Eigenvalues of the hermitian Wilson-Dirac operator and chiral properties of the domain-wall fermion

TL;DR

This paper investigates the chiral properties of domain-wall QCD by analyzing the eigenvalues of the hermitian Wilson-Dirac operator and comparing them with the anomalous quark mass, using numerical simulations with different gauge actions.

Contribution

It provides new insights into the spectral properties of the Wilson-Dirac operator and their relation to chiral symmetry breaking in domain-wall fermions.

Findings

Density of zero eigenvalues measured and compared with anomalous quark mass.

Results show correlation between eigenvalue spectrum and chiral symmetry properties.

Comparison between different gauge actions highlights their impact on chiral behavior.

Abstract

Chiral properties of QCD formulated with the domain-wall fermion (DWQCD) are studied using the anomalous quark mass m_{5q} and the spectrum of the 4-dimensional Wilson-Dirac operator. Numerical simulations are made with the standard plaquette gauge action and a renormalization-group improved gauge action. Results are reported on the density of zero eigenvalue obtained with the accumulation method, and a comparison is made with the results for m_{5q}.