[en] We study the quenched chiral behavior of hadrons with the pseudoscalar mass as low as ∼ 280 MeV. We look for quenched chiral logs in the pion mass, determine the renormalized quark mass, and observe quenched artifacts in the a₀ and N* propagators. The calculation is done on a quenched lattice of size 20⁴ and a = 0.148(2) fm using overlap fermions and an improved gauge action

[en] We report our calculation of the pion decay constant f_π, the axial renormalization constant Z_A, and the quenched chiral logarithms from the overlap fermions. The calculation is done on a quenched 20⁴ lattice at a=0.148 fm using tree level tadpole improved gauge action. The smallest pion mass we reach is about 280 MeV. The lattice size is about 4 times the Compton wavelength of the lowest mass pion

[en] We introduce the ''Sequential Empirical Bayes Method'', an adaptive constrained-curve fitting procedure for extracting reliable priors. These are then used in standard augmented-chi-square fits on separate data. This better stabilizes fits to lattice QCD overlap-fermion data at very low quark mass where a priori values are not otherwise known. We illustrate the efficacy of the method with data from overlap fermions, on a quenched 16³ x 28 lattice with spatial size La = 3.2 fm and pion mass as low as ∼ 180 MeV

[en] The chiral properties of the pseudoscalar mesons are studied numerically on a quenched 20⁴ lattice with the overlap fermion. We elucidate the role of the zero modes in the meson propagators, particularly that of the pseudoscalar meson. The non-perturbative renormalization constant Z_A is determined from the axial Ward identity and the pion decay constants f_π is calculated from which we determine the lattice spacing to be 0.157 fm.. We look for quenched chiral log in the pseudoscalar decay constants and the pseudoscalar masses for both equal and unequal quark masses. We find that, given limited statistics, it is difficult to see quenched logs in pseudoscalar masses with equal or unequal quark masses. Whereas, it is relatively clear to see them in the pseudoscalar matrix element and the ratio of the pseudoscalar matrix element to f_π. The chiral log parameter delta turns out to be consistent with that predicted from quenched chiral perturbative theory

[en] We study the quenched chiral behavior of the pion with mass as low as ∼ 180 MeV. The calculation is done on a quenched lattice of size 16³ x 28 and a = 0.2 fm with 80 configurations using overlap fermions and an improved gauge action. Using an improved constrained curve fitting technique, we find that the ground state pseudoscalar mass versus bare quark mass behavior is well controlled with small statistical errors; this permits a reliable fit of the quenched chiral log effects, a determination of the chiral log parameter ((delta) = 0.26(3)), and an estimate of the renormalized mass of the light quark (m^#ovr MS#(μ = 2 GeV) = 3.7(3) MeV)

[en] We discuss the utility of low-lying Dirac eigenmodes for studying the nature of topological charge fluctuations in QCD. The implications of previous results using the local chirality histogram method are discussed, and the new results using the overlap Dirac operator in Wilson gauge backgrounds at lattice spacings ranging from a ∼ 0.04 fm to a ∼ 0.12 fm are reported. While the degree of local chirality does not change appreciably closer to the continuum limit, we find that the size and density of local structures responsible for chiral peaking do change significantly. The resulting values are in disagreement with the assumptions of the Instanton Liquid Model. We conclude that the fluctuations of topological charge in the QCD vacuum are not locally quantized

[en] The overlap fermion offers the tremendous advantage of exact chiral symmetry on the lattice, but is numerically intensive. This can be made affordable while still providing large lattice volumes, by using coarse lattice spacing, given that good scaling and localization properties are established. Here, using overlap fermions on quenched Iwasaki gauge configurations, we demonstrate directly that the overlap Dirac operator's range is comfortably small in lattice units for each of the lattice spacings 0.20 fm, 0.17 fm, and 0.13 fm (and scales to zero in physical units in the continuum limit). In particular, our direct results contradict recent speculation that an inverse lattice spacing of 1 GeV is too low to have satisfactory localization. Furthermore, hadronic masses (available on the two coarser lattices) scale very well

[en] It is popular to probe the structure of the QCD vacuum indirectly by studying individual fermion eigenmodes, because this provides a natural way to filter out UV fluctuations. The double-peaking in the distribution of the local chiral orientation parameter (X) has been offered as evidence, by some, in support of a particular model of the vacuum. Here we caution that the X-distribution peaking varies significantly with various versions of the definition of X. Furthermore, each distribution varies little from that resulting from a random reshuffling of the left-handed (and independently the right-handed) fields, which destroys any QCD-induced left-right correlation; that is, the double-peaking is mostly a phase-space effect. We propose a new universal definition of the X parameter whose distribution is uniform for randomly reshuffled fields. Any deviations from uniformity for actual data can then be directly attributable to QCD-induced dynamics. We find that the familiar double peak disappears

[en] The overlap fermion offers the considerable advantage of exact chiral symmetry on the lattice, but is numerically intensive. This can be made affordable while still providing large lattice volumes, by using coarse lattice spacing, given that good scaling and localization properties are established. Here, using overlap fermions on quenched Iwasaki gauge configurations, we demonstrate directly that, with appropriate choice of negative Wilson's mass, the overlap Dirac operator's range is comfortably small in lattice units for each of the lattice spacings 0.20 fm, 0.17 fm, and 0.13 fm (and scales to zero in physical units in the continuum limit). In particular, our direct results contradict recent speculation that an inverse lattice spacing of 1 GeV is too low to have satisfactory localization. Furthermore, hadronic masses (available on the two coarser lattices) scale very well

[en] We introduce the ''Sequential Empirical Bayes Method'', an adaptive constrained-curve fitting procedure for extracting reliable priors. These are then used in standard augmented-χ² fits on separate data. This better stabilizes fits to lattice QCD overlap-fermion data at very low quark mass where a priori values are not otherwise known. Lessons learned (including caveats limiting the scope of the method) from studying artificial data are presented. As an illustration, from local-local two-point correlation functions, we obtain masses and spectral weights for ground and first-excited states of the pion, give preliminary fits for the a₀ where ghost states (a quenched artifact) must be dealt with, and elaborate on the details of fits of the Roper resonance and S₁₁(N^1/2-) previously presented elsewhere. The data are from overlap fermions on a quenched 16³ x 28 lattice with spatial size La = 3.2 fm and pion mass as low as ∼180 MeV