Chiral Symmetry and the Residual Mass in Lattice QCD with the Optimal Domain-Wall Fermion

TL;DR

This paper derives the axial Ward identity for lattice QCD with domain-wall fermions, providing a formula and bounds for the residual mass, which measures chiral symmetry breaking due to finite fifth dimension extension.

Contribution

It introduces a new formula for the residual mass and establishes an upper bound for chiral symmetry breaking in optimal domain-wall fermion lattice QCD.

Findings

Derived the axial Ward identity for domain-wall fermions

Provided a formula to measure residual mass

Established an upper bound for residual mass

Abstract

We derive the axial Ward identity for lattice QCD with domain-wall fermions, and from which we obtain a formula for the residual mass (45)-(46), that can be used to measure the chiral symmetry breaking due to the finite extension Ns in the fifth dimension. Furthermore, we obtain an upper bound for the residual mass in lattice QCD with the optimal domain-wall fermion.