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We analyze the localization properties for eigenvectors of the Dirac operator in quenched lattice QCD in the vicinity of the deconfinement phase transition. Studying the characteristic differences between the Z_3 sectors above the critical temperature T_c, we find indications for the presence of calorons.
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We study quark confinement physics using lattice QCD. In the maximally abelian (MA) gauge, the off-diagonal gluon amplitude is strongly suppressed, and then the off-diagonal gluon phase shows strong randomness, which leads to a large effective off-diagonal gluon mass, M_off=1.2GeV. Due to the large off-diagonal gluon mass in the MA gauge, low-energy QCD is abelianized like nonabelian Higgs theories. In the MA gauge, there appears a macroscopic network of the monopole world-line covering the whole system. We extract and analyze the dual gluon field B_mu from the monopole-current system in the MA gauge, and evaluate the dual gluon mass as m_B = 0.4-0.5GeV in the infrared region, which is a lattice-QCD evidence of the dual Higgs mechanism by monopole condensation. Even without explicit use of gauge fixing, we can define the maximal abelian projection by introducing a ``gluonic Higgs field phi(x), whose hedgehog singularities lead to monopoles. From infrared abelian dominance and infrared monopole condensation, infrared QCD is describable with the dual Ginzburg-Landau theory. In relation to the color-flux-tube picture for baryons, we study the three-quark (3Q) ground-state potential V_3Q in SU(3) lattice QCD at the quenched level, with the smearing technique for enhancement of the ground-state component. With accuracy better than a few %, V_3Q is well described by a sum of the two-body Coulomb part and the three-body linear confinement part sigma_3Q L_min, where L_min denotes the minimal value of the total length of the color flux tube linking the three quarks. Comparing with the Q-barQ potential, we find a universal feature of the string tension and the OGE result for the Coulomb coefficient.
This document is one of a series of whitepapers from the USQCD collaboration. Here, we discuss opportunities for lattice QCD in quark and lepton flavor physics. New data generated at Belle II, LHCb, BES III, NA62, KOTO, and Fermilab E989, combined with precise calculations of the relevant hadronic physics, may reveal what lies beyond the Standard Model. We outline a path toward improvements of the precision of existing lattice-QCD calculations and discuss groundbreaking new methods that allow lattice QCD to access new observables.
We calculate the light meson spectrum and the light quark masses by lattice QCD simulation, treating all light quarks dynamically and employing the Iwasaki gluon action and the nonperturbatively O(a)-improved Wilson quark action. The calculations are made at the squared lattice spacings at an equal distance a^2~0.005, 0.01 and 0.015 fm^2, and the continuum limit is taken assuming an O(a^2) discretization error. The light meson spectrum is consistent with experiment. The up, down and strange quark masses in the bar{MS} scheme at 2 GeV are bar{m}=(m_{u}+m_{d})/2=3.55^{+0.65}_{-0.28} MeV and m_s=90.1^{+17.2}_{-6.1} MeV where the error includes statistical and all systematic errors added in quadrature. These values contain the previous estimates obtained with the dynamical u and d quarks within the error.
We present lattice results on the valence-quark structure of the pion using a coordinate space method within the framework of Large Momentum Effective Theory (LaMET). In this method one relies on the matrix elements of a Euclidean correlator in boosted hadronic states, which have an operator product expansion at short distance that allows us to extract the moments of PDFs. We renormalize the Euclidean correlator by forming the reduced Ioffe-time distribution (rITD), and reconstruct the second and fourth moments of the pion PDF by taking into account of QCD evolution effects.
Over the past few years new physics methods and algorithms as well as the latest supercomputers have enabled the study of the QCD thermodynamic phase transition using lattice gauge theory numerical simulations with unprecedented control over systematic errors. This is largely a consequence of the ability to perform continuum extrapolations with physical quark masses. Here we review recent progress in lattice QCD thermodynamics, focussing mainly on results that benefit from the use of physical quark masses: the crossover temperature, the equation of state, and fluctuations of the quark number susceptibilities. In addition, we place a special emphasis on calculations that are directly relevant to the study of relativistic heavy ion collisions at RHIC and the LHC.
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