Nonperturbative calculation of ZV and ZA in domain-wall QCD on a finite box

Abstract

We report on a nonperturbative evaluation of the renormalization factors for the vector and axial-vector currents, ${Z}_{V}$ and ${Z}_{A},$ in the quenched domain-wall QCD (DWQCD) with plaquette and renormalization-group-improved gauge actions. We take the Dirichlet boundary condition for both gauge and domain-wall fermion fields on the finite box, and introduce flavor-chiral Ward-Takahashi identities to calculate the renormalization factors. As a test of the method, we numerically confirm the expected relation that ${Z}_{V}\ensuremath{\simeq}{Z}_{A}$ in DWQCD. Employing two different box sizes for the numerical simulations at several values of the gauge coupling constant ${g}^{2}$ and the domain-wall height M, we extrapolate ${Z}_{V}$ to infinite volume to remove $a/L$ errors. We finally give the interpolation formula of ${Z}_{V}$ in the infinite volume as a function of ${g}^{2}$ and M.