Perturbative renormalization functions of local operators for staggered fermions with stout improvement

TL;DR

This paper computes perturbative renormalization functions for staggered fermions with stout smearing, providing detailed results in multiple schemes and parameters, enhancing the precision of lattice QCD calculations.

Contribution

It presents the first 1-loop perturbative calculation of renormalization functions for staggered fermions with stout improvement, including comprehensive parameter dependence.

Findings

Renormalization functions in RI' and MSbar schemes are provided.

Dependence on stout parameters, fermion mass, gauge fixing, and scale is explicitly shown.

Results are made accessible via a Mathematica package.

Abstract

In this paper we present the perturbative computation of the renormalization functions for the quark field and for a complete set of ultra-local fermion bilinears. The computation of the relevant Green's functions was carried out at 1-loop level for the staggered action using massive fermions. The gluon links which appear both in the fermion action and in the definition of the bilinears have been improved by applying a stout smearing procedure up to 2 times, iteratively. In the gluon sector we employed the Symanzik improved gauge action for different sets of values of the Symanzik coefficients. The renormalization functions are presented in (two variants of) the RI' and in the MSbar renormalization scheme; the dependence on all stout parameters, as well as on the fermion mass, the gauge fixing parameter and the renormalization scale, is shown explicitly. This work is related to our recent paper [Phys. Rev. D86 (2012) 094512, arXiv:1209.6015]. To make our results easily accessible to the reader, we include them in the distribution package of this paper, as a Mathematica input file, Staggered.m.