One loop matching factors for improved staggered four-fermion operators with improved glue

TL;DR

This paper calculates one-loop matching factors for HYP-smeared staggered four-fermion operators using Symanzik-improved gauge action, enhancing precision in weak matrix element computations on MILC lattices.

Contribution

It introduces the use of Symanzik-improved gauge action for calculating matching factors, providing explicit results for B_K operator and comparing improvements over previous methods.

Findings

Symanzik-improved gauge action reduces one-loop coefficient corrections.

Explicit matching factors for B_K operator are provided.

Comparison shows improved gauge action benefits over mean-field improvement.

Abstract

We present results for matching factors for staggered four-fermion operators constructed using HYP-smeared fat links both in the action and the operators. We use perturbation theory to calculate the matching factors and work to one-loop order. The new feaure of this work is the use of the Symanzik-improved gauge action, as opposed to the Wilson gauge action. Our results are needed for our ongoing calculation of weak matrix elements using HYP-smeared staggered valence quarks and operators on MILC lattices. We give explicit results for matching factors of the operator needed to calculate $B_K$. We compare the impact of the improvement of the gauge action on one-loop coefficients with that of mean-field improvement of the operators.