Chiral symmetry restoration and axial vector renormalization for Wilson fermions

TL;DR

This paper proves that chiral symmetry restoration in Wilson fermions leads to a unique renormalization constant for the axial vector current, derived from lattice Ward identities and computed at one loop order.

Contribution

It provides a strict all-orders proof that the axial vector flavor mixing current is non-anomalous and determines its renormalization constant from irrelevant operators.

Findings

The renormalization constant is largely independent of lattice realization.

Chiral symmetry restoration implies a unique multiplicative renormalization.

The constant is computed at one loop order.

Abstract

Lattice gauge theories with Wilson fermions break chiral symmetry. In the U(1) axial vector current this manifests itself in the anomaly. On the other hand it is generally expected that the axial vector flavour mixing current is non-anomalous. We give a short, but strict proof of this to all orders of perturbation theory, and show that chiral symmetry restauration implies a unique multiplicative renormalization constant for the current. This constant is determined entirely from an irrelevant operator in the Ward identity. The basic ingredients going into the proof are the lattice Ward identity, charge conjugation symmetry and the power counting theorem. We compute the renormalization constant to one loop order. It is largely independent of the particular lattice realization of the current.