Search

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

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 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

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

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.

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 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.

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 $.

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 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)

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

We calculate the form factor of the quark energy momentum tensor and thereby extract the quark orbital angular momentum of the nucleon. The calculation is done on a quenched $16^3 \times 24$ lattice at $\beta = 6.0$ and with Wilson fermions at $\kappa$ = 0.148, 0.152, 0.154 and 0.155. We calculate the disconnected insertion stochastically which employs the $Z_2$ noise with an unbiased subtraction. This proves to be an efficient method of reduce the error from the noise. We find that the total quark contribution to the proton spin is $0.29 \pm 0.07$. From this we deduce that the quark orbital angular momentum is $0.17 \pm 0.08$ and predict the gluon spin to be $0.21 \pm 0.07$, i.e. about 40% of the proton spin is due to the glue., Comment: LATTICE99(Matrix Elements), 3 pages, 3 figures

We reply to Nathan Isgur's critique that is directed at some of the conclusions drawn from the lattice simulation of valence QCD, regarding the valence quark model and effective chiral theories., Comment: 12 pages, 6 figures

We present results on hadron masses and quark condensate from Neuberger's overlap fermion. The scaling and chiral properties and finite volume effects from this new Dirac operator are studied. We find that the generalized Gell-Mann-Oakes-Renner relation is well satisfied down to the physical u and d quark mass range. We find that in the range of the lattice spacing we consider, the $\pi$ and $\rho$ masses at a fixed $m_{\pi}/m_{\rho}$ ratio have weak $O(a^2)$ dependence., Comment: LATTICE99(Chiral Fermions), 3 pages, 6 figures

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

Results for the isovector axial form factors of the proton from a lattice QCD calculation are presented for both point-split and local currents. They are obtained on a quenched $16^{3} \times 24$ lattice at $\beta= 6.0$ with Wilson fermions for a range of quark masses from strange to charm. We determine the finite lattice renormalization for both the local and point-split currents of heavy quarks. Results extrapolated to the chiral limit show that the $q^2$ dependence of the axial form factor agrees reasonably well with experiment. The axial coupling constant $g_A$ calculated for the local and the point-split currents is about 6\% and 12\% smaller than the experimental value respectively., Comment: 8 pages, 5 figures (included in part 2), UK/93-01

In an effort to expose the mechanism for chiral-symmetry restoration in high-temperature QCD, we use numerical simulations of lattice QCD with staggered fermions to obtain information about possible effective chiral models. We propose the strategy of comparing expressions built from expectation values of low-order polynomials of macroscopic'' meson fields, such as a Mexican-hat statistic'' {l angle}{pi}{sup 2}{sigma}{r angle}/{l angle}{pi}{sup 2}{r angle}{l angle}{sigma}{r angle}{minus}1, computed locally in terms of the quark fields in lattice QCD and in terms of the meson fields in the effective model. We find that, at least at our chosen couplings, QCD behaves like a nonlinear {sigma} model with little change in the local effective potential across the phase transition. This conclusion supports the hypothesis that chiral-symmetry restoration occurs through random fluctuations in a fixed-length order parameter. Included in this work is a thorough test of symmetry breaking and restoration as manifested in the nonlocal staggered chiral fields.

A Monte Carlo variational calculation of glueball masses is performed in SU (2) lattice gauge theory for coupling less than 1. The preliminary upper bounds are obtained, on a 4 3 ×8 lattice, M (0 + )=1.38±0.26 GeV, M (2 + )=1.39±0.41 GeV. Evidence of the existence of differences from the results for g 2 > 1 is observed.

We calculate the quark orbital angular momentum of the nucleon from the quark energy-momentum tensor form factors on the lattice. The disconnected insertion is estimated stochastically which employs the $Z_2$ noise with an unbiased subtraction. This reduced the error by a factor of 4 with negligible overhead. The total quark contribution to the proton spin is found to be $0.30 \pm 0.07$. From this and the quark spin content we deduce the quark orbital angular momentum to be $0.17 \pm 0.06$ which is $\sim 34$% of the proton spin. We further predict that the gluon angular momentum to be $0.20 \pm 0.07$, i. e. $\sim$ 40% of the proton spin is due to the glue., Comment: 4 pages, 7 figures

A valence QCD theory is developed to study the valence quark properties of hadrons. To keep only the valence degrees of freedom, the pair creation through the Z graphs is deleted in the connected insertions; whereas, the sea quarks are eliminated in the disconnected insertions. This is achieved with a new ``valence QCD'' lagrangian where the action in the time direction is modified so that the particle and antiparticle decouple. The theory has the vector and axial $U(2N_F)$ symmetry in the particle-antiparticle space. Through lattice simulation, it appears that this is dynamically broken down to $U_q(N_F) \times U_{\bar{q}}(N_F)$. Furthermore, the lattice simulation reveals spin degeneracy in the hadron masses and SU(6) relations in the ratios of $F_A/D_A, F_S/D_S$, and $\mu^n/\mu^p$. This leads to an approximate $U_q(2N_F) \times U_{\bar{q}}(2N_F)$ symmetry which is the basis for the valence quark model. We find that the masses of N, $\Delta, \rho, \pi, a_1$, and $a_0$ all drop precipitously compared to their counterparts in the quenched QCD calculation. This is interpreted as due to the disapperance of the `constituent' quark mass which is dynamically generated through tadpole diagrams. Form the near degeneracy between N and $\Delta$ for the quark masses we have studied (ranging from one to four times the strange mass), we conclude that the origin of the hyper-fine splitting in the baryon is largely attibuted to the Goldstone boson exchanges between the quarks. These are the consequences of lacking chiral symmetry in valence QCD. We discuss its implication on the models of hadrons., Comment: 68 pages, LaTex, 36 postscript figures including 1 color figure

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 in the range 0.1fm ? 0.2fm. These matrix elements are needed to predict the glueball branching ratios in J/ radiative decays which will help to 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 also studied. The lattice spacing dependence of our results is very small and the continuum limits are reliably extrapolated, This work is supported by DOE Grants DEFG05- 84ER40154 and DE-FG02-02ER45967. Y. Chen is partly supported by NSFC (No.10075051, 12035040) and CAS (KJCX2-SW-N02).