Perturbative Matching of the staggered four-fermion operators for e'/e

TL;DR

This paper computes one-loop perturbative corrections for staggered fermion operators used in weak matrix element calculations, enabling precise matching between continuum and lattice formulations.

Contribution

It provides the complete one-loop renormalization of staggered four-fermion operators, including matching coefficients in the NDR scheme, which was previously incomplete.

Findings

Calculated one-loop matching coefficients for staggered fermion operators.

Provided the full one-loop renormalization including penguin diagrams.

Enabled more accurate lattice QCD computations of weak decay parameters.

Abstract

Using staggered fermions, we calculate the perturbative corrections to the bilinear and four-fermion operators that are used in the numerical study of weak matrix elements for $\epsilon'/\epsilon$. We present results for one-loop matching coefficients between continuum operators, calculated in the Naive Dimensional Regularization (NDR) scheme, and gauge invariant staggered fermion operators. These results, combined with existing results for penguin diagrams, provide the complete one-loop renormalization of the staggered four-fermion operators.