Improved bilinears in lattice QCD with non-degenerate quarks

TL;DR

This paper extends the improvement program for bilinear operators in lattice QCD with Wilson fermions to non-degenerate quarks, analyzing the number of coefficients and their determination across different flavor configurations.

Contribution

It provides a systematic extension of the improvement program to non-degenerate quarks and discusses how to determine the coefficients using Ward identities.

Findings

More improvement coefficients are needed for non-degenerate quarks.

Nearly all coefficients can be determined for three or four flavors.

Many coefficients remain undetermined for two flavors.

Abstract

We describe the extension of the improvement program for bilinear operators composed of Wilson fermions to non-degenerate dynamical quarks. We consider two, three and four flavors, and both flavor non-singlet and singlet operators. We find that there are many more improvement coefficients than with degenerate quarks, but that, for three or four flavors, nearly all can be determined by enforcing vector and axial Ward identities. The situation is worse for two flavors, where many more coefficients remain undetermined.