Perturbative renormalization factors of bilinear quark operators for improved gluon and quark actions in lattice QCD

Abstract

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 ${c}_{2}{+c}_{3}$ 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 ${(c}_{1}=\ensuremath{-}{1/12,c}_{2}{=c}_{3}=0)$ and for the choices suggested by Wilson ${(c}_{1}=\ensuremath{-}{0.252,c}_{2}{=0,c}_{3}=\ensuremath{-}0.17)$ and by Iwasaki ${(c}_{1}=\ensuremath{-}{0.331,c}_{2}{=c}_{3}=0$ and ${c}_{1}=\ensuremath{-}{0.27,c}_{2}{+c}_{3}=\ensuremath{-}0.04)$ 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.