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 $O\left(a\right)\mathrm{}$-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 ${(c}_1=-{0.331,c}_2{=c}_3=0\mathrm{}$ 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.