Lattice QCD calculation of s-wave hadron scattering lengths in the channels π-π, π-N, K-N,K-N and N-N is carried out in the quenched approximation at β = 6/g 2 = 5.7. A variant of the method of wall source is developed for this purpose, which reduces the computer time by a factor L 3 on an L 3 × T lattice compared to the conventional point source method and avoids the Fierz mixing problem. A version of the method in which gauge configurations are not fixed to any gauge can be extended to calculate disconnected quark loop contributions in hadron two-and three-point functions. An analytical estimate of statistical errors for this method is worked out, and the magnitude of errors without and with gauge fixing is compared for the case of π-π four-point functions calculated with the Kogut-Susskind quark action. For π-π scattering both I = 0 and 2 scattering lengths are evaluated using the Kogut-Susskind and Wilson quark actions on a 12 3 ×20 lattice. For the same size of lattice, π-N, K-N andK-N scattering lenghts are calculated with the Wilson quark action. For the π-π and π-N cases simulation results are consistent with the predictions of current algebra and PCAC within one to two standard deviations up to quite heavy quark masses corresponding to m π /m ρ ≈ 0.74, while for the K-N andK-N cases the agreement is within a factor of two. For N-N scattering a phenomenological study with one-boson exchange potentials indicate that the deuteron becomes unbound if the quark mass is increased beyond 30-40% of the physical value. Simulations with the Wilson action on a 20 4 lattice with heavy quarks with m π /m ρ ≈ 0.74 − 0.95 show that the nucleon-nucleon force is attractive for both spin triplet and singlet channels, and that the scattering lengths are substantially larger compared to those for the π-π and π-N cases even for such heavy quarks. Problem of statistical errors which has to be overcome toward a more realistic calculation of hadron scattering lengths is discussed.

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.

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A report is presented on our continued effort to elucidate the continuum limit of BK using the quenched Kogut-Susskind quark action. By adding to our previous simulations one more point at β = 6.65 employing a 56 3 × 96 lattice, we now confirm the expected O(a 2 ) behavior of BK with the Kogut-Susskind action. A simple continuum extrapolation quadratic in a leads to BK (NDR, 2 GeV) = 0.598(5). As our final value of BK in the continuum we present BK (NDR, 2 GeV)=0.628(42), as obtained by a fit including an α M S (1/a) 2 term arising from the lattice-continuum matching with the one-loop renormalization.

Full pion four-point functions at zero momentum are calculated with Kogut-Susskind quarks on a 12 3 x20 lattice at ^ = 5.7 and ^=0.01 in quenched lattice QCD, employing the wall source method without gauge fixing. For both 7=0 and 2 channels, results for the s-wave scattering lengths are in agreement with the prediction of current algebra and PCAC (partial conservation of axial-vector current).