Perturbative chiral violations for domain-wall QCD with improved gauge actions

TL;DR

This paper studies how improved gauge actions in domain-wall QCD reduce chiral violations, finding significant residual mass suppression with certain actions, but limited effects on some renormalization constants, and highlights limitations of one-loop perturbation theory.

Contribution

It demonstrates that improved gauge actions can substantially reduce chiral violations in domain-wall fermions, especially the residual mass, through perturbative calculations.

Findings

Significant reduction in residual mass with DBW2 action.

Chiral suppression observed in power-divergent mixing coefficients.

One-loop perturbation theory often overestimates chiral violations.

Abstract

We investigate, in the framework of perturbation theory at finite $N_s$, the effectiveness of improved gauge actions in suppressing the chiral violations of domain-wall fermions. Our calculations show substantial reductions of the residual mass when it is compared at the same value of the gauge coupling, the largest suppression being obtained when the DBW2 action is used. Similar effects can also be observed for a power-divergent mixing coefficient which is chirally suppressed. No significant reduction instead can be seen in the case of the difference between the vector and axial-vector renormalization constants when improved gauge actions are used in place of the plaquette action. We also find that one-loop perturbation theory is not an adequate tool to carry out comparisons at the same energy scale (of about 2 GeV), and in fact in this case even an enhancement of the chiral violations is frequently obtained.