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 (L-s) induces an effective quark mass (m(eff)) which complicates the chiral limit. In this work, we study the size of the effective mas as the function of L-s and the domain-wall height mo 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.