Chiral violations in domain-wall QCD from one-loop perturbation theory at finiteNs

Abstract

We present perturbative calculations made with domain-wall fermions which possess a finite number of points N{sub s} in the extra fifth dimension. We have derived the required propagator functions, investigated the one-loop properties of quark amplitudes at finite N{sub s}, and evaluated three quantities that can provide insights on chirality-breaking effects from the perturbative side. First we have computed the residual mass for various choices of N{sub s} and of the domain-wall height M. We have found that this radiatively induced mass approaches zero reasonably fast with the extent of the fifth dimension, depending on M and on a lesser extent on the coupling g{sub 0}. We have also computed the differences of the renormalization constants of the vector and axial-vector currents and of the scalar and pseudoscalar densities. Finally we have calculated the chirally forbidden mixing (which at finite N{sub s} is suppressed only partially) of an operator which describes the lowest moment of the g{sub 2} structure function. The quantities that we have studied turn out to lose gauge invariance when N{sub s} is not infinite. We have also found that anomalous dimensions of operators at finite N{sub s} generally depend on N{sub s} and M. In particular,more » the vector and axial-vector currents have in general a nonzero anomalous dimension at finite N{sub s}.« less