Renormalization group transformation in lattice QCD with quarks

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This project aims at a research of improved actions in quantum chromodynamics (QCD) with dynamical quarks, using the renormalization group method. Because the gauge part of the lattice action introduce lattice artifacts of O(a^2), with a the lattice spacing, it has been considerd that an improvement of the quark part, which has O(a) errors with the standard Wilson fermion action, might remove the major prt of the lattice artifacts in numerical simulations. However, the most problematic lattice artifact, the violation of the chiral symmetry on the lattice, is due to the doublers, whose effects cannot be estimated by a naive order counting in α. In order to suppress the contamination of doublers in physical observables, the maximum momentum in the background gauge configuration should be small. Here, we note that a renormalization group (RG) transformation directly suppress such high momentum modes. Therefore, unlike the case of Symanzik improvement program which is based on a naive power counting in α, we expect that a RG-improved gauge action is efficient to suppress lattice artifacts due to doublers. We study the combination of a RG-improved gauge action and a clover-improved quark action.From a systematic comparative study of improved and standard actions, we found that improvement is necessary both for the gauge and quark parts. We then started to apply our combination of improved actions to the problems of light hadron mass spectrum, light quark mass, static quark potential, the U (1) problem, decay constants and mass spectrum for hadrons including heavy quarks, b and c, and performed the first systematic study of hadron properties in full QCD including a continuum extrapolation. We also studied the equaton of state for QCD at finite temperature. From these studies, importance of dynamical quarks, and also of action improvements, is confirmed.