We present the first results of the PACS-CS project which aims to simulate 2 þ 1 flavor lattice QCD on the physical point with the nonperturbatively OðaÞ-improved Wilson quark action and the Iwasaki gauge action. Numerical simulations are carried out at ¼ 1:9, corresponding to the lattice spacing of a ¼ 0:0907ð13Þ fm, on a 32 3 Â 64 lattice with the use of the domain-decomposed HMC algorithm to reduce the up-down quark mass. Further algorithmic improvements make possible the simulation whose up-down quark mass is as light as the physical value. The resulting pseudoscalar meson masses range from 702 MeV down to 156 MeV, which clearly exhibit the presence of chiral logarithms. An analysis of the pseudoscalar meson sector with SU(3) chiral perturbation theory reveals that the next-to-leading order corrections are large at the physical strange quark mass. In order to estimate the physical up-down quark mass, we employ the SU(2) chiral analysis expanding the strange quark contributions analytically around the physical strange quark mass. The SU(2) low energy constants " l 3 and " l 4 are comparable with the recent estimates by other lattice QCD calculations. We determine the physical point together with the lattice spacing employing m , m K and m as input. The hadron spectrum extrapolated to the physical point shows an agreement with the experimental values at a few % level of statistical errors, albeit there remain possible cutoff effects. We also find that our results of f , f K and their ratio, where renormalization is carries out perturbatively at one loop, are compatible with the experimental values. For the physical quark masses we obtain m MS ud and m MS s extracted from the axial-vector Ward-Takahashi identity with the perturbative renormalization factors. We also briefly discuss the results for the static quark potential.

We reconsider constraints on the eigenvalue density of the Dirac operator in the chiral symmetric phase of 2 flavor QCD at finite temperature. To avoid possible ultra-violet(UV) divergences, we work on a lattice, employing the overlap Dirac operator, which ensures the exact "chiral" symmetry at finite lattice spacings. Studying multi-point correlation functions in various channels and taking their thermodynamical limit (and then taking the chiral limit), we obtain stronger constraints than those found in the previous studies: both the eigenvalue density at the origin and its first and second derivatives vanish in the chiral limit of 2 flavor QCD. In addition we show that the axial U(1) anomaly becomes invisible in susceptibilities of scalar and pseudo scalar mesons, suggesting that the 2nd order chiral phase transition with the O(4) scaling is not realized in 2 flavor QCD.Possible lattice artifacts when non-chiral lattice Dirac operator is employed are briefly discussed.

We calculate one-loop renormalization factors of bilinear operators made of physical quark fields for domain-wall QCD. We find that finite parts of such renormalization factors have reasonable values at 1-loop except an overlap factor between the physical quark field and the zero mode in the theory. We point out that the 1-loop estimate of overall renormalization factors becomes unreliable at the coupling where numerical simulations are currently performed, due to the presence of this overlap factor. We show that this problem disappears if the mean-field improved perturbation theory is employed for renormalization factors. ͓S0556-2821͑99͒01709-9͔

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We carry out a feasibility study for the lattice QCD calculation of the neutron electric dipole moment (NEDM) in the presence of the $\theta$ term. We develop the strategy to obtain the nucleon EDM from the CP-odd electromagnetic form factor $F_3$ at small $\theta$, in which NEDM is given by $\lim_{q^2\to 0}\theta F_3(q^2)/(2m_N)$ where $q$ is the momentum transfer and $m_N$ is the nucleon mass. We first derive a formula which relates $F_3$, a matrix element of the electromagnetic current between nucleon states, with vacuum expectation values of nucleons and/or the current. In the expansion of $\theta$, the parity-odd part of the nucleon-current-nucleon three-point function contains contributions not only from the parity-odd form factors but also from the parity-even form factors multiplied by the parity-odd part of the nucleon two-point function, and therefore the latter contribution must be subtracted to extract $F_3$. We then perform an explicit lattice calculation employing the domain-wall quark action with the RG improved gauge action in quenched QCD at $a^{-1}\simeq 2$ GeV on a $16^3\times 32\times 16$ lattice. At the quark mass $m_f a =0.03$, corresponding to $m_\pi/m_\rho \simeq 0.63$, we accumulate 730 configurations, which allow us to extract the parity-odd part in both two- and three-point functions. Employing two different Dirac $\gamma$ matrix projections, we show that a consistent value for $F_3$ cannot be obtained without the subtraction described above. We obtain $F_3(q^2\simeq 0.58 \textrm{GeV}^2)/(2m_N) =$ $-$0.024(5) $e\cdot$fm for the neutron and $F_3(q^2\simeq 0.58 \textrm{GeV}^2)/(2m_N) =$ 0.021(6) $e\cdot$fm for the proton.Comment: LaTeX2e, 43 pages, 42 eps figures, uses revtex4 and graphicx, comments added and typos corrected, final version to appear in Phys. Rev.

We calculate one-loop renormalization factors of bilinear quark operators for the gluon action including six-link loops and an O(a)-improved quark action in the limit of a massless quark. We find that finite parts of the one-loop coefficients of renormalization factors diminish monotonically as either of the coefficients c 1 or c 2 ϩc 3 of the six-link terms is decreased below zero. Detailed numerical results are given, for general values of the clover coefficient, for the tree-level improved gluon action in the Symanzik approach (c 1 ϭϪ1/12,c 2 ϭc 3 ϭ0) and for the choices suggested by Wilson (c 1 ϭϪ0.252,c 2 ϭ0,c 3 ϭϪ0.17) and by Iwasaki (c 1 ϭ Ϫ0.331,c 2 ϭc 3 ϭ0 and c 1 ϭϪ0.27,c 2 ϩc 3 ϭϪ0.04) from renormalization-group analyses. Compared with the case of the standard plaquette gluon action, the finite parts of the one-loop coefficients are reduced by 10-20 % for the Symanzik action, and approximately by a factor of 2 for the renormalization-group improved gluon actions. ͓S0556-2821͑98͒04517-2͔

We perform a lattice QCD study of the meson decay from the N f ¼ 2 þ 1 full QCD configurations generated with a renormalization group improved gauge action and a nonperturbatively OðaÞ-improved Wilson fermion action. The resonance parameters, the effective ! coupling constant and the resonance mass, are estimated from the P-wave scattering phase shift for the isospin I ¼ 1 two-pion system. The finite size formulas are employed to calculate the phase shift from the energy on the lattice. Our calculations are carried out at two quark masses, m ¼ 410 MeV (m =m ¼ 0:46) and m ¼ 300 MeV (m =m ¼ 0:35), on a 32 3 Â 64 (La ¼ 2:9 fm) lattice at the lattice spacing a ¼ 0:091 fm. We compare our results at these two quark masses with those given in the previous works using N f ¼ 2 full QCD configurations and the experiment.

The energy-momentum tensor plays an important role in QCD thermodynamics. Its expectation value contains information of the pressure and the energy density as its diagonal part. Further properties like viscosity and specific heat can be extracted from its correlation function. A nonperturbative evaluation of it on the lattice is called. Recently a new method based on the gradient flow was introduced to calculate the energy-momentum tensor on the lattice, and has been successfully applied to quenched QCD. In this paper, we apply the gradient flow method to calculate the energy-momentum tensor in ( We also apply the gradient flow method to evaluate the chiral condensate taking advantage of the gradient flow method that renormalized quantities can be directly computed avoiding the difficulty of explicit chiral violation with lattice quarks. We compute the renormalized chiral condensate in the MS scheme at renormalization scale µ = 2 GeV with a high precision to study the temperature dependence of the chiral condensate and its disconnected susceptibility. Even with the Wilson-type quark action which violates the chiral symmetry explicitly, we obtain the chiral condensate and its disconnected susceptibility showing a clear signal of pseudocritical temperature at T ∼ 190 MeV related to the chiral restoration crossover.