Residual chiral symmetry breaking in domain-wall fermions

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 β and the physical volume $V.\mathrm{}$ We measure the mass by calculating the small eigenvalues of the Hermitian domain-wall Dirac operator $\left[H_{\mathrm{DWF}}{(m}_0\right)]$ in the topologically-nontrivial quenched $\mathrm{SU}\left(3\right)\mathrm{}$ 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 β. The effect of the choice of the lattice gluon action is also studied.