A nonperturbative determination of the O(a) improvement coefficient c_A and the scaling of f_pi and m^{MSbar}

TL;DR

This paper nonperturbatively determines the O(a) improvement coefficient c_A using the LANL method, analyzing systematic errors, and compares results with previous studies and perturbation theory, impacting the scaling of f_pi and m^{MSbar}.

Contribution

It provides a reliable nonperturbative estimate of c_A and examines the effects of systematic errors and method differences on lattice QCD results.

Findings

Reliable estimates of c_A can be extracted with proper tuning.

Systematic errors affect the accuracy of c_A determination.

Using their c_A values reduces lattice spacing dependence of f_pi and m^{MSbar}.

Abstract

We report on an investigation of the LANL method for determining the O(a) improvement coefficient c_A nonperturbatively. We find we are able to extract reliable estimates for the coefficient using this method. However, our study of systematic errors shows that for very accurate determinations of c_A, the smearing function must be tuned and the volume fixed to keep the O(a) ambiguity in c_A fixed as beta varies. Consistency was found with previous results from the LANL group and (within fairly large errors) 1-loop perturbation theory; c_A does not change significantly over the range beta=5.93-6.2. The big difference between our results and those of the ALPHA collaboration, around beta=6.0, show that the O(a) differences in c_A between the different methods can be large. We find that the lattice spacing dependence of f_pi and the renormalised quark mass is much smaller using our values of the coefficient compared to those of the ALPHA collaboration.