to explain the physics of hole-doped cuprates for a\nwide range of parameters. We show exploratory results on the phase diagram of\nthe theory.\n On the other hand, we are interested in the 4 dimensional theory with 2 sets\nof fundamental scalar (Higgs) fields, which is relevant to the 2 Higgs Doublet\nModel (2HDM), a proposed extension to the Standard Model of particle physics.\nThe goal is to understand the particle spectrum of the theory at zero\ntemperature and the electroweak phase transition at finite temperature. We\npresent exploratory results on scale setting and the multi-parameter phase\ndiagram of this theory.", "category": "hep-lat" }, { "text": "A strategy to study the role of the charm quark in explaining the\n Delta{I}=1/2 rule: We present a strategy designed to separate several possible origins of the\nwell-known enhancement of the Delta{I}=1/2 amplitude in non-leptonic kaon\ndecays. In particular, we seek to disentangle the contribution of physics at\nthe typical QCD scale (soft-gluon exchange) from the effects at the scale of\nthe charm quark mass. This is achieved by considering QCD with an unphysically\nlight charm quark, so that the theory possesses an approximate SU(4)_L x\nSU(4)_R chiral symmetry. By computing the relevant operator matrix elements and\nmonitoring their values as the charm quark mass departs from the\nSU(4)-symmetric situation, the role of the charm quark can be assessed. We\nstudy the influence of the charm quark mass in Chiral Perturbation Theory.\nFirst results from lattice simulations in the SU(4)-symmetric limit are also\ndiscussed.", "category": "hep-lat" }, { "text": "$ \u0394$ baryon spectroscopy in lattice QCD: A variational analysis is performed within the framework of lattice QCD to\nextract the masses of the spin-3/2 positive parity $ \\Delta^+ $ baryons,\nincluding radial excitations. $2+1$ flavour dynamical gauge-field\nconfigurations provided by the PACS-CS collaboration via the ILDG are\nconsidered. To improve our interpolator basis, we perform an iterative process\nof source and sink smearing and solve a generalised eigenvalue problem using\nthe resulting fermion operators. We obtain a clear signal for the ground and\nfirst excited states at a light quark mass corresponding to $ m_\\pi = 413 $\nMeV. Furthermore, we show that one can use the eigenvectors obtained in this\nmethod to investigate the nature of these states, allowing us to classify our\nresults as $ 1s $ and $ 2s $ states for the ground and first excited states\nrespectively. Finally, we briefly highlight the method of Hamiltonian Effective\nField Theory which can be used to make comparison with quark model\nexpectations.", "category": "hep-lat" }, { "text": "Review on Composite Higgs Models: Composite Higgs Models explore the possibility that the Higgs boson is an\nexcitation of a new strongly interacting sector giving rise to electro-weak\nsymmetry breaking. After describing how this new sector can be embedded into\nthe Standard Model of elementary particle physics meeting experimental\nconstraints, I will review efforts by the community to explore the physics of\nthe new strong interaction using methods of lattice field theory. Challenges in\nunderstanding the numerical results are discussed and an outlook is given on\npossible future directions allowing to confirm or reject the composite Higgs\nhypothesis.", "category": "hep-lat" }, { "text": "Neural multigrid for gauge theories and other disordered systems: We present evidence that multigrid works for wave equations in disordered\nsystems, e.g. in the presence of gauge fields, no matter how strong the\ndisorder, but one needs to introduce a \"neural computations\" point of view into\nlarge scale simulations: First, the system must learn how to do the simulations\nefficiently, then do the simulation (fast).\n The method can also be used to provide smooth interpolation kernels which are\nneeded in multigrid Monte Carlo updates.", "category": "hep-lat" }, { "text": "New lattice approaches to the $\u0394I=1/2$ rule: Lattice QCD should allow a derivation of the $\\Delta I=1/2$ rule from first\nprinciples, but numerical calculations to date have been plagued by a variety\nof problems. After a brief review of these problems, we present several new\nmethods for calculating $K\\to\\pi\\pi$ amplitudes. These are designed for Wilson\nfermions, though they can be used also with staggered fermions. They all\ninvolve a non-perturbative determination of matching coefficients. We show how\nproblems of operator mixing can be greatly reduced by using point-split\nhadronic currents, and how CP violating parts of the $K\\to\\pi\\pi$ amplitudes\ncan be calculated by introducing a fake top quark. Many of the methods can also\nbe applied to the calculation of two body non-leptonic B-meson decays.", "category": "hep-lat" }, { "text": "Quark-gluon vertex with an off-shell O(a)-improved chiral fermion action: We perform a study the quark-gluon vertex function with a quenched Wilson\ngauge action and a variety of fermion actions. These include the domain wall\nfermion action (with exponentially accurate chiral symmetry) and the Wilson\nclover action both with the non-perturbatively improved clover coefficient as\nwell as with a number of different values for this coefficient. We find that\nthe domain wall vertex function behaves very well in the large momentum\ntransfer region. The off-shell vertex function for the on-shell improved clover\nclass of actions does not behave as well as the domain wall case and,\nsurprisingly, shows only a weak dependence on the clover coefficient $c_{SW}$\nfor all components of its Dirac decomposition and across all momenta. Including\noff-shell improvement rotations for the clover fields can make this action\nyield results consistent with those from the domain wall approach, as well as\nhelping to determine the off-shell improved coefficient $c_q^\\prime$.", "category": "hep-lat" }, { "text": "Frontiers of finite temperature lattice QCD: I review a selection of recent finite temperature lattice results of the past\nyears. First I discuss the extension of the equation of state towards high\ntemperatures and fi- nite densities, then I show recent results on the QCD\ntopological susceptibility at high temperatures and highlight its relevance for\ndark matter search.", "category": "hep-lat" }, { "text": "Recent results in high temperature lattice gauge theories: We review some analytic results on the deconfinement transition in pure\nlattice gauge theories. In particular we discuss the relationship between the\ndeconfinement transition in the $(d+1)$-dimensional $SU(2)$ model and the\nmagnetization transition in the $d$-dimensional Ising model. This analysis\nleads to a precise estimate of the deconfinement temperature which agrees well\nwith that obtained with a Montecarlo simulation in the case in which the\nlattice has only one link in the compactified time direction.", "category": "hep-lat" }, { "text": "Non-perturbative parton mass for the gluon: A gauge invariant, non-local observable is constructed in pure gauge theory,\nwhich is identical to the gluon propagator in a particular gauge, permitting to\ndefine a non-perturbative parton mass for the gluon. This mass can be shown to\nbe related to the 1P-1S mass splitting of heavy quarkonia. Preliminary\nnumerical results for 3d SU(2) yield m_A=0.37(6)g^2, while from the \\bar{b}b\nspectrum one infers m_A\\approx 420 MeV for QCD.", "category": "hep-lat" }, { "text": "Subtleties and Fancies in Gauge Theory Non Trivial Vacuum: The one loop effective potential for a non-Abelian gauge configuration is\nanalyzed using the background field method. The Savvidy result and the\nnon-Abelian ansatz, the other alternative possible background that generates a\nconstant color magnetic field configuration, are compared. This second\npossibility is very interesting because it avoids the possible coordinate\nsingularity, ${\\rm Det}B_i^a=0$, and it is easy to implement in lattice\nsimulations. We emphasize the interesting dependence of the potential by the\ngauge fixing parameter $\\alpha$, when the loop expansion is performed around a\nnon trivial background configuration. Finally, we point out some crucial\ndifferences in analyzing the vacuum structure between non-Abelian gauge\ntheories and the cases of scalar and Abelian gauge theories.", "category": "hep-lat" }, { "text": "The Weak-Coupling Limit of 3D Simplicial Quantum Gravity: We investigate the weak-coupling limit, kappa going to infinity, of 3D\nsimplicial gravity using Monte Carlo simulations and a Strong Coupling\nExpansion. With a suitable modification of the measure we observe a transition\nfrom a branched polymer to a crinkled phase. However, the intrinsic geometry of\nthe latter appears similar to that of non-generic branched polymer, probable\nexcluding the existence of a sensible continuum limit in this phase.", "category": "hep-lat" }, { "text": "The three-dimensional, three-state Potts Model in an External Field: We analyze the critical behaviour of the three-dimensional, three-state Potts\nmodel in the presence of an external ordering field. From a finite size scaling\nanalysis on lattices of size up to 70**3 we determine the critical endpoint of\nthe line of first order phase transitions as (b_c, h_c) =(0.54938(2),\n0.000775(10)). We determine the relevant temperature like and symmetry breaking\ndirections at this second order critical point and explicitly verify that it is\nin the universality class of the three-dimensional Ising model.", "category": "hep-lat" }, { "text": "Color Structure of Gluon Field Magnetic Mass: The color structure of the gluon field magnetic mass is investigated in the\nlattice SU(2) gluodynamics. To realize that, the interaction between a\nmonopole-antimonopole string and external neutral Abelian chromomagnetic field\nflux is considered. The string is introduced in the way proposed by Srednicki\nand Susskind. The neutral Abelian field flux is introduced through the twisted\nboundary conditions. Monte Carlo simulations are performed on 4D lattices at\nfinite temperature. It is shown that the presence of the Abelian field flux\nweakens the screening of the string field. That means decreasing the gluon\nmagnetic mass for this environment. The contribution of the neutral Abelian\nfield has the form of \"enhancing\" factor in the fitting functions. This\nbehavior independently confirms the long-range nature of the neutral Abelian\nfield reported already in the literature. The comparison with analytic\ncalculations is given.", "category": "hep-lat" }, { "text": "Polyakov loop fluctuations in SU(3) lattice gauge theory and an\n effective gluon potential: We calculate the Polyakov loop susceptibilities in the SU(3) lattice gauge\ntheory using the Symanzik improved gauge action on different-sized lattices.\nThe longitudinal and transverse fluctu- ations of the Polyakov loop, as well\nas, that of its absolute value are considered. We analyze their properties in\nrelation to the confinement-deconfinement phase transition. We also present\nresults based on simulations of (2+1)-flavor QCD on 32^3 x 8 lattice using\nHighly Improved Staggered Quark (HISQ) action by the HotQCD collaboration. The\ninfluences of fermions on the Polyakov loop fluctuations are discussed. We\nshow, that ratios of different susceptibilities of the Polyakov loop are\nsensitive probes for critical behavior. We formulate an effective model for the\nPolyakov loop potential and constrain its parameters from existing quenched\nlattice data including fluctuations. We emphasize the role of fluctuations to\nfully explore the thermodynamics of pure gauge theory within an effective\napproach.", "category": "hep-lat" }, { "text": "Color screening potential at finite density in two-flavor lattice QCD\n with Wilson fermions: We investigate chemical-potential (\\mu) dependence of static-quark free\nenergies in both the real and imaginary \\mu regions, performing lattice QCD\nsimulations at imaginary \\mu and extrapolating the results to the real \\mu\nregion with analytic continuation. Lattice QCD calculations are done on a\n16^{3}\\times 4 lattice with the clover-improved two-flavor Wilson fermion\naction and the renormalization-group improved Iwasaki gauge action.\nStatic-quark potential is evaluated from the Polyakov-loop correlation\nfunctions in the deconfinement phase. As the analytic continuation, the\npotential calculated at imaginary \\mu=i\\mu_{\\rm I} is expanded into a\nTaylor-expansion series of i\\mu_{\\rm I}/T up to 4th order and the pure\nimaginary variable i\\mu_{\\rm I}/T is replaced by the real one \\mu_{\\rm R}/T. At\nreal \\mu, the 4th-order term weakens \\mu dependence of the potential sizably.\nAt long distance, all of the color singlet and non-singlet potentials tend to\ntwice the single-quark free energy, indicating that the interactions between\nheavy quarks are fully color-screened for finite \\mu. For both real and\nimaginary \\mu, the color-singlet q{\\bar q} and the color-antitriplet qq\ninteraction are attractive, whereas the color-octet q{\\bar q} and the\ncolor-sextet qq interaction are repulsive. The attractive interactions have\nstronger \\mu/T dependence than the repulsive interactions. The color-Debye\nscreening mass is extracted from the color-singlet potential at imaginary \\mu,\nand the mass is extrapolated to real \\mu by analytic continuation. The\nscreening mass thus obtained has stronger \\mu dependence than the prediction of\nthe leading-order thermal perturbation theory at both real and imaginary \\mu.", "category": "hep-lat" }, { "text": "The chiral phase transition for QCD with sextet quarks: QCD with 2 massless colour-sextet quarks is studied as a model of Walking\nTechnicolor. We simulate lattice QCD with 2 light color-sextet staggered quarks\nat finite temperature, and use the dependence of the coupling at the chiral\ntransition on the temporal extent, $N_t$, of the lattice in lattice units to\nstudy the running of the bare lattice coupling with lattice spacing. Our goal\nis to determine whether this theory is QCD-like and `walks', or if it is\nconformal. If it is QCD-like, the coupling at the chiral transition should tend\nto zero as $N_t \\rightarrow \\infty$ in a manner controlled by asymptotic\nfreedom, i.e. by the perturbative $\\beta$-function. On the other hand, if this\ntheory is conformal, this coupling will approach a non-zero limit in the $N_t\n\\rightarrow \\infty$ limit. We are extending our simulations on an $N_t=8$\nlattice to determine the position of the chiral transition with greater\naccuracy, and are performing simulations on an $N_t=12$ lattice.", "category": "hep-lat" }, { "text": "$B_s \\to K \\ell \u03bd$ form factors from lattice QCD: We report the first lattice QCD calculation of the form factors for the\nstandard model tree-level decay $B_s\\to K \\ell\\nu$. In combination with future\nmeasurement, this calculation will provide an alternative exclusive\nsemileptonic determination of $|V_{ub}|$. We compare our results with previous\nmodel calculations, make predictions for differential decay rates and branching\nfractions, and predict the ratio of differential branching fractions between\n$B_s\\to K\\tau\\nu$ and $B_s\\to K\\mu\\nu$. We also present standard model\npredictions for differential decay rate forward-backward asymmetries,\npolarization fractions, and calculate potentially useful ratios of $B_s\\to K$\nform factors with those of the fictitious $B_s\\to\\eta_s$ decay. Our lattice\nsimulations utilize NRQCD $b$ and HISQ light quarks on a subset of the MILC\nCollaboration's $2+1$ asqtad gauge configurations, including two lattice\nspacings and a range of light quark masses.", "category": "hep-lat" }, { "text": "Low-energy Scattering and Effective Interactions of Two Baryons at\n $m_\u03c0\\sim 450$ MeV from Lattice Quantum Chromodynamics: The interactions between two octet baryons are studied at low energies using\nlattice QCD (LQCD) with larger-than-physical quark masses corresponding to a\npion mass of $m_{\\pi}\\sim 450$ MeV and a kaon mass of $m_{K}\\sim 596$ MeV. The\ntwo-baryon systems that are analyzed range from strangeness $S=0$ to $S=-4$ and\ninclude the spin-singlet and triplet $NN$, $\\Sigma N$ ($I=3/2$), and $\\Xi\\Xi$\nstates, the spin-singlet $\\Sigma\\Sigma$ ($I=2$) and $\\Xi\\Sigma$ ($I=3/2$)\nstates, and the spin-triplet $\\Xi N$ ($I=0$) state. The $s$-wave scattering\nphase shifts, low-energy scattering parameters, and binding energies when\napplicable, are extracted using L\\\"uscher's formalism. While the results are\nconsistent with most of the systems being bound at this pion mass, the\ninteractions in the spin-triplet $\\Sigma N$ and $\\Xi\\Xi$ channels are found to\nbe repulsive and do not support bound states. Using results from previous\nstudies at a larger pion mass, an extrapolation of the binding energies to the\nphysical point is performed and is compared with experimental values and\nphenomenological predictions. The low-energy coefficients in pionless EFT\nrelevant for two-baryon interactions, including those responsible for $SU(3)$\nflavor-symmetry breaking, are constrained. The $SU(3)$ symmetry is observed to\nhold approximately at the chosen values of the quark masses, as well as the\n$SU(6)$ spin-flavor symmetry, predicted at large $N_c$. A remnant of an\naccidental $SU(16)$ symmetry found previously at a larger pion mass is further\nobserved. The $SU(6)$-symmetric EFT constrained by these LQCD calculations is\nused to make predictions for two-baryon systems for which the low-energy\nscattering parameters could not be determined with LQCD directly in this study,\nand to constrain the coefficients of all leading $SU(3)$ flavor-symmetric\ninteractions, demonstrating the predictive power of two-baryon EFTs matched to\nLQCD.", "category": "hep-lat" }, { "text": "Heavy quark free energies for three quark systems at finite temperature: We study the free energy of static three quark systems in singlet, octet,\ndecuplet and average color channels in the quenched approximation and in\n2-flavor QCD at finite temperature. We show that in the high temperature phase\nsinglet and decuplet free energies of three quark systems are well described by\nthe sum of the free energies of three diquark systems plus self energy\ncontributions of the three quarks. In the confining low temperature phase we\nfind evidence for a Y-shaped flux tube in SU(3) pure gauge theory, which is\nless evident in 2-flavor QCD due to the onset of string breaking. We also\ncompare the short distance behavior of octet and decuplet free energies to the\nfree energies of single static quarks in the corresponding color\nrepresentations.", "category": "hep-lat" }, { "text": "Axial Charges of Octet Baryons in Two-flavor Lattice QCD: We evaluate the strangeness-conserving $N N$, $\\Sigma\\Sigma$, $\\Xi\\Xi$,\n$\\Lambda\\Sigma$ and the strangeness-changing $\\Lambda N$, $\\Sigma N$,\n$\\Lambda\\Xi$, $\\Sigma\\Xi$ axial charges in lattice QCD with two flavors of\ndynamical quarks and extend our previous work on\npseudoscalar-meson-octet-baryon coupling constants so as to include\n$\\pi\\Xi\\Xi$, $K\\Lambda\\Xi$ and $K\\Sigma\\Xi$ coupling constants. We find that\nthe axial charges have rather weak quark-mass dependence and the breaking in\nSU(3)-flavor symmetry is small at each quark-mass point we consider.", "category": "hep-lat" }, { "text": "f_B and the Heavy-light Spectrum from NRQCD: The present status of lattice calculations of the B spectrum and f_B, using\nNRQCD for the b quark, is discussed.", "category": "hep-lat" }, { "text": "CL2QCD - Lattice QCD based on OpenCL: We present the Lattice QCD application CL2QCD, which is based on OpenCL and\ncan be utilized to run on Graphic Processing Units as well as on common CPUs.\nWe focus on implementation details as well as performance results of selected\nfeatures. CL2QCD has been successfully applied in LQCD studies at finite\ntemperature and density and is available at\nhttp://code.compeng.uni-frankfurt.de/projects/clhmc .", "category": "hep-lat" }, { "text": "The (LATTICE) QCD Potential and Running Coupling: How to Accurately\n Interpolate between Multi-Loop QCD and the String Picture: We present a simple parameterization of a running coupling constant, defined\nvia the static potential, that interpolates between 2-loop QCD in the UV and\nthe string prediction in the IR. Besides the usual $\\Lam$-parameter and the\nstring tension, the coupling depends on one dimensionless parameter,\ndetermining how fast the crossover from UV to IR behavior occurs (in principle\nwe know how to take into account any number of loops by adding more\nparameters). Using a new Ansatz for the LATTICE potential in terms of the\ncontinuum coupling, we can fit quenched and unquenched Monte Carlo results for\nthe potential down to ONE lattice spacing, and at the same time extract the\nrunning coupling to high precision. We compare our Ansatz with 1-loop results\nfor the lattice potential, and use the coupling from our fits to quantitatively\ncheck the accuracy of 2-loop evolution, compare with the Lepage-Mackenzie\nestimate of the coupling extracted from the plaquette, and determine Sommer's\nscale $r_0$ much more accurately than previously possible. For pure SU(3) we\nfind that the coupling scales on the percent level for $\\beta\\geq 6$.", "category": "hep-lat" }, { "text": "The QCD Equation of State: Results for the equation of state in 2+1 flavor QCD at zero net baryon\ndensity using the Highly Improved Staggered Quark (HISQ) action by the HotQCD\ncollaboration are presented. The strange quark mass was tuned to its physical\nvalue and the light (up/down) quark masses fixed to $m_l = 0.05m_s$\ncorresponding to a pion mass of 160 MeV in the continuum limit. Lattices with\ntemporal extent $N_t=6$, 8, 10 and 12 were used. Since the cutoff effects for\n$N_t>6$ were observed to be small, reliable continuum extrapolations of the\nlattice data for the phenomenologically interesting temperatures range $130\n\\mathord{\\rm MeV} < T < 400 \\mathord{\\rm MeV}$ could be performed. We discuss\nstatistical and systematic errors and compare our results with other published\nworks.", "category": "hep-lat" }, { "text": "Chiral gauge theories on the lattice without gauge fixing?: We discuss two proposals for a non-perturbative formulation of chiral gauge\ntheories on the lattice. In both cases gauge symmetry is broken by the\nregularization. We aim at a dynamical restoration of symmetry. If the gauge\nsymmetry breaking is not too severe this procedure could lead in the continuum\nlimit to the desired chiral gauge theory.", "category": "hep-lat" }, { "text": "Higgs boson mass bounds in the presence of a very heavy fourth quark\n generation: We study the effect of a potential fourth quark generation on the upper and\nlower Higgs boson mass bounds. This investigation is based on the numerical\nevaluation of a chirally invariant lattice Higgs-Yukawa model emulating the\nsame Higgs-fermion coupling structure as in the Higgs sector of the electroweak\nStandard Model. In particular, the considered model obeys a Ginsparg-Wilson\nversion of the underlying ${SU}(2)_L\\times {U}(1)_Y$ symmetry, being a global\nsymmetry here due to the neglection of gauge fields in this model. We present\nour results on the modification of the upper and lower Higgs boson mass bounds\ninduced by the presence of a hypothetical very heavy fourth quark doublet.\nFinally, we compare these findings to the standard scenario of three fermion\ngenerations.", "category": "hep-lat" }, { "text": "Pion Polarizabilities and Volume Effects in Lattice QCD: We use chiral perturbation theory to study the extraction of pion\nelectromagnetic polarizabilities from lattice QCD. Chiral extrapolation\nformulae are derived for partially quenched QCD, and quenched QCD simulations.\nOn a torus, volume dependence of electromagnetic observables is complicated by\nSO(4) breaking, as well as photon zero-mode interactions. We determine finite\nvolume corrections to the Compton scattering tensor of pions. We argue,\nhowever, that such results cannot be used to ascertain volume corrections to\npolarizabilities determined in lattice QCD with background field methods.\nConnection is lacking because momentum expansions are not permitted in finite\nvolume. Our argument also applies to form factors. Volume effects for\nelectromagnetic moments cannot be deduced from finite volume form factors.", "category": "hep-lat" }, { "text": "Spectral functions at small energies and the electrical conductivity in\n hot, quenched lattice QCD: In lattice QCD, the Maximum Entropy Method can be used to reconstruct\nspectral functions from euclidean correlators obtained in numerical\nsimulations. We show that at finite temperature the most commonly used\nalgorithm, employing Bryan's method, is inherently unstable at small energies\nand give a modification that avoids this. We demonstrate this approach using\nthe vector current-current correlator obtained in quenched QCD at finite\ntemperature. Our first results indicate a small electrical conductivity above\nthe deconfinement transition.", "category": "hep-lat" }, { "text": "Calculation of $\u03c1$ meson decay width from the PACS-CS configurations: We present preliminary results on the $\\rho$ meson decay width from $N_f=2+1$\nfull QCD configurations generated by PACS-CS Collaboration. The decay width is\nestimated from the $P$-wave scattering phase shift for the isospin $I=1$\ntwo-pion system. The finite size formula presented by L\\\"uscher in the center\nof mass frame and its extension to non-zero total momentum frame by Rummukainen\nand Gottlieb are employed for the calculations of the phase shift. Our\ncalculations are carried out at $m_\\pi=410\\ {\\rm MeV}$ ($m_\\pi/m_\\rho=0.46$)\nand $a=0.091\\ {\\rm fm}$ on a $32^3\\times 64$ ($La=2.9 {\\rm fm}$) lattice.", "category": "hep-lat" }, { "text": "Testing universality and the fractional power prescription for the\n staggered fermion determinant: In [Phys.Rev.Lett.92:162002 (2004), hep-lat/0312025] expressions for the\ncontinuous Euclidean time limits of various lattice fermion determinants were\nderived and compared in order to test universality expectations in Lattice QCD.\nHere we review that work with emphasis on its relevance for assessing the\nfractional power prescription for the determinant in dynamical staggered\nfermion simulations. Some new supplementary material is presented; in\nparticular the status of the \"universality anomaly\" is clarified: it is shown\nto be gauge field-independent and therefore physically inconsequential.", "category": "hep-lat" }, { "text": "Fast algorithms for simulating chiral fermions in U(1)lattice gauge\n theory: In order to develop fast inversion algorithms we have used overlap solvers in\ntwo dimensions. Lattice QED theory with U(1) group symmetry in two dimensional\nspace-times dimensions has always been a testing ground for algorithms. By the\nother side, motivated by our previews work that the two-grid algorithm converge\nfaster than the standard iterative methods for overlap inversion but not for\nall quark masses, we thought to test this idea in less dimensions such as U(1)\ngauge theory. Our main objective of this paper it is to implement and develop\nthe idea of a two level algorithm in a new algorithm coded in QCDLAB. This\nimplementation is presented in the preconditioned GMRESR algorithm, as our new\ncontribution in QCDLAB package. The preconditioned part of our algorithm,\ndifferent from the one of [18], is the approximation of the overlap operator\nwith the truncated overlap operator with finite N3 dimension. We have tested it\nfor 100 statistically independent configurations on 32 x 32 lattice background\nU(1) field at coupling constant \\b{eta}=1 and for different bare quark masses\nmq = [0.5, 0.45, 0.4, 0.35, 0.3, 0.25, 0.2, 0.15, 0.1]. We have compared the\nconvergence history of the preconditioned GMRESR residual norm with another\noverlap inverter of QCDLAB as an optimal one, such as SHUMR. We have shown that\nour algorithm converges faster than SHUMR for different quark masses. Also, we\nhave demonstrated that it saves more time for light quarks compared to SHUMR\nalgorithm. Our algorithm is approximately independent from the quark mass. This\nis a key result in simulations with chiral fermions in lattice theories. By the\nother side, if we compare the results of [18] for quark mass 0.1 in SU(3),\nresults that our chosen preconditioned saves a factor of 2 but in U(1). Our\nnext step is to test this algorithm in SU(3) and to adopt it in parallel.", "category": "hep-lat" }, { "text": "Formulation of chiral gauge theories: We present a formulation of chiral gauge theories, which admits more general\nspectra of Dirac operators and reveals considerably more possibilities for the\nstructure of the chiral projections. Our two forms of correlation functions\nboth also apply in the presence of zero modes and for any value of the index.\nThe decomposition of the total set of pairs of bases into equivalence classes\nis carefully analyzed. Transformation properties are derived.", "category": "hep-lat" }, { "text": "Center-symmetric dimensional reduction of hot Yang-Mills theory: It is expected that incorporating the center symmetry in the conventional\ndimensionally reduced effective theory for high-temperature SU(N) Yang-Mills\ntheory, EQCD, will considerably extend its applicability towards the\ndeconfinement transition. The construction of such a center-symmetric effective\ntheory for the case of two colors is reviewed and lattice simulation results\nare presented. The simulations demonstrate that unlike EQCD, the new\ncenter-symmetric theory undergoes a second order confining phase transition in\ncomplete analogy with the full theory.", "category": "hep-lat" }, { "text": "Radially Excited States of 1P Charmonia and X(3872): The excited states of charmonia are numerically investigated in quenched\nlattice QCD with improved gauge and Wilson fermion actions formulated on\nanisotropic lattices. Through a constrained curve fitting algorithm, the masses\nof the first excited states in $0^{++}$, $1^{++}$, and $1^{+-}$ channels are\ndetermined to be 3.825(88), 3.853(57), and 3.858(70) GeV, respectively.\nFurthormore, a node structure is also observed in the Bethe-Salpeter amplitude\nof the $1^{++}$ first excited state. These observations indicate that X(3872)\ncould be the first radial excitation of $\\chi_{c1}$.", "category": "hep-lat" }, { "text": "Three-Flavor Partially Quenched Chiral Perturbation Theory at NNLO for\n Meson Masses and Decay Constants: We discuss Partially Quenched Chiral Perturbation Theory (PQ$\\chi$PT) and\npossible fitting strategies to Lattice QCD data at next-to-next-to-leading\norder (NNLO) in the mesonic sector. We also present a complete calculation of\nthe masses of the charged pseudoscalar mesons, in the supersymmetric\nformulation of PQ$\\chi$PT. Explicit analytical results are given for up to\nthree nondegenerate sea quark flavors, along with the previously unpublished\nexpression for the pseudoscalar meson decay constant for three nondegenerate\nsea quark flavors. The numerical analysis in this paper demonstrates that the\ncorrections at NNLO are sizable, as expected from earlier work.", "category": "hep-lat" }, { "text": "Axial Anomaly in Lattice Abelian Gauge Theory in Arbitrary Dimensions: Axial anomaly of lattice abelian gauge theory in hyper-cubic regular lattice\nin arbitrary even dimensions is investigated by applying the method of exterior\ndifferential calculus. The topological invariance, gauge invariance and\nlocality of the axial anomaly determine the explicit form of the topological\npart. The anomaly is obtained up to a multiplicative constant for finite\nlattice spacing and can be interpreted as the Chern character of the abelian\nlattice gauge theory.", "category": "hep-lat" }, { "text": "The finite temperature transition for 3-flavour lattice QCD at finite\n isospin density: We simulate 3-flavour lattice QCD with a small chemical potential $\\mu_I$ for\nisospin, at temperatures close to the finite temperature transition. Using\nquark masses just above the critical mass for zero chemical potential, we\ndetermine the position of the transition from hadronic matter to a quark-gluon\nplasma as a function of $\\mu_I$. We see evidence for a critical endpoint where\nthe transition changes from a crossover to a first-order transition as $\\mu_I$\nis increased. We argue that QCD at finite $\\mu_I$ and QCD at finite\nquark-numberchemical potential $\\mu$ should behave similarly in this region.", "category": "hep-lat" }, { "text": "Physics From Breit-Frame Regularization Of a Lattice Hamiltonian: We suggest a Hamiltonian formulation on a momentum lattice using a physically\nmotivated regularization using the Breit-frame which links the maximal parton\nnumber to the lattice size. This scheme restricts parton momenta to positive\nvalues in each spatial direction. This leads to a drastic reduction of degrees\nof freedom compared to a regularization in the rest frame (center at zero\nmomentum). We discuss the computation of physical observables like (i) mass\nspectrum in the critical region, (ii) structure and distribution functions,\n(iii) $S$-matrix, (iv) finite temperature and finite density thermodynamics in\nthe Breit-frame regularization. For the scalar $\\phi^{4}_{3+1}$ theory we\npresent numerical results for the mass spectrum in the critical region. We\nobserve scaling behavior for the mass of the ground state and for some higher\nlying states. We compare our results with renormalization group results by\nL\\\"uscher and Weisz. Using the Breit-frame, we calculate for $QCD$ the relation\nbetween the $W^{\\mu \\nu}$ tensor, structure functions (polarized and\nunpolarized) and quark distribution functions. We use the improved parton-model\nwith a scale dependence and take into account a non-zero parton mass. In the\nBjorken limes we find the standard relations between $F_{1}$, $F_{2}$, $g_{1}$\nand the quark distribution functions. We discuss the r\\^ole of helicity. We\npresent numerical results for parton distribution functions in the scalar\nmodel. For the $\\phi^{4}$-model we find no bound state with internal parton\nstructure. For the $\\phi^{3}$-model we find a distribution function with parton\nstructure similar to Altarelli-Parisi behavior of $QCD$.", "category": "hep-lat" }, { "text": "Stabilizing the electroweak vacuum by higher dimensional operators in a\n Higgs-Yukawa model: The Higgs boson discovery at the LHC with a mass of approximately 126 GeV\nsuggests, that the electroweak vacuum of the standard model may be metastable\nat very high energies. However, any new physics beyond the standard model can\nchange this picture. We want to address this important question within a\nlattice Higgs-Yukawa model as the limit of the standard model (SM). In this\nframework we will probe the effect of a higher dimensional operator for which\nwe take a $(\\phi^{\\dagger}\\phi)^3$-term. Such a term could easily originate as\na remnant of physics beyond the SM at very large scales.\n As a first step we investigate the phase diagram of the model including such\na $(\\phi^{\\dagger}\\phi)^3$ operator. Exploratory results suggest the existence\nof regions in parameter space where first order transitions turn to second\norder ones, indicating the existence of a tri-critical line. We will explore\nthe phase structure and the consequences for the stability of the SM, both\nanalytically by investigating the constraint effective potential in lattice\nperturbation theory, and by studying the system non-perturbatively using\nlattice simulations.", "category": "hep-lat" }, { "text": "The chiral transition in two-flavor QCD: QCD with N_f=2 is a specially interesting system to investigate the chiral\ntransition. The order of the transition has still not been established. We\nreport the results of an in-depth numerical investigation performed with\nstaggered fermions on lattices with L_t=4 and L_s=12,16,20,24,32 and quark\nmasses am_q ranging from 0.01335 to 0.307036. Using finite-size techniques we\ncompare the scaling behavior of a number of thermodynamical susceptibilities\nwith the expectations of O(4) and O(2) universality classes. Clear disagreement\nis observed. Indications of a first order transition are found.", "category": "hep-lat" }, { "text": "Nucleon form factors and structure functions with N_f=2+1 dynamical\n domain wall fermions: We report isovector form factors and low moments of structure functions of\nnucleon in numerical lattice quantum chromodynamics (QCD) from the on-going\ncalculations by the RIKEN-BNL-Columbia (RBC) and UKQCD Collaborations with\n(2+1) dynamical flavors of domain-wall fermion (DWF) quarks. We calculate the\nmatrix elements with four light quark masses, corresponding to pion mass values\nof m_\\pi = 330-670 MeV, while the dynamical strange mass is fixed at a value\nclose to physical, on (2.7 fm)^3 spatial volume. We found that our axial\ncharge, g_A, at the lightest mass exhibits a large deviation from the heavier\nmass results. This deviation seems to be a finite-size effect as the g_A value\nscales with a single parameter, m_\\pi L, the product of pion mass and linear\nspatial lattice size. The scaling is also seen in earlier 2-flavor dynamical\nDWF and Wilson quark calculations. Without this lightest point, the three\nheavier mass results show only very mild mass dependence and linearly\nextrapolate to g_A=1.16(6). We determined the four form factors, the vector\n(Dirac), induced tensor (Pauli), axial vector and induced pseudoscalar, at a\nfew finite momentum transfer values as well. At the physical pion mass the\nform-factors root mean square radii determined from the momentum-transfer\ndependence %of the form factors are 20-30% smaller than the corresonding\nexperiments. The ratio of the isovector quark momentum to helicity fractions, <\nx>_{u-d}/< x>_{\\Delta u - \\Delta d} is in agreement with experiment without\nmuch mass dependence including the lightest point. We obtain an estimate,\n0.81(2), by a constant fit. Although the individual momentum and helicity\nfractions are yet to be renormalized, they show encouraging trend toward\nexperiment.", "category": "hep-lat" }, { "text": "Form factor for Dalitz decays from $J/\u03c8$ to light pseudoscalars: We calculate the form factor $M(q^2)$ for the Dalitz decay $J/\\psi\\to\n\\gamma^*(q^2)\\eta_{(N_f=1)}$ with $\\eta_{(N_f)}$ being the SU($N_f$) flavor\nsinglet pseudoscalar meson. The difference among the partial widths\n$\\Gamma(J/\\psi\\to \\gamma \\eta_{(N_f)})$ at different $N_f$ can be attributed in\npart to the $\\mathbf{U}_A(1)$ anomaly that induces a $N_f$ scaling. $M(q^2)$'s\nin $N_f=1,2$ are both well described by the single pole model\n$M(q^2)=M(0)/(1-q^2/\\Lambda^2)$. Combined with the known experimental results\nof the Dalitz decays $J/\\psi\\to Pe^+e^-$, the pseudoscalar mass $m_P$\ndependence of the pole parameter $\\Lambda$ is approximated by\n$\\Lambda(m_P^2)=\\Lambda_1(1-m_P^2/\\Lambda_2^2)$ with\n$\\Lambda_1=2.64(4)~\\mathrm{GeV}$ and $\\Lambda_2=2.97(33)~\\mathrm{GeV}$. These\nresults provide inputs for future theoretical and experimental studies on the\nDalitz decays $J/\\psi\\to Pe^+e^-$.", "category": "hep-lat" }, { "text": "Noise, sign problems, and statistics: We show how sign problems in simulations of many-body systems can manifest\nthemselves in the form of heavy-tailed correlator distributions, similar to\nwhat is seen in electron propagation through disordered media. We propose an\nalternative statistical approach for extracting ground state energies in such\nsystems, illustrating the method with a toy model and with lattice data for\nunitary fermions.", "category": "hep-lat" }, { "text": "The critical end point in QCD: In this talk I present the logic behind, and examine the reliability of,\nestimates of the critical end point (CEP) of QCD using the Taylor expansion\nmethod.", "category": "hep-lat" }, { "text": "The principle of indirect elimination: The principle of indirect elimination states that an algorithm for solving\ndiscretized differential equations can be used to identify its own\nbad-converging modes. When the number of bad-converging modes of the algorithm\nis not too large, the modes thus identified can be used to strongly improve the\nconvergence. The method presented here is applicable to any standard algorithm\nlike Conjugate Gradient, relaxation or multigrid. An example from theoretical\nphysics, the Dirac equation in the presence of almost-zero modes arising from\ninstantons, is studied. Using the principle, bad-converging modes are removed\nefficiently. Applied locally, the principle is one of the main ingredients of\nthe Iteratively Smooting Unigrid algorithm.", "category": "hep-lat" }, { "text": "Excited mesons from $N_f=2$ dynamical Clover Wilson lattices: We study mesons on the lattice with a special focus on excited states. For\nthat purpose we construct several quark sources with different spatial\nsmearings, including p-waves. These quark sources are then combined with the\nappropiate Dirac structures to form meson interpolators of definite spin. We\nuse these operators to construct a cross correlation matrix from which we\nextract ground and excited meson states using the variational method. For the\ncalculations we use gauge configurations with $N_f=2$ dynamical Clover Wilson\nfermions provided by the CP-PACS collaboration. We show preliminary results for\npseudoscalar, scalar, vector and pseudovector mesons.", "category": "hep-lat" }, { "text": "$B_K$ with improved staggered fermions: analysis using SU(2) staggered\n chiral perturbation theory: We report updated results for $B_K$ calculated using HYP-smeared staggered\nfermions on the MILC asqtad 2+1 flavor lattices. We use four different lattice\nspacings ($a \\approx$ 0.12, 0.09, 0.06 and 0.045 fm) to control the continuum\nextrapolation. We use SU(2) staggered chiral perturbation theory to do the data\nanalysis. We find that $B_K(\\text{NDR}, \\mu=2 \\text{GeV}) = 0.526 \\pm 0.007 \\pm\n0.024$ and $\\hat{B}_K = B_K(\\text{RGI}) = 0.720 \\pm 0.010 \\pm 0.033$. Here the\nfirst error is statistical and the second systematic. The dominant source of\nerror is that due to our use of a truncated (one-loop) matching factor.", "category": "hep-lat" }, { "text": "Critical Exponents of the 3D Ising Universality Class From Finite Size\n Scaling With Standard and Improved Actions: We propose a method to obtain an improved Hamiltonian (action) for the Ising\nuniversality class in three dimensions. The improved Hamiltonian has suppressed\nleading corrections to scaling. It is obtained by tuning models with two\ncoupling constants. We studied three different models: the +1,-1 Ising model\nwith nearest neighbour and body diagonal interaction, the spin-1 model with\nstates 0,+1,-1, and nearest neighbour interaction, and phi**4-theory on the\nlattice (Landau-Ginzburg Hamiltonian). The remarkable finite size scaling\nproperties of the suitably tuned spin-1 model are compared in detail with those\nof the standard Ising model. Great care is taken to estimate the systematic\nerrors from residual corrections to scaling. Our best estimates for the\ncritical exponents are nu= 0.6298(5) and eta= 0.0366(8), where the given error\nestimates take into account the statistical and systematic uncertainties.", "category": "hep-lat" }, { "text": "The QCD phase diagram at nonzero quark density: We determine the phase diagram of QCD on the \\mu-T plane for small to\nmoderate chemical potentials. Two transition lines are defined with two\nquantities, the chiral condensate and the strange quark number susceptibility.\nThe calculations are carried out on N_t =6,8 and 10 lattices generated with a\nSymanzik improved gauge and stout-link improved 2+1 flavor staggered fermion\naction using physical quark masses. After carrying out the continuum\nextrapolation we find that both quantities result in a similar curvature of the\ntransition line. Furthermore, our results indicate that in leading order the\nwidth of the transition region remains essentially the same as the chemical\npotential is increased.", "category": "hep-lat" }, { "text": "The $\u03c1$-resonance with physical pion mass from $N_f=2$ lattice QCD: We present the first-ever lattice computation of pi pi-scattering in the I=1\nchannel with Nf=2 dynamical quark flavours obtained including an ensemble with\nphysical value of the pion mass. Employing a global fit to data at three values\nof the pion mass, we determine the universal parameters of the rho-resonance.\nWe carefully investigate systematic uncertainties by determining energy\neigenvalues using different methods and by comparing inverse amplitude method\nand Breit-Wigner type parametrizations. Overall, we find mass 786(20) MeV and\nwidth 180(6) MeV, including statistical and systematic uncertainties. In stark\ndisagreement with the previous Nf=2 extrapolations from higher than physical\npion mass results, our mass value is in good agreement with experiment, while\nthe width is slightly too high.", "category": "hep-lat" }, { "text": "The Charmonium Potential at Non-Zero Temperature: The potential between charm and anti-charm quarks is calculated\nnon-perturbatively using physical, rather than static quarks at temperatures on\nboth sides of the deconfinement transition $T_{\\rm C}$, using a lattice\nsimulation with 2+1 dynamical quark flavours. We used the HAL QCD\ntime-dependent method, originally developed for inter-nucleon potentials. Our\nlattices are anisotropic, with temporal lattice spacing less than the spatial\none which enhances the information content of our correlators at each\ntemperature. Local-extended charmonium correlators were calculated efficiently\nby contracting propagators in momentum rather than coordinate space. We find no\nsignificant variation in the central potential for temperatures in the confined\nphase. As the temperature increases into the deconfinement phase, the potential\nflattens, consistent with the expected weakening interaction. We fit the\npotential to both the (a) Cornell and (b) Debye-screened potential forms, with\nthe latter better reproducing the data. The zero temperature string tension\nobtained from (a) agrees with results obtained elsewhere, and it decreases with\ntemperature, but at a slower rate than from the static quark approximation. The\nDebye mass from (b) is close to zero for small temperatures, but starts to\nincrease rapidly around $T_{\\rm C}$. The spin-dependent potential is found to\nhave a repulsive core and a distinct temperature dependence above $T_{\\rm C}$\nat distances $\\sim 1$ fm.", "category": "hep-lat" }, { "text": "A Study of the $N=2$ Kazakov-Migdal Model: We study numerically the SU(2) Kazakov-Migdal model of `induced QCD'. In\ncontrast to our earlier work on the subject we have chosen here {\\it not} to\nintegrate out the gauge fields but to keep them in the Monte Carlo simulation.\nThis allows us to measure observables associated with the gauge fields and\nthereby address the problem of the local $Z_2$ symmetry present in the model.\nWe confirm our previous result that the model has a line of first order phase\ntransitions terminating in a critical point. The adjoint plaquette has a clear\ndiscontinuity across the phase transition, whereas the plaquette in the\nfundamental representation is always zero in accordance with Elitzur's theorem.\nThe density of small $Z_2$ monopoles shows very little variation and is always\nlarge. We also find that the model has extra local U(1) symmetries which do not\nexist in the case of the standard adjoint theory. As a result, we are able to\nshow that two of the angles parameterizing the gauge field completely decouple\nfrom the theory and the continuum limit defined around the critical point can\ntherefore not be `QCD'.", "category": "hep-lat" }, { "text": "Lattice Artefacts In The Non-Abelian Debye Screening Mass In One Loop\n Order: We compute the electric screening mass in lattice QCD with Wilson fermions at\nfinite temperature and chemical potential to one-loop order, and show that\nlattice artefacts arising from a finite lattice spacing result in an\nenhancement of the screening mass as compared to the continuum. We discuss the\nmagnitude of this enhancement as a function of the temperature and chemical\npotential for lattices with different number of lattice sites in the temporal\ndirection that can be implemented in lattice simulations. Most of the\nenhancement is found to be due to the fermion loop contribution.", "category": "hep-lat" }, { "text": "$O(a^2)$-improved actions for heavy quarks and scaling studies on\n quenched lattices: We investigate a new class of improved relativistic fermion action on the\nlattice with a criterion to give excellent energy-momentum dispersion relation\nas well as to be consistent with tree-level $O\\left(a^{2}\\right)$-improvement.\nMain application in mind is that for heavy quark for which $ma\\simeq O(0.5)$.\nWe present tree-level results and a scaling study on quenched lattices.", "category": "hep-lat" }, { "text": "Excited States of U(1)$_{2+1}$ Lattice Gauge Theory from Monte Carlo\n Hamiltonian: We address an old problem in lattice gauge theory - the computation of the\nspectrum and wave functions of excited states. Our method is based on the\nHamiltonian formulation of lattice gauge theory. As strategy, we propose to\nconstruct a stochastic basis of Bargmann link states, drawn from a physical\nprobability density distribution. Then we compute transition amplitudes between\nstochastic basis states. From a matrix of transition elements we extract energy\nspectra and wave functions. We apply this method to U(1)$_{2+1}$ lattice gauge\ntheory. We test the method by computing the energy spectrum, wave functions and\nthermodynamical functions of the electric Hamiltonian of this theory and\ncompare them with analytical results. We observe a reasonable scaling of\nenergies and wave functions in the variable of time. We also present first\nresults on a small lattice for the full Hamiltonian including the magnetic\nterm.", "category": "hep-lat" }, { "text": "THE QCD ABACUS: A New Formulation for Lattice Gauge Theories: A quantum Hamiltonian is constructed for SU(3) lattice QCD entirely from\ncolor triplet Fermions --- the standard quarks and a new Fermionic\n``constituent'' of the gluon we call ``rishons''. The quarks are represented by\nDirac spinors on each site and the gauge fields by rishon-antirishon bilinears\non each link which together with the local gauge transforms are the generators\nof an SU(6) algebra. The effective Lagrangian for the path integral lives in\n$R^4 \\times S^1$ Euclidean space with a compact ``fifth time'' of circumference\n($\\beta$) and non-Abelian charge ($e^2$) both of which carry dimensions of\nlength. For large $\\beta$, it is conjectured that continuum QCD is reached and\nthat the dimensionless ratio $g^2 = e^2/\\beta$ becomes the QCD gauge coupling.\nThe quarks are introduced as Kaplan chiral Fermions at either end of the finite\nslab in fifth time. This talk will emphasize the gauge and algebraic structure\nof the rishon or link Fermions and the special properties that may lead to fast\ndiscrete dynamics for numerical simulations and new theoretical insight.", "category": "hep-lat" }, { "text": "Numerical tests of the electroweak phase transition and thermodynamics\n of the electroweak plasma: The finite temperature phase transition in the SU(2) Higgs model at a Higgs\nboson mass $M_H \\simeq 34$ GeV is studied in numerical simulations on\nfour-dimensional lattices with time-like extensions up to $L_t=5$. The effects\nof the finite volume and finite lattice spacing on masses and couplings are\nstudied in detail. The errors due to uncertainties in the critical hopping\nparameter are estimated. The thermodynamics of the electroweak plasma near the\nphase transition is investigated by determining the relation between energy\ndensity and pressure.", "category": "hep-lat" }, { "text": "Landau gauge gluon and ghost propagators from two-flavor lattice QCD at\n T > 0: In this contribution we extend our unquenched computation of the Landau gauge\ngluon and ghost propagators in lattice QCD at non-zero temperature. The study\nwas aimed at providing input for investigations employing continuum functional\nmethods. We show data which correspond to pion mass values between 300 and 500\nMeV and are obtained for a lattice size 32**3 x 12. The longitudinal and\ntransversal components of the gluon propagator turn out to change smoothly\nthrough the crossover region, while the ghost propagator exhibits only a very\nweak temperature dependence. For a pion mass of around 400 MeV and the\nintermediate temperature value of approx. 240 MeV we compare our results with\nadditional data obtained on a lattice with smaller Euclidean time extent N_t =\n8, 10 and find a reasonable scaling behavior.", "category": "hep-lat" }, { "text": "Massless Fermions on the Lattice: We consider a nonlocal lattice action for fermions fermion doubling in\nlattice theories. It is shown, that it is possible to avoid the fermionic\ndoubling in the case of free fermions, but this approach does not reproduce\nresults for the effective action for gauge fields in the continuum theory,\nbecause the high frequency fermion modes have a strong dependence on the gauge\nfield.", "category": "hep-lat" }, { "text": "The pion form factor on the lattice at zero and finite temperature: We calculate the electromagnetic form factor of the pion in quenched lattice\nQCD. The non-perturbatively improved Sheikoleslami-Wohlert lattice action is\nused together with the consistently O(a) improved current. We calculate the\npion form factor for masses down to m_pi = 360 MeV, extract the charge radius,\nand extrapolate toward the physical pion mass. In the second part, we discuss\nresults for the pion form factor and charge radius at 0.93 T_c and compare with\nzero temperature results.", "category": "hep-lat" }, { "text": "Disconnected contributions to D-meson semi-leptonic decay form factors: We calculate the disconnected contribution to the form factor for the\nsemileptonic decay of a D-meson into a final state, containing a flavor singlet\neta meson. We use QCDSF n_f=2+1 configurations at the flavor symmetric point\nm_u=m_d=m_s and the partially quenched approximation for the relativistic charm\nquark. Several acceleration and noise reduction techniques for the stochastic\nestimation of the disconnected loop are tested.", "category": "hep-lat" }, { "text": "Finite Size Scaling and ``perfect'' actions: the three dimensional Ising\n model: Using Finite-Size Scaling techniques, we numerically show that the first\nirrelevant operator of the lattice $\\lambda\\phi^4$ theory in three dimensions\nis (within errors) completely decoupled at $\\lambda=1.0$. This interesting\nresult also holds in the Thermodynamical Limit, where the renormalized coupling\nconstant shows an extraordinary reduction of the scaling-corrections when\ncompared with the Ising model. It is argued that Finite-Size Scaling analysis\ncan be a competitive method for finding improved actions.", "category": "hep-lat" }, { "text": "K \\to \u03c0\u03c0decay amplitudes from the lattice: In order to directly compute physical two-pion K-decay amplitudes using\nlattice methods we must prepare a two-pion state with non-zero relative\nmomentum. Building upon a proposal of Lellouch and L\\\"uscher, we describe a\nfinite-volume method to realize such a state as the lowest energy state of two\npions.", "category": "hep-lat" }, { "text": "Linear broadening of the confining string in Yang-Mills theory at low\n temperature: The logarithmic broadening predicted by the systematic low-energy effective\nfield theory for the confining string has recently been verified in numerical\nsimulations of (2+1)-d SU(2) lattice Yang-Mills theory at zero temperature. The\nsame effective theory predicts linear broadening of the string at low non-zero\ntemperature. In this paper, we verify this prediction by comparison with very\nprecise Monte Carlo data. The comparison involves no additional adjustable\nparameters, because the low-energy constants of the effective theory have\nalready been fixed at zero temperature. It yields very good agreement between\nthe underlying Yang-Mills theory and the effective string theory.", "category": "hep-lat" }, { "text": "Accelerating lattice QCD simulations with 2 flavours of staggered\n fermions on multiple GPUs using OpenACC - a first attempt: We present the results of an effort to accelerate a Rational Hybrid Monte\nCarlo (RHMC) program for lattice quantum chromodynamics (QCD) simulation for 2\nflavours of staggered fermions on multiple Kepler K20X GPUs distributed on\ndifferent nodes of a Cray XC30. We do not use CUDA but adopt a higher level\ndirective based programming approach using the OpenACC platform. The lattice\nQCD algorithm is known to be bandwidth bound; our timing results illustrate\nthis clearly, and we discuss how this limits the parallelization gains. We\nachieve more than a factor three speed-up compared to the CPU only MPI program.", "category": "hep-lat" }, { "text": "Phase diagram of QCD in strong background magnetic field: We discuss the phase diagram of QCD in the presence of a strong background\nmagnetic field, providing numerical evidence, based on lattice simulations of\nQCD with $2+1$ flavours and physical quark masses, that the QCD crossover turns\ninto a first order phase transition for large enough magnetic field, with a\ncritical endpoint located between $eB=4$ GeV$^2$ (where we found an analytic\ncrossover at a pseudo-critical temperature $T_c=(98\\pm3)$ MeV) and $eB=9$\nGeV$^2$ (where the measured critical temperature is $T_c=(63\\pm5)$ MeV).", "category": "hep-lat" }, { "text": "Gauge Invariance and Confinement in Noncompact Simulations of SU(2): Wilson loops have been measured at strong coupling, $\\beta=0.5$, on a $12^4$\nlattice in a noncompact simulation of pure SU(2) in which random compact gauge\ntransformations impose a kind of lattice gauge invariance. The Wilson loops\nsuggest a confining potential.", "category": "hep-lat" }, { "text": "The 't Hooft-Veneziano limit of the Polyakov loop models: The broad class of U(N) and SU(N) Polyakov loop models on the lattice are\nsolved exactly in the combined large N, Nf limit, where N is a number of colors\nand Nf is a number of quark flavors, and in any dimension. In this 't\nHooft-Veneziano limit the ratio N/Nf is kept fixed. We calculate both the free\nenergy and various correlation functions. The critical behavior of the models\nis described in details at finite temperatures and non-zero baryon chemical\npotential. Furthermore, we prove that the calculation of the N-point (baryon)\ncorrelation function reduces to the geometric median problem in the confinement\nphase. In the deconfinement phase we establish an existence of the complex\nmasses and an oscillating decay of correlations in a certain region of\nparameters.", "category": "hep-lat" }, { "text": "Charmonium Potentials at Finite Temperature: The charmonium states at non-zero temperature are studied on anisotropic\nlattices with 2 dynamical quark flavours. Non-local operators are used to\ndetermine the Nambu-Bethe-Salpeter (NBS) wavefunctions via both conventional\nfitting methods and the Maximum Entropy Method. The interquark potential is\ndetermined from the solution of the Schrodinger equation, given the NBS\nwavefunction as input following the HAL QCD method. We observe a temperature\ndependent potential which becomes steeper as the temperature decreases.", "category": "hep-lat" }, { "text": "A Connection Between Complex-Temperature Properties of the 1D and 2D\n Spin $s$ Ising Model: Although the physical properties of the 2D and 1D Ising models are quite\ndifferent, we point out an interesting connection between their\ncomplex-temperature phase diagrams. We carry out an exact determination of the\ncomplex-temperature phase diagram for the 1D Ising model for arbitrary spin $s$\nand show that in the $u_s=e^{-K/s^2}$ plane (i) it consists of $N_{c,1D}=4s^2$\ninfinite regions separated by an equal number of boundary curves where the free\nenergy is non-analytic; (ii) these curves extend from the origin to complex\ninfinity, and in both limits are oriented along the angles $\\theta_n =\n(1+2n)\\pi/(4s^2)$, for $n=0,..., 4s^2-1$; (iii) of these curves, there are\n$N_{c,NE,1D}=N_{c,NW,1D}=[s^2]$ in the first and second (NE and NW) quadrants;\nand (iv) there is a boundary curve (line) along the negative real $u_s$ axis if\nand only if $s$ is half-integral. We note a close relation between these\nresults and the number of arcs of zeros protruding into the FM phase in our\nrecent calculation of partition function zeros for the 2D spin $s$ Ising model.", "category": "hep-lat" }, { "text": "Repairing Stevenson's step in the 4d Ising model: In a recent paper Stevenson claimed that analysis of the data on the wave\nfunction renormalization constant near the critical point of the 4d Ising model\nis not consistent with analytical expectations. Here we present data with\nimproved statistics and show that the results are indeed consistent with\nconventional wisdom once one takes into account the uncertainty of lattice\nartifacts in the analytical computations.", "category": "hep-lat" }, { "text": "High Spin Glueballs from the Lattice: We discuss the principles underlying higher spin glueball calculations on the\nlattice. For that purpose, we develop numerical techniques to rotate Wilson\nloops by arbitrary angles in lattice gauge theories close to the continuum. As\na first application, we compute the glueball spectrum of the SU(2) gauge theory\nin 2+1 dimensions for both parities and for spins ranging from 0 up to 4\ninclusive. We measure glueball angular wave functions directly, decomposing\nthem in Fourier modes and extrapolating the Fourier coefficients to the\ncontinuum. This allows a reliable labelling of the continuum states and gives\ninsight into the way rotation symmetry is recovered. As one of our results, we\ndemonstrate that the D=2+1 SU(2) glueball conventionally labelled as J^P = 0^-\nis in fact 4^- and that the lightest ``J=1'' state has, in fact, spin 3.", "category": "hep-lat" } ]