Non-perturbative renormalization for a renormalization group improved gauge action

TL;DR

This paper non-perturbatively determines renormalization constants for vector and axial-vector currents in quenched QCD using a renormalization group improved gauge action, revealing smaller values than perturbative estimates and persistent scaling violations.

Contribution

It provides the first non-perturbative calculations of $Z_V$ and $Z_A$ for a specific improved gauge and quark action using the Schrödinger functional method.

Findings

Non-perturbative $Z_V$ and $Z_A$ are about 10% smaller than one-loop perturbative values.

Scaling violations in meson decay constants persist even after non-perturbative renormalization.

Non-perturbative renormalization reduces but does not eliminate discrepancies in decay constants.

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 Schr\"odinger 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 $f_\pi$ and $f_\rho$ observed with the one-loop renormalization factors remains even with non-perturbative renormalization.