Improving the lattice axial vector current

TL;DR

This paper proposes a point-split axial vector current for Wilson and clover fermions that exactly satisfies the lattice Ward identity, improving the consistency between lattice and continuum formulations.

Contribution

It introduces a new lattice axial vector current that respects the Ward identity exactly, including order $O(a)$ effects, and verifies this through perturbative and preliminary nonperturbative checks.

Findings

The point-split current satisfies the lattice Ward identity at one-loop order.

Including irrelevant operators maintains renormalisation invariance of the Ward identity.

Preliminary nonperturbative results support the theoretical findings.

Abstract

For Wilson and clover fermions traditional formulations of the axial vector current do not respect the continuum Ward identity which relates the divergence of that current to the pseudoscalar density. Here we propose to use a point-split or one-link axial vector current whose divergence exactly satisfies a lattice Ward identity, involving the pseudoscalar density and a number of irrelevant operators. We check in one-loop lattice perturbation theory with SLiNC fermion and gauge plaquette action that this is indeed the case including order $O(a)$ effects. Including these operators the axial Ward identity remains renormalisation invariant. First preliminary results of a nonperturbative check of the Ward identity are also presented.