Recent progress in calculating weak matrix elements using staggered fermions

TL;DR

This paper reviews recent advances in calculating weak matrix elements with staggered fermions, including perturbative matching, improved techniques, and preliminary results relevant to CP violation.

Contribution

It provides a comprehensive review of progress in weak matrix element calculations using improved staggered fermions, including new one-loop matching formulas and preliminary CP violation results.

Findings

Development of one-loop matching formulas for staggered fermions

Preliminary results on weak matrix elements relevant to CP violation

Construction of lattice operators with complete $g^2$ corrections

Abstract

We present a chronological review of the progress in calculating weak matrix elements using staggered fermions. We review the perturbative calculation of one-loop matching formula including both current-current diagrams and penguin diagrams using improved staggered fermions. We also present preliminary results of weak matrix elements relevant to CP violation calculated using the improved (HYP (II)) staggered fermions. Since the complete set of matching coefficients at the one-loop level became available recently, we have constructed lattice operators with all the $g^2$ corrections included. The main results include both $\Delta I = 3/2$ and $\Delta I = 1/2$ contributions.