Calculations of the quark masses and smallest eigenvalues of Wilson-Dirac operator in domain-wall formalism

In the domain-wall formulation of chiral fermion, the finite separation between domain-walls (Ls) induces an effective quark mass (meff) which complicates the chiral limit. In this work, we study the size of the effective mass as the function of Ls and the domain-wall height m0 by calculating the smallest eigenvalue of the hermitian domain-wall Dirac operator in the topologically-nontrivial background fields. Our numerical result is consistent with a previous study of the effective mass from the GMOR relation