Non-perturbative renormalization for a renormalization group improved gauge action

Abstract

Renormalization constants of vector ($Z_V$) and axial-vector ($Z_A$) currents are determined non-perturbatively in quenched QCD for a renormalization group improved gauge action and a tadpole improved clover quark action using the Schrödinger functional method. Non-perturbative values of $Z_V$ and $Z_A$ turn out to be smaller than the one-loop perturbative values by $O(10$ at $a^{-1}\approx 1$ GeV. A sizable scaling violation of meson decay constants $f_{\ddot{I}}€$ and $f_{\ddot{I}}$ observed with the one-loop renormalization factors remains even with non-perturbative renormalization.

Lattice2001(improvement), 3 pages, 7 figures