Effect of r averaging on Chiral Anomaly in Lattice QCD with Wilson Fermion: Finite volume and cutoff effects

TL;DR

This paper investigates how averaging over the Wilson parameter r reduces cutoff effects in lattice QCD calculations of the chiral anomaly, especially in the pseudoscalar density term, across various volumes and fermion masses.

Contribution

It demonstrates that r averaging effectively removes cutoff effects in the anomaly and pseudoscalar density terms for Wilson fermions, improving agreement with continuum results.

Findings

r averaging reduces cutoff effects in anomaly calculations

Pseudoscalar density term becomes am-independent with r averaging

Finite volume effects are mitigated by r averaging in Wilson fermions

Abstract

We demonstrate the effectiveness of averaging over the Wilson parameter r (which has been proposed earlier) in removing the cutoff effects of naive Wilson fermions in both the anomaly term and the pseudoscalar density term in the flavor singlet axial Ward identity at O(g^2) involving slowly varying background gauge fields. We show that it is the physical fermion contribution which is largely influenced by the r averaging. We have studied the possible interplay between finite size and cutoff effects by investigating in detail naive, O(a) improved and OStm Wilson fermion cases for a range of volumes and lattice fermion mass (am). For naive Wilson fermions r averaging is shown to remove the effects of the interplay. We have shown that for the pseudoscalar density term to O (g^2) the lattice result differs from the continuum result by exhibiting considerable am dependence which appears to be a manifestation of cutoff effects with naive Wilson fermion. The pseudoscalar density term to O(g^2) is shown to be almost independent of am when r-averaging is performed.