Singlet vs Nonsinglet Perturbative Renormalization factors of Staggered Fermion Bilinears

TL;DR

This paper computes the difference in renormalization factors between singlet and nonsinglet staggered fermion bilinear operators on the lattice, using two-loop perturbation theory with improved gluons and smearing techniques.

Contribution

It introduces a new method for handling divergent integrals specific to the staggered fermion formalism and provides two-loop perturbative results for renormalization factor differences.

Findings

Two-loop difference computed for singlet and nonsinglet operators.

Method developed for divergent integrals in staggered formalism.

Results enable better estimates of singlet operator renormalization factors.

Abstract

In this paper we present the perturbative computation of the difference between the renormalization factors of flavor singlet ($\sum_f\bar\psi_f\Gamma\psi_f$, $f$: flavor index) and nonsinglet ($\bar\psi_{f_1} \Gamma \psi_{f_2}, f_1 \neq f_2$) bilinear quark operators (where $\Gamma = \mathbb{1},\,\gamma_5,\,\gamma_{\mu},\,\gamma_5\,\gamma_{\mu},\, \gamma_5\,\sigma_{\mu\,\nu}$) on the lattice. The computation is performed to two loops and to lowest order in the lattice spacing, using Symanzik improved gluons and staggered fermions with twice stout-smeared links. The stout smearing procedure is also applied to the definition of bilinear operators. A significant part of this work is the development of a method for treating some new peculiar divergent integrals stemming from the staggered formalism. Our results can be combined with precise simulation results for the renormalization factors of the nonsinglet operators, in order to obtain an estimate of the renormalization factors for the singlet operators. The results have been published in Physical Review D.