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

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