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

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.

18 pages, 3 figures, 3 Appendices. Version accepted for publication in Phys. Rev. D

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• Complete flavor decomposition of the spin and momentum fraction of the proton using lattice QCD simulations at physical pion mass
• One-loop renormalization of staple-shaped operators in continuum and lattice regularizations
• Renormalization of Wilson-line operators in the presence of nonzero quark masses
• Singlet vs Nonsinglet Perturbative Renormalization of Fermion Bilinears
• Improved renormalization scheme for nonlocal operators
• Singlet vs Nonsinglet Perturbative Renormalization factors of Staggered Fermion Bilinears