Chiral symmetry restoration and axial vector renormalization for Wilson   fermions
  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. 
T. Reisz and H. J. Rothe