Perturbative matching of staggered four-fermion operators with hypercubic fat links

TL;DR

This paper computes one-loop matching coefficients for staggered four-fermion operators with fat links, reducing large perturbative corrections and improving the accuracy of lattice QCD calculations.

Contribution

It provides the first detailed calculation of one-loop matching coefficients for improved staggered fermion operators with hypercubic fat links, including numerical results.

Findings

One-loop corrections are reduced to 10-20%.

Results apply to operators with pseudo-Goldstone pion taste.

The approach resolves large perturbative correction issues.

Abstract

We calculate the one-loop matching coefficients between continuum and lattice four-fermion operators for lattice operators constructed using staggered fermions and improved by the use of fattened links. In particular, we consider hypercubic fat links and SU(3) projected Fat-7 links, and their mean-field improved versions. We calculate only current-current diagrams, so that our results apply for operators whose flavor structure does not allow ``eye-diagrams''. We present general formulae, based on two independent approaches, and give numerical results for the cases in which the operators have the taste (staggered flavor) of the pseudo-Goldstone pion. We find that the one-loop corrections are reduced down to the 10-20% level, resolving the problem of large perturbative corrections for staggered fermion calculations of matrix elements.