Non–perturbative Renormalization of the Axial Current with Improved Wilson Quarks *

We present a new normalization condition for the axial current, which is derived from the PCAC relation with non–vanishing mass. Using this condition reduces the O(r0m) corrections to the axial current normalization constant ZA for an easier chiral extrapolation in the cases, where simulations at zero quark–mass are not possible. The method described here also serves as a preparation for a determination of ZA in the full two–flavor theory. 1. Introduction Due to the explicit breaking of chiral symmetry in a lattice theory with Wilson quarks a finite renormalization constant Z A for the isovector ax-ial current is needed so that Ward identities take their canonical form up to small lattice corrections. Otherwise a safe extrapolation to the continuum can not be achieved for physical quantities involving this current. The function Z A (g 0) [1] currently used by the ALPHA collaboration was obtained by requiring that certain chiral Ward identities are satisfied in the O(a) on–shell improved lattice theory up to O(a 2) cutoff effects. This normalization condition is evaluated at zero quark mass and hence the mass term in the PCAC relation was dropped. However, even in the framework of the Schrödinger functional simulations at vanishing quark mass are not possible if the physical volume , or equivalently the renormalized coupling, is too large. For the large couplings one therefore evaluates the normalization condition at finite quark mass and extrapolates to the chiral point. Since the mass term was ignored in the derivation of the normalization condition this introduces an error of O(r 0 m) in Z A. The Sommer scale r 0 [2] is used as a typical hadronic scale. Here we present a normalization condition for the axial current, which is derived using the full PCAC relation. This reduces the O(r 0 m) errors in Z A to O(am) and therefore results in a much flatter chiral extrapolation.