Singlet vs Nonsinglet Perturbative Renormalization of Fermion Bilinears

TL;DR

This paper calculates the two-loop perturbative differences in renormalization functions between flavor singlet and nonsinglet fermion bilinear operators on the lattice, across various improved actions and fermion formulations.

Contribution

It provides the first comprehensive two-loop perturbative evaluation of singlet versus nonsinglet operator renormalization differences for multiple lattice actions and fermion types.

Findings

Two-loop differences computed for various lattice actions.

Results applicable to staggered, Wilson, and Iwasaki fermions.

Enhanced understanding of operator renormalization in lattice QCD.

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 (TL) Symanzik and Iwasaki gluons, twisted mass and 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.