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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 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 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

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 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.

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 $\ensuremath{\approx}0.5.$

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.

We report on a lattice QCD calculation of the strangeness magnetic moment of the nucleon. Our result is $G_M^s(0) = - 0.36 \pm 0.20 $. The sea contributions from the u and d quarks are about 80% larger. However, they cancel to a large extent due to their electric charges, resulting in a smaller net sea contribution of $ - 0.097 \pm 0.037 ��_N$ to the nucleon magnetic moment. As far as the neutron to proton magnetic moment ratio is concerned, this sea contribution tends to cancel out the cloud-quark effect from the Z-graphs and result in a ratio of $ -0.68 \pm 0.04$ which is close to the SU(6) relation and the experiment. The strangeness Sachs electric mean-square radius $< r_s^2>_E$ is found to be small and negative and the total sea contributes substantially to the neutron electric form factor., 10 pages, 5 figures, LaTex, UK/97-23, ADP-97-55/T281