Residual Chiral Symmetry Breaking in Domain-Wall Fermions

TL;DR

This paper investigates how the effective quark mass in domain-wall fermions depends on the fifth dimension size, gauge coupling, and volume, revealing exponential decay with fifth dimension and dependence on quantum fluctuations.

Contribution

It provides a detailed analysis of residual chiral symmetry breaking in domain-wall fermions, including effects of gauge coupling, volume, and gluon action choices.

Findings

Residual mass is nearly volume-independent.

Mass decays exponentially with fifth dimension size.

Quantum fluctuations significantly influence residual mass.

Abstract

We study the effective quark mass induced by the finite separation of the domain walls in the domain-wall formulation of chiral fermion as the function of the size of the fifth dimension ($L_s$), the gauge coupling $\beta$ and the physical volume $V$. We measure the mass by calculating the small eigenvalues of the hermitian domain-wall Dirac operator ($H_{\rm DWF}(m_0))$ in the topologically-nontrivial quenched SU(3) gauge configurations. We find that the induced quark mass is nearly independent of the physical volume, decays exponentially as a function of $L_s$, and has a strong dependence on the size of quantum fluctuations controlled by $\beta$. The effect of the choice of the lattice gluon action is also studied.