Search

The Roper state is extracted with valence overlap fermions on a $2+1$-flavor domain-wall fermion lattice (spacing $a = 0.114$ fm and $m_{\pi} = 330$ MeV) using both the Sequential Empirical Bayes (SEB) method and the variational method. The results are consistent, provided that a large smearing-size interpolation operator is included in the variational calculation to have better overlap with the lowest radial excitation. Similar calculations carried out for an anisotropic clover lattice with similar parameters find the Roper $\approx 280$ MeV higher than that of the overlap fermion. The fact that the prediction of the Roper state by overlap fermions is consistently lower than those of clover fermions, chirally improved fermions, and twisted-mass fermions over a wide range of pion masses has been dubbed a "Roper puzzle." To understand the origin of this difference, we study the hairpin $Z$-diagram in the isovector scalar meson ($a_0$) correlator in the quenched approximation. Comparing the $a_0$ correlators for clover and overlap fermions, at a pion mass of 290 MeV, we find that the spectral weight of the ghost state with clover fermions is smaller than that of the overlap at $a = 0.12$ fm and $0.09$ fm, whereas the whole $a_0$ correlators of clover and overlap at $a = 0.06$ fm coincide within errors. This suggests that chiral symmetry is restored for clover at $a \le 0.06$ fm and that the Roper should come down at and below this $a$. We conclude that this work supports a resolution of the "Roper puzzle" due to $Z$-graph type chiral dynamics. This entails coupling to higher components in the Fock space (e.g. $N\pi$, $N\pi\pi$ states) to induce the effective flavor-spin interaction between quarks as prescribed in the chiral quark model, resulting in the parity-reversal pattern as observed in the experimental excited states of $N, \Delta$ and $\Lambda$., Comment: 15 pages, 16 figures, revised manuscript accepted for publication in Phys. Rev. D

We use overlap fermions as valence quarks to calculate meson masses in a wide quark mass range on the $2+1$-flavor domain-wall fermion gauge configurations generated by the RBC and UKQCD Collaborations. The well-defined quark masses in the overlap fermion formalism and the clear valence quark mass dependence of meson masses observed from the calculation facilitate a direct derivation of physical current quark masses through a global fit to the lattice data, which incorporates $O(a^2)$ and $O(m_c^4a^4)$ corrections, chiral extrapolation, and quark mass interpolation. Using the physical masses of $D_s$, $D_s^*$ and $J/\psi$ as inputs, Sommer's scale parameter $r_0$ and the masses of charm quark and strange quark in the $\overline{\rm MS}$ scheme are determined to be $r_0=0.465(4)(9)$ fm, $m_c^{\overline{\rm MS}}(2\,{\rm GeV})=1.118(6)(24)$ GeV (or $m_c^{\overline{\rm MS}}(m_c)=1.304(5)(20)$ GeV), and $m_s^{\overline{\rm MS}}(2\,{\rm GeV})=0.101(3)(6)\,{\rm GeV}$, respectively. Furthermore, we observe that the mass difference of the vector meson and the pseudoscalar meson with the same valence quark content is proportional to the reciprocal of the square root of the valence quark masses. The hyperfine splitting of charmonium, $M_{J/\psi}-M_{\eta_c}$, is determined to be 119(2)(7) MeV, which is in good agreement with the experimental value. We also predict the decay constant of $D_s$ to be $f_{D_s}=254(2)(4)$ MeV. The masses of charmonium $P$-wave states $\chi_{c0}, \chi_{c1}$ and $h_c$ are also in good agreement with experiments., Comment: 19 pages, 15 figures, revised version accepted for publication in PRD

We calculate the lattice two-point function of topological charge density in pure-glue QCD using the discretization of the operator based on the overlap Dirac matrix. Utilizing data at three lattice spacings it is shown that the continuum limit of the correlator complies with the requirement of non-positivity at non-zero distances. For our choice of the overlap operator and the Iwasaki gauge action we find that the size of the positive core is ~2a (with a being the lattice spacing) sufficiently close to the continuum limit. This result confirms that the overlap-based topological charge density is a valid local operator over realistic backgrounds contributing to the QCD path integral, and is important for the consistency of recent results indicating the existence of a low-dimensional global brane-like topological structure in the QCD vacuum. We also confirm the divergent short-distance behavior of the correlator, and the non-integrable nature of the associated contact part., 13 pages, 5 figures

Using the constrained-curve fitting method and overlap fermions with the lowest pion mass at 180 MeV, we observe that the masses of the first positive and negative parity excited states of the nucleon tend to cross over as the quark masses are taken to the chiral limit. Both results at the physical pion mass agree with the experimental values of the Roper resonance (N1/2+(1440)) and S-11 (N1/2- (1535)). This is seen for the first time in a lattice QCD calculation. These results are obtained on a quenched Iwasaki 16(3) x 28 lattice with a = 0.2 fm. We also extract the ghost eta'N states (a quenched artifact) which are shown to decouple from the nucleon interpolation field above mpi similar to 300 MeV. From the quark mass dependence of these states in the chiral region, we conclude that spontaneously broken chiral symmetry dictates the dynamics of light quarks in the nucleon. (C) 2004 Elsevier B.V. All rights reserved.

We present renormalization constants of overlap quark bilinear operators on 2+1-flavor domain wall fermion configurations. Both overlap and domain wall fermions have chiral symmetry on the lattice. The scale independent renormalization constant for the local axial vector current is computed using a Ward Identity. The renormalization constants for the scalar, pseudoscalar and vector current are calculated in the RI-MOM scheme. Results in the MS-bar scheme are obtained by using perturbative conversion ratios. The analysis uses in total six ensembles with lattice sizes 24^3x64 and 32^3x64., 7 pages, 10 figures, presented at the 31st International Symposium on Lattice Field Theory (LATTICE 2013), 29 July - 3 August 2013, Mainz, Germany

We test iterative algorithms, MR, QMRγ5 and BiCGγ5, to compare their efficiency in matrix inversion with multi-quarks (shifted matrices) within one iteration process. Our results on the 83 × 12 and 163 × 24 show that MR admits multi-quark calculation with less memory requirement, whereas QMR is faster for the single quark calculation.

We present a calculation of the strangeness and charmness contents $⟨N|\overline{s}s|N⟩$ and $⟨N|\overline{c}c|N⟩$ of the nucleon from dynamical lattice QCD with $2+1$ flavors. The calculation is performed with overlap valence quarks on $2+1$-flavor domain-wall fermion gauge configurations. The configurations are generated by the RBC collaboration on a ${24}^{3}\ifmmode\times\else\texttimes\fi{}64$ lattice with sea-quark mass $a{m}_{l}=0.005$, $a{m}_{s}=0.04$, and inverse lattice spacing ${a}^{\ensuremath{-}1}=1.73\text{ }\text{ }\mathrm{GeV}$. Both actions have chiral symmetry which is essential in avoiding contamination due to the operator mixing with other flavors. The nucleon propagator and the quark loops are both computed with stochastic grid sources, while low-mode substitution and low-mode averaging methods are used respectively which substantially improve the signal-to-noise ratio. We obtain the strangeness matrix element ${f}_{{T}_{s}}={m}_{s}⟨N|\overline{s}s|N⟩/{M}_{N}=0.0334(62)$, and the charmness content ${f}_{{T}_{c}}={m}_{c}⟨N|\overline{c}c|N⟩/{M}_{N}=0.094(31)$ which is resolved from zero by $3\ensuremath{\sigma}$ precision for the first time.

We report on a lattice QCD calculation of the flavor-singlet axial coupling constant $g_A$ of the proton from the axial-vector current. The simulation is carried out at $\beta = 6$ on a quenched $16^3 \times 24$ lattice. An extrapolation to the chiral limit shows that the connected insertion (valence and cloud parts) is $0.62 \pm 0.09$, which is close to $g_A^8$. The disconnected insertion (vacuum polarization from the sea quark) for the $u$ or $d$ quark is $- 0.12\pm 0.01 $ and the $s$ quark also contributes $-0.12\pm 0.01$. The total $g_A^1$ is thus $0.25 \pm 0.12$ which is in agreement with experiments. In addition, we find $g_A^3 = 1.20 \pm 0.11$, $g_A^8 = 0.61 \pm 0.13$ and $F_A/D_A = 0.60 \pm 0.02$, also in agreement with experiments., Comment: 8 pages, latex, 7 figures in uuencoded postscript file, minor typo changes.

The $\pi NN$ form factor $g_{\pi NN}(q^2)$ is obtained from a quenched lattice QCD calculation of the pseudoscalar form factor $g_P(q^2)$ of the proton with pion pole dominance. We find that $g_{\pi NN}(q^2)$ fitted with the monopole form agrees well with the Goldberger-Treiman relation and is much preferred over the dipole form. The monopole mass is determined to be $0.75 \pm 0.14 {\rm GeV}$ which shows that $g_{\pi NN}(q^2)$ is rather soft. The extrapolated $\pi N$ coupling constant $g_{\pi NN} = 12.7 \pm 2.4$ is quite consistent with the phenomenological values. We also compare $g_{\pi NN}(q^2)$ with the axial form factor $g_A(q^2)$ to check the pion dominance in the induced pseudoscalar form factor $h_A(q^2)$ vis \`{a} vis chiral Ward identity., Comment: 8 pages of text plus 4 postscript figures (128 kbytes)

We study the quenched chiral behavior of the pion with mass as low as $\approx 180$ MeV. The calculation is done on a quenched lattice of size $16^3\times 28$ 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 ($m^{\bar{MS}}(\mu=2 {\rm GeV}) = 3.7(3) {\rm MeV}$)., Comment: Lattice2002(spectrum), 3 pages, 3 figures

Stochastic noise estimator method is a powerful tool to calculate the disconnected insertion involving quark loops. We study the variance reduction technique with unbiased subtraction. We use the complex $Z_2$ noise to calculate the quark loops on a $16^3 \times 24$ lattice with $\beta = 6.0$ and $\kappa$ = 0.154. Unbiased subtraction method is performed by using hoping parameter expansion. We report on the variance reduction for the point-split vector current as a function of the number of subtraction terms and the number of noise used., Comment: Lattice 2002 (matrixel), 3 pages

The structure of topological charge fluctuations in the QCD vacuum is strongly restricted by the spectral negativity of the Euclidean 2-point correlator for $x\neq 0$ and the presence of a positive contact term. Some examples are considered which illustrate the physical origin of these properties., Lattice 2002 Conference Proceedings

Using the constrained-fitting method based on Bayesian priors, we extract the masses of the two lowest states of octet and decuplet baryons with both parities. The calculation is done on quenched 16^3x28 lattices of a=0.2 fm using an improved gauge action and overlap fermions, with the pion mass as low as 180 MeV. The Roper state N(1440)1/2+ is clearly observed for the first time as the 1st-excited state of the nucleon from the standard interpolating field. Together with other baryons, our preliminary results indicate that the level-ordering of the low-lying baryon states on the lattice is largely consistent with experiment. The realization is helped by cross-overs between the excited 1/2+ and 1/2- states in the region of pion mass from 300 to 400 MeV., 3 pages, 5 figures, talk at Lattice 2002 (spectrum)

Using the Euclidean path-integral formulation for the hadronic tensor, we show that the large difference between u\ifmmode\bar\else\textasciimacron\fi{} and d\ifmmode\bar\else\textasciimacron\fi{} does not come from the disconnected quark-loop insertion. Rather, it can come from the connected (quark line) insertion involving quarks propagating backwards in time. We study the influence of the backward time propagator in the axial-vector and scalar matrix elements in lattice gauge calculations and give an estimate of the violation of the Gottfried sum rule.

The calculation of the nucleon strangeness form factors from Nf = 2 + 1 clover fermion lattice QCD is presented. Disconnected insertions are evaluated using the Z(4) stochastic method, along with unbiased subtractions from the hopping parameter expansion. We find that increasing the number of nucleon sources for each configuration improves the signal significantly. We obtain Gs M(0) = −0.017(25)(07), which is consistent with experimental values, and has an order of magnitude smaller error. Preliminary results for the strangeness contribution to the second moment of the parton distribution function are also presented., AIP Conf. Proc. 1374

Matrix elements of the form $ $ are calculated using the lattice QCD Monte Carlo method. Here, $|G>$ is a glueball state with quantum numbers $ 0^{++}$, $ 2^{++}$, $ 0^{-+}$ and $G$ is the gluon field strength operator. The matrix elements are obtained from the hybrid correlation functions of the fuzzy and plaquette operators performed on the $12^{4}$ and $14^{4}$ lattices at $��= 5.9 $ and $5.96$ respectively. These matrix elements are compared with those from the QCD sum rules and the tensor meson dominance model. They are the non-perturbative matrix elements needed in the calculation of the partial widths of $J/��$ radiative decays into glueballs., 12 pages, UK/92-05

We report results of our calculation on the π N σ term and the flavor-singlet axial charge of the nucleon in the framework of quenched lattice QCD. The disconnected insertions which involve contributions from the sea quarks are evaluated with the stochastic estimator with the Z 2 noise which yields minimum variances. We find the sea-quark contribution to the π N sigma term to be ∼ 1 2 − 1 4 of that of the dynamical fermion calculation. Whereas, the sea-quark contribution to the flavor-singlet g A is negative and large enough to cancel the valence (connected insertion) contribution substantially to resolve the “proton spin crisis”.

The overlap fermion propagator is calculated on 2+1 flavor domain wall fermion gauge configurations on 16^3 x 32, 24^3 x 64 and 32^3 x 64 lattices. With HYP smearing and low eigenmode deflation, it is shown that the inversion of the overlap operator can be expedited by ~ 20 times for the 16^3 x 32 lattice and ~ 80 times for the 32^3 x 64 lattice. Through the study of hyperfine splitting, we found that the O(m^2a^2) error is small and these dynamical fermion lattices can adequately accommodate quark mass up to the charm quark. The low energy constant \Delta_{mix} which characterizes the discretization error of the pion made up of a pair of sea and valence quarks in this mixed action approach is calculated via the scalar correlator with periodic and anti-periodic boundary conditions. It is found to be small which shifts a 300 MeV pion mass by ~ 10 to 19 MeV on these sets of lattices. We have studied the signal-to-noise issue of the noise source for the meson and baryon. It is found that the many-to-all meson and baryon correlators with Z_3 grid source and low eigenmode substitution is efficient in reducing errors for the correlators of both mesons and baryons. With 64-point Z_3 grid source and low-mode substitution, it can reduce the statistical errors of the light quark (m_{\pi} ~ 200 - 300 MeV) meson and nucleon correlators by a factor of ~ 3-4 as compared to the point source. The Z_3 grid source itself can reduce the errors of the charmonium correlators by a factor of ~ 3., Comment: 30 pages, 18 figures, replaced with the version to be published in PRD

We present the N{sub f}=2+1 clover fermion lattice QCD calculation of the nucleon strangeness form factors. We evaluate disconnected insertions using the Z(4) stochastic method, along with unbiased subtractions from the hopping parameter expansion. We find that increasing the number of nucleon sources for each configuration improves the signal significantly. We obtain G{sub M}{sup s}(0)=-0.017(25)(07), where the first error is statistical, and the second is the uncertainties in Q{sup 2} and chiral extrapolations. This is consistent with experimental values, and has an order of magnitude smaller error.

We extend the study of lowest moments, $$ and $$, of the parton distribution function of the nucleon to include those of the sea quarks; this entails a disconnected insertion calculation in lattice QCD. This is carried out on a $16^3 \times 24$ quenched lattice with Wilson fermion. The quark loops are calculated with $Z_2$ noise vectors and unbiased subtractions, and multiple nucleon sources are employed to reduce the statistical errors. We obtain 5$\sigma$ signals for $$ for the $u,d,$ and $s$ quarks, but $$ is consistent with zero within errors. We provide results for both the connected and disconnected insertions. The perturbatively renormalized $$ for the strange quark at $\mu = 2$ GeV is $_{s+\bar{s}} = 0.027 \pm 0.006$ which is consistent with the experimental result. The ratio of $$ for $s$ vs. $u/d$ in the disconnected insertion with quark loops is calculated to be $0.88 \pm 0.07$. This is about twice as large as the phenomenologically fitted $\displaystyle\frac{< x>_{s+\bar{s}}}{< x>_{\bar{u}}+< x>_{\bar{d}}}$ from experiments where $\bar{u}$ and $\bar{d}$ include both the connected and disconnected insertion parts. We discuss the source and implication of this difference., Comment: 50 Pages 58 Figures

Preliminary results on the isovector and isoscalar axial-vector form factors of the proton from a lattice QCD calculation are presented and discussed. The results are based on a quenched 16 3 × 24 lattice at β = 6.0 with Wilson fermions at κ = 0.152. Results from the smeared source are compared with those from the point source. It is found that the smeared source gives somewhat better results at zero momentum transfer but worse results at high momentum transfers. Our results also suggest that the quark loop contribution to the flavor-singlet axial-vector current may play an important role in understanding the quark-spin content of the proton as determined from the recent EMC experiment.

We study the ${a}_{0}$ and $\ensuremath{\sigma}$ mesons with the overlap fermion in the chiral regime with the pion mass as low as 182 MeV in the quenched approximation. After the ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\pi}$ ghost states are separated, we find the ${a}_{0}$ mass with the $q\overline{q}$ interpolation field to be almost independent of the quark mass in the region below the strange quark mass. The chirally extrapolated results are consistent with ${a}_{0}(1450)$ being the $u\overline{d}$ meson and ${K}_{0}^{*}(1430)$ being the $u\overline{s}$ meson with calculated masses at $1.42\ifmmode\pm\else\textpm\fi{}0.13\text{ }\text{ }\mathrm{GeV}$ and $1.41\ifmmode\pm\else\textpm\fi{}0.12\text{ }\text{ }\mathrm{GeV}$, respectively. We also calculate the scalar mesonium with a tetraquark interpolation field. In addition to the two-pion scattering states, we find a state at $\ensuremath{\sim}550\text{ }\text{ }\mathrm{MeV}$. Through the study of volume dependence, we confirm that this state is a one-particle state, in contrast to the two-pion scattering states. This suggests that the observed state is a tetraquark mesonium which is quite possibly the $\ensuremath{\sigma}(600)$ meson.

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 $1 {\rm GeV}$ is too low to have satisfactory localization. Furthermore, hadronic masses (available on the two coarser lattices) scale very well., Comment: Lattice 2005 (chiral fermions), 6 pages, 4 figures

PUBLISHED, The glueball-to-vacuum matrix elements of local gluonic operators in scalar, tensor, and pseudoscalar channels are investigated numerically on several anisotropic lattices with the spatial lattice spacing ranging from 0.1?0.2 fm. These matrix elements are needed to predict the glueball branching ratios in J= radiative decays which will help identify the glueball states in experiments. Two types of improved local gluonic operators are constructed for a self-consistent check and the finite-volume effects are studied. We find that lattice spacing dependence of our results is very weak and the continuum limits are reliably extrapolated, as a result of improvement of the lattice gauge action and local operators. We also give updated glueball masses with various quantum numbers., This work is supported in part by U.S. Department of Energy under Grants No. DE-FG05-84ER40154 and No. DE-FG02-95ER40907. The computing resources at NERSC (operated by DOE under No. DE-AC03- 76SF00098) and SCCAS (Deepcomp 6800) are also acknowledged. Y. Chen and S. J. Dong are partly supported by NSFC (No. 10075051, No. 10235040) and CAS (No. KJCX2-SW-N02). C. Morningstar is also supported by NSF under Grant No. PHY-0354982.

We have recently presented evidence that in configurations dominating the regularized pure-glue QCD path integral, the topological charge density constructed from overlap Dirac operator organizes into an ordered space-time structure. It was pointed out that, among other properties, this structure exhibits two important features: it is low-dimensional and geometrically global, i.e. consisting of connected sign-coherent regions with local dimensions 1, 10 pages, 3 figures; v2: typos corrected, minor modifications; v3: misprint in Eqs. (2,3) fixed

We present the first study of the charmonium spectrum using overlap fermions, on quenched configurations. Simulations are performed on $16^3 \times 72$ lattices, with Wilson gauge action at $\beta$ = 6.3345. We demonstrate that we have discretization errors under control at about 5%. We obtain 88(4) MeV for hyperfine splitting using the $r_0$ scale, and 121(6) MeV using the ($1\bar{P}-1\bar{S}$) scale. This paper raises the possibility that the discrepancy between the lattice results and the experimental value for charmonium hyperfine splitting can be resolved using overlap fermions to simulate the charm quark on lattice., Comment: 10 pages, 9 figures

The quenched chiral logarithms are examined on a 16(3)x28 lattice with Iwasaki gauge action and overlap fermions. The pion decay constant f(pi) is used to set the lattice spacing, a=0.200(3) fm. With pion mass as low as similar to180 MeV, we see the quenched chiral logarithms clearly in m(pi)(2)/m and f(P), the pseudoscalar decay constant. We analyze the data to determine how low the pion mass needs to be in order for the quenched one-loop chiral perturbation theory (chiPT) to apply. With the constrained curve-fitting method, we are able to extract the quenched chiral logarithmic parameter delta together with other low-energy parameters. Only for m(pi)less than or equal to300 MeV do we obtain a consistent and stable fit with a constant delta which we determine to be 0.24(3)(4) (at the chiral scale Lambda(chi)=0.8 GeV). By comparing to the 12(3)x28 lattice, we estimate the finite volume effect to be about 2.7% for the smallest pion mass. We also fitted the pion mass to the form for the re-summed cactus diagrams and found that its applicable region is extended farther than the range for the one-loop formula, perhaps up to m(pi)similar to500-600 MeV. The scale independent delta is determined to be 0.20(3) in this case. We study the quenched non-analytic terms in the nucleon mass and find that the coefficient C-1/2 in the nucleon mass is consistent with the prediction of one-loop chiPT. We also obtain the low energy constant L-5 from f(pi). We conclude from this study that it is imperative to cover only the range of data with the pion mass less than similar to300 MeV in order to examine the chiral behavior of the hadron masses and decay constants in quenched QCD and match them with quenched one-loop chiPT.

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., Lattice 2004(topology), Fermilab, June 21-26, 2004; 3 pages, 4 figures

We present a quenched lattice QCD calculation of spin-1/2 five-quark states with $uudd\bar{s}$ quark content for both positive and negative parities. We do not observe any bound pentaquark state in these channels for either I = 0 or I =1. The states we found are consistent with KN scattering states which are checked to exhibit the expected volume dependence of the spectral weight. The results are based on overlap-fermion propagators on two lattices, 12^3 x 28 and 16^3 x 28, with the same lattice spacing of 0.2 fm, and pion mass as low as ~ 180 MeV., accepted for publication in Phys. Rev. D

We report results of our calculation on the $\pi N\sigma$ term and quark spin content of the nucleon on the quenched $16^3 \times 24$ lattice at $\beta = 6.0$. The disconnected insertions which involve contributions from the sea quarks are calculated with the stochastic $Z_2$ noise algorithm. As a physical test of the algorithm, we show that the forward matrix elements of the vector and pseudoscalar currents for the disconnected insertions are indeed consistent with the known results of zero. We tried the Wuppertal smeared source and found it to be more noisy than the point source. With unrenormalized $m_q=4.42(17)$MeV, we find the $\pi N\sigma$ term to be $39.2\pm 5.2$ MeV. The strange quark condensate in the nucleon is large, i.e. $\langle N|\bar{s}s|N\rangle = 1.16 \pm 0.54$. For the quark spin content, we find $\Delta u =0.78\pm 0.07$, $\Delta d =-0.42\pm 0.07$, and $\Delta s = -0.13\pm 0.06$. The flavor-singlet axial charge $g_A^1 = \Delta \Sigma =0.22\pm 0.09 $.

We consider the lattice topological charge density introduced by Hasenfratz, Laliena, and Niedermayer and propose its eigenmode expansion as a tool to investigate the structure of topological charge fluctuations in QCD. The resulting effective density is built from local chiralities studied previously. At every order of the expansion, the density exactly sums up to the global topological charge, and the leading term describes the maximally smooth space-time distribution of charge relevant for propagating light fermions. We use this framework to demonstrate our previous suggestion that the bulk of the topological charge in QCD does not effectively appear in the form of quantized unit lumps. Our conclusion implies that it is unlikely that the mixing of ``would-be'' zero modes associated with such lumps is the prevalent microscopic mechanism for spontaneous chiral symmetry breaking in QCD. We also present the first results quantitatively characterizing the space-time behavior of effective densities. For coherent fluctuations contained in spherical regions, we find a continuous distribution of associated charges essentially ending at $\ensuremath{\approx}0.5.$

While sign-coherent 4-dimensional structures cannot dominate topological charge fluctuations in the QCD vacuum at all scales due to reflection positivity, it is possible that enhanced coherence exists over extended space-time regions of lower dimension. Using the overlap Dirac operator to calculate topological charge density, we present evidence for such structure in pure-glue SU(3) lattice gauge theory. It is found that a typical equilibrium configuration is dominated by two oppositely-charged sign-coherent connected structures (``sheets'') covering about 80% of space-time. Each sheet is built from elementary 3-d cubes connected through 2-d faces, and approximates a low-dimensional curved manifold (or possibly a fractal structure) embedded in the 4-d space. At the heart of the sheet is a ``skeleton'' formed by about 18% of the most intense space-time points organized into a global long-range structure, involving connected parts spreading over maximal possible distances. We find that the skeleton is locally 1-dimensional and propose that its geometrical properties might be relevant for understanding the possible role of topological charge fluctuations in the physics of chiral symmetry breaking., Comment: 4 pages RevTeX, 4 figures; v2: 6 pages, 5 figures, more explanations provided, figure and references added, published version

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 $16^3\times 28$ lattice with spatial size La=3.2 fm and pion mass as low as $\sim$ 180 MeV., Comment: Lattice2003(machine), 3 pages, 3 figures

Recently, we have pointed out that sign-coherent 4-dimensional structures can not dominate topological charge fluctuations in QCD vacuum at all scales. Here we show that an enhanced lower-dimensional coherence is possible. In pure SU(3) lattice gauge theory we find that in a typical equilibrium configuration about 80% of space-time points are covered by two oppositely-charged connected structures built of elementary 3-dimensional coherent hypercubes. The hypercubes within the structure are connected through 2-dimensional common faces. We suggest that this coherence is a manifestation of a low-dimensional order present in the QCD vacuum. The use of a topological charge density associated with Ginsparg-Wilson fermions ("chiral smoothing") is crucial for observing this structure., 3 pages, 1 figure; Proceedings of the "Confinement V" Conference, Gargnano, Italy, Sep 10-14, 2002

The reasons for using low-lying Dirac eigenmodes to probe the local structure of topological charge fluctuations in QCD are discussed, and it is pointed out that the qualitative double-peaked behavior of the local chiral orientation probability distribution in these modes is necessary, but not sufficient for dominance of instanton-like fluctuations. The results with overlap Dirac operator in Wilson gauge backgrounds at lattice spacings ranging from a~0.04 fm to a~0.12 fm are reported, and it is found that the size and density of local structures responsible for double-peaking of the distribution are in disagreement with the assumptions of the Instanton Liquid Model. More generally, our results suggest that vacuum fluctuations of topological charge are not effectively dominated by locally quantized (integer-valued) lumps in QCD., 29 pages, 13 figures; v2: minor improvements in presentation, results and conclusions unchanged, version to appear in PRD

The chiral properties of the pseudoscalar mesons are studied numerically on a quenched ${20}^{4}$ 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 is found to be almost independent of the quark mass for the range of quark masses we study; this implies that the ${O(a}^{2})$ error is small. The pion decay constant ${f}_{\ensuremath{\pi}}$ is calculated from which we determine the lattice spacing to be 0.148 fm. We look for the quenched chiral log in the pseudoscalar decay constants and the pseudoscalar masses and we find clear evidence for its presence. The chiral log parameter $\ensuremath{\delta}$ is determined to be in the range 0.15--0.4, which is consistent with that predicted from quenched chiral perturbation theory.

The local structure of low-lying eigenmodes of the overlap Dirac operator is studied. It is found that these modes cannot be described as linear combinations of 't Hooft ''would-be'' zeromodes associated with instanton excitations that underly the Instanton Liquid Model. This implies that the instanton liquid scenario for spontaneous chiral symmetry breaking in QCD is not accurate. More generally, our data suggests that the vacuum fluctuations of topological charge are not effectively dominated by localized lumps of unit charge with which the topological ''would-be'' zeromodes could be associated.

We report our calculation of the pion decay constant $f_\pi$, the axial renormalization constant $Z_A$, and the quenched chiral logarithms from the overlap fermions. The calculation is done on a quenched $20^4$ 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., Comment: Lattice2001(Hadronic Matrix Elements), 3pages, 5figures

We study the quenched chiral behavior of hadrons with the pseudoscalar mass as low as $\approx 280$ MeV. We look for quenched chiral logs in the pion mass, determine the renormalized quark mass, and observe quenched artifacts in the $a_0$ and $N^*$ propagators. The calculation is done on a quenched lattice of size $20^4$ and $a = 0.148(2)$ fm using overlap fermions and an improved gauge action., Comment: Lattice2001(spectrum), 3 pages, 4 figures (uses rotate.sty)

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., Comment: 3 pages, 4 figures, Lattice2001(confinement)

Quark loop effects are studied with the stochastic matrix inversion algorithm. Z2 microcanonical noise is introduced to study the deviation from the orthonormality condition for finite configurations and compare with other noises. The results of the quark loops for various currents on a 163 × 24 lattice at β = 6.0 with Wilson fermion (κ = .148) are obtained for the Z2microcanonical noise. The results on the quark condensate, the topological susceptibility are given. We also discuss the feasibility for the two-point and three-point function calculations.

The chiral symmetry relation and scaling of the overlap fermions are studied numerically on the quenched lattices at 3 couplings with about the same physical volume. We find that the generalized Gell-Mann-Oakes-Renner relation is satisfied to better than 1% down to the smallest quark mass at $m_0a = 0.006$. We also obtain the quark mass from the PCAC relation and the pseudoscalar masses. The renormalization group invariant quark mass is shown to be fairly independent of scale. The $\pi$ and $\rho$ masses at a fixed $m_{\pi}/m_{\rho}$ ratio indicate small $O(a^2)$ corrections. It is found that the critical slowing down sets in abruptly at a very small quark mass close to those of the physical u and d quarks., Comment: 8 pages, 5 figures, re-worked references and corrected minor typos

We calculate the strange magnetic moment of the nucleon on a quenched $16^3 \times 24$ lattice at $\beta = 6.0$, and with Wilson fermions at $\kappa$ = 0.148, 0.152, and 0.154. The strange quark contribution from the disconnected insertion is estimated stochastically by employing the $Z_2$ noise method. Using an unbiased subtraction along with the help of charge conjugation and hermiticity, we reduce the error by a factor of 2 with negligible overhead. Our result is $G_{M}^{s} = -0.28\pm0.10 \mu_{N}$., Comment: Lattice 2000 (Hadronic Matrix Elements), 4 pages 2 figs