Perturbative calculation of O(a) improvement coefficients

TL;DR

This paper calculates O(a) improvement coefficients perturbatively using the BLM scale setting, compares them to non-perturbative results, and discusses discrepancies likely due to power corrections.

Contribution

It provides perturbative calculations of O(a) improvement coefficients with BLM scale setting and compares them to non-perturbative results, highlighting areas of agreement and discrepancy.

Findings

Normalization factors agree well with non-perturbative results.

Large discrepancies found in O(a) improvement coefficients.

Power corrections likely cause non-perturbative discrepancies.

Abstract

We compute several coefficients needed for O(a) improvement of currents in perturbation theory, using the Brodsky-Lepage-Mackenzie prescription for choosing an optimal scale q*. We then compare the results to non-perturbative calculations. Normalization factors of the vector and axial vector currents show good agreement, especially when allowing for small two-loop effects. On the other hand, there are large discrepancies in the coefficients of O(a) improvement terms. We suspect that they arise primarily from power corrections inherent in the non-perturbative methods.