Nonperturbative renormalization of meson decay constants in quenched QCD for a renormalization group improved gauge action

Renormalization constants (Z-factors ) of vector and axial-vector currents are determined nonperturbatively in quenched QCD for a renormalization group improved gauge action and a tadpole-improved clover quark action using the Schroedinger functional method. Nonperturbative values of Z-factors turn out to be smaller than 1-loop perturbative values by O(15%) at a lattice spacing of a{sup -1}{approx_equal} 1 GeV. The pseudoscalar and vector meson decay constants calculated with the nonperturbative Z-factors show a much better scaling behavior compared to previous results obtained with tadpole-improved one-loop Z-factors. In particular, the nonperturbative Z-factors normalized at infinite physical volume show that the scaling violations of the decay constants are within about 10% up to the lattice spacing a{sup -1}{approx}1 GeV. The continuum estimates obtained from data in the range a{sup -1}{approx} 1-2 GeV agree with those determined from finer lattices (a{sup -1}{approx}2-4 GeV) with the standard action.