Current Renormalisation Constants with an O(a)-improved Fermion Action

TL;DR

This paper accurately determines the renormalisation constants of bilinear quark operators using chiral Ward identities for an improved lattice action, highlighting discrepancies with perturbative predictions and implications for meson decay constants.

Contribution

It provides non-perturbative calculations of renormalisation constants for the Sheikholeslami-Wohlert lattice action at beta=6.2, with improved accuracy and comparison to perturbative results.

Findings

Z_V close to perturbative value of 0.83

Z_A significantly higher than perturbative estimate

Reduces discrepancy in pseudoscalar meson decay constants

Abstract

Using chiral Ward identities, we determine the renormalisation constants of bilinear quark operators for the Sheikholeslami-Wohlert action lattice at beta=6.2. The results are obtained with a high degree of accuracy. For the vector current renormalisation constant we obtain Z_V=0.817(2)(8), where the first error is statistical and the second is due to mass dependence of Z_V. This is close to the perturbative value of 0.83. For the axial current renormalisation constant we obtain Z_A = 1.045(+10 -14), significantly higher than the value obtained in perturbation theory. This is shown to reduce the difference between lattice estimates and the experimental values for the pseudoscalar meson decay constants, but a significant discrepancy remains. The ratio of pseudoscalar to scalar renormalisation constants, Z_P/Z_S, is less well determined, but seems to be slightly lower than the perturbative value.