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In this paper we present the perturbative evaluation of the differencebetween the renormalization functions of flavor singlet and nonsinglet bilinearquark operators on the lattice. The computation is performed to two loops andto lowest order in the lattice spacing, for a class of improved latticeactions, including Wilson, tree-level (TL) Symanzik and Iwasaki gluons, twistedmass and SLiNC Wilson fermions, as well as staggered fermions with twicestout-smeared links. In the staggered formalism, the stout smearing procedureis also applied to the definition of bilinear operators.

Singlet vs Nonsinglet Perturbative Renormalization of Fermion Bilinears