A nonperturbative determination of cA

TL;DR

This paper presents a non-perturbative method to determine the axial current improvement coefficient c_A using correlators and derivative order adjustments, revealing dependencies and convergence towards perturbative values.

Contribution

The authors introduce a non-perturbative approach to calculate c_A that accounts for derivative order effects, improving consistency across momentum cases.

Findings

c_A depends strongly on derivative order used

Lower order derivatives yield inconsistent c_A values

Improved derivatives lead to consistent, perturbative-like c_A values

Abstract

We describe a non-perturbative determination of $c_A$ using correlators containing the axial-vector and pseudoscalar currents at zero and non-zero momentum. We apply the method of Bhattacharya et al to extract $c_A$ from the requirement that the ratio of appropriate correlators for the PCAC relation becomes independent of time in the excited state region. We find that the result depends strongly on the order of the derivatives used in the PCAC relation. We also find that, using the lowest order derivatives, we cannot get a consistent value of $c_A$ between zero and non-zero momentum cases. The $c_A$ values that we obtain as we improve the derivatives are consistent and decrease in magnitude heading towards the perturbative result.