Effect of r averaging on chiral anomaly in lattice QCD with Wilson fermion: finite volume and cutoff effects

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 Takahashi identity at $\mathcal{O}\left( {{g^2}} \right)$ 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, $\mathcal{O}(a)$ 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 $\mathcal{O}\left( {{g^2}} \right)$ 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 $\mathcal{O}\left( {{g^2}} \right)$ is shown to be almost independent of am when r-averaging is performed.