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

In this paper we present the perturbative computation of the renormalization functions for the quark field and for a complete set of ultralocal fermion bilinears. The computation of the relevant Green’s functions are carried out at one-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 are improved by applying a stout smearing procedure up to two times, iteratively. In the gluon sector we employ the Symanzik improved gauge action for different sets of values of the Symanzik coefficients. The renormalization functions are presented in (two variants of) the ${\mathrm{RI}}^{\prime }$ and in the $\overline{\mathrm{MS}}$ 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. D 86, 094512 (2012)]. 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.”