Research in lattice QCD via large scale numerical simulations

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There are several research results in lattice gauge theories. (a) Lattice QCD simulations with 2 light dynamical quarks have been performed at 3 different lattice spacings, in order to take the continuum limit of physical observables. It has been found that hadron spectra such as meson masses in the continuum limit become much closer to corresponding experimental values than in the quenched QCD where the dynamical quark effect is neglected. We then have started the lattice QCD simulation with 2+1 dynamical quarks, where 2 are degenerate up and down quarks and 1 is a strange quark. Again performing the continuum extrapolation form data at 3 different lattice spacings, we have confirmed that hadron masses in the continuum limit agree with experimental values within errors. (b) We have calculated electroweak matrix elements such as K meson B parameters using domain-wall quarks, which has a good chiral symmetry on the lattice. We found that the scaling violation of B parametr is much reduced in quenched QCD compared with other non-chiral quarks, so that a more reliable value of B parameter is obtained. Furthermore we have started 2+1 full QCD simulations with domain-wall quarks and calculated hadron spectra and electroweak matrix elements. (c) We have calculated decay constants and form factors of B mesons, needed to determine Kobayashi-Maskawa matrix. Calculations have been performed in both quenched and full QCD simulations, in order to estimate an effect of the light dynamical quark to these quantities. (d) The QCD equation of state, which is needed to investigate QCD phase transition at heavy ion collision experiments, has been determined in QCD with dynamical quarks. (e) We have proposed new formulation of chiral perturbation theory, which includes the lattice spacing effect of lattice quark field used in simulations. We have checked the validity of this formulation by comparing its predictions with numerical data.