Renormalization constants using quark states in Landau gauge

TL;DR

This paper presents a method to determine renormalization constants for quark bilinear operators in Landau gauge by analyzing matrix elements between external quark states, given one improvement constant.

Contribution

It introduces a technique to derive all necessary renormalization constants from a single known improvement constant using external quark states in a fixed gauge.

Findings

All renormalization constants can be obtained from one known constant.

The method simplifies the process of renormalization in lattice QCD.

It provides a practical approach for O(a) improvement of quark bilinears.

Abstract

We show that given one O(a) improvement constant, b_m, all the remaining quantities needed to define the renormalized and O(a) improved dimension-3 quark bilinears can be obtained by studying the matrix elements of these operators between external quark states in a fixed gauge.