Non-perturbative renormalization of meson decay constants in quenched QCD for a renormalization group improved gauge action

TL;DR

This paper non-perturbatively determines renormalization constants for meson decay constants in quenched QCD using a renormalization group improved gauge action, leading to improved scaling behavior and more accurate continuum estimates.

Contribution

It provides the first non-perturbative calculation of Z-factors for vector and axial-vector currents in quenched QCD with a renormalization group improved gauge action, improving the accuracy of decay constant determinations.

Findings

Non-perturbative Z-factors are about 15% smaller than one-loop perturbative values.

Decay constants show better scaling with non-perturbative Z-factors.

Scaling violations are within 10% up to 1 GeV lattice spacing.

Abstract

Renormalization constants ($Z$-factors) of vector and axial-vector 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 $Z$-factors turn out to be smaller than one-loop perturbative values by $O(15%)$ at lattice spacing of $a^{-1}\approx$ 1 GeV. The pseudoscalar and vector meson decay constants calculated with the non-perturbative $Z$-factors show a much better scaling behavior compared to previous results obtained with tadpole improved one-loop $Z$-factors. In particular, the non-perturbative $Z$-factors normalized at infinite physical volume show that scaling violation of the decay constants are within about 10% up to the lattice spacing $a^{-1}\sim 1$ GeV. The continuum estimates obtained from data in the range $a^{-1}=$ 1 -- 2 GeV agree with those determined from finer lattices ($a^{-1}\sim 2-4$ GeV) with the standard action.