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

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 $Z_V\simeq Z_A$ 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.