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, Zv and ZA, 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≃ZA in DWQCD. Employing two different box sizes for the numerical simulations at several values of the gauge coupling constant g2 and the domain-wall height M, we extrapolate Zv to infinite volume to remove a/L errors. We finally give the interpolation formula of ZV in the infinite volume as a function of g2 and M.