Chiral violations in domain-wall QCD from one-loop perturbation theory at finite $N_s$

TL;DR

This paper investigates chiral symmetry violations in domain-wall QCD with finite fifth-dimensional extent using one-loop perturbation theory, analyzing residual mass, operator renormalization, and mixing effects.

Contribution

It provides a detailed perturbative analysis of chiral violations at finite N_s, including residual mass and operator mixing, which are crucial for lattice QCD simulations.

Findings

Residual mass approaches zero quickly with increasing N_s

Chiral violations depend on N_s and M, with larger N_s reducing violations

Gauge invariance and anomalous dimensions are affected by finite N_s

Abstract

We present perturbative calculations made with domain-wall fermions which possess a finite number of points $N_s$ in the extra fifth dimension. We have derived the required propagator functions, investigated the one-loop properties of quark amplitudes at finite $N_s$ 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 $N_s$ 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 $g_0$. 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 $N_s$ is suppressed only partially) of an operator which describes the lowest moment of the $g_2$ structure function. In general we see that at $M=1.8$, where simulations are usually performed, values of $N_s=20$ or larger would be desirable in order for chiral violations to be negligible. The quantities that we have studied turn out to lose gauge invariance when $N_s$ is not infinite. We have also found that anomalous dimensions of operators at finite $N_s$ generally depend on $N_s$ and $M$. In particular, the vector and axial-vector currents have in general a nonzero anomalous dimension at finite $N_s$.