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

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) = -1/12,c(2) = c(3) = 0) and for the choices suggested by Wilson (c(1) = -0.252,c(2) = 0,c(3) = -0.17) and by Iwasaki (c(1) = - 0.331,c(2) = c(3) = 0 and c(1) = -0.27,c(2) + c(3) = -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. [S0556-2821(98)04517-2].