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 (Formula presented)-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 (Formula presented) or (Formula presented) 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 (Formula presented) and for the choices suggested by Wilson (Formula presented) and by Iwasaki (Formula presented) and (Formula presented) 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. © 1998 The American Physical Society.