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 $L_s$ and sensitivity to quantum fluctuations.

Contribution

It provides a detailed analysis of residual chiral symmetry breaking in domain-wall fermions, highlighting the dependence on $L_s$, $eta$, and the gluon action.

Findings

Residual mass decays exponentially with $L_s$

Nearly independent of physical volume

Strong dependence on gauge coupling $eta$

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 ($H_{\rm DWF}(m_0=1.8))$ 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.