Perturbative Corrections for Staggered Fermion Bilinears

TL;DR

This paper computes perturbative corrections for staggered fermion bilinears, including non-local and improved operators, showing reduced corrections with certain techniques, aiding more accurate weak matrix element calculations.

Contribution

It extends previous calculations by including non-local, improved, and gauge-invariant operators, and assesses tadpole correction methods for staggered fermion bilinears.

Findings

Smaller perturbative corrections for improved operators

Gauge link projections reduce correction sizes

Mean-field method effectively sums tadpole contributions

Abstract

We calculate the perturbative corrections to fermion bilinears that are used in numerical simulations when extracting weak matrix elements using staggered fermions. This extends previous calculations of Golterman and Smit, and Daniel and Sheard. In particular, we calculate the corrections for non-local bilinears defined in Landau gauge with gauge links excluded. We do this for the simplest operators, i.e. those defined on a $2^4$ hypercube, and for tree level improved operators which live on $4^4$ hypercubes. We also consider gauge invariant operators in which the ``tadpole'' contributions are suppressed by projecting the sums of products of gauge links back in to the gauge group. In all cases, we find that the variation in the size of the perturbative corrections is smaller than those with the gauge invariant unimproved operators. This is most strikingly true for the smeared operators. We investigate the efficacy of the mean-field method of Lepage and Mackenzie at summing up tadpole contributions. In a companion paper we apply these results to four-fermion operators.