Singlet versus nonsinglet perturbative renormalization of fermion bilinears

Abstract

In this paper, we present the perturbative evaluation of the difference between the renormalization functions of flavor singlet and nonsinglet bilinear quark operators on the lattice. The computation is performed to two loops and to lowest order in the lattice spacing, for a class of improved lattice actions, including Wilson, tree-level Symanzik and Iwasaki gluons, twisted mass and Stout Link Non-perturbative Clover (SLiNC) Wilson fermions, as well as staggered fermions with twice stout-smeared links. In the staggered formalism, the stout smearing procedure is also applied to the definition of bilinear operators.