Perturbative Determination of Mass Dependent $O(a)$ Improvement Coefficients for the Vector and Axial Vector Currents with a Relativistic Heavy Quark Action

TL;DR

This paper computes mass-dependent renormalization and improvement coefficients for vector and axial vector currents in a relativistic heavy quark framework, extending on-shell $O(a)$ improvement to large quark masses.

Contribution

It provides the first perturbative calculation of $O(a)$ improvement coefficients for heavy quark currents accounting for large $m_Qa$ effects, including various gauge actions.

Findings

All coefficients are free from infrared divergences.

Results are provided as functions of $m_Qa$ for different gauge actions.

The method extends on-shell $O(a)$ improvement to heavy quark masses.

Abstract

We carry out a perturbative determination of mass dependent renormalization factors and $O(a)$ improvement coefficients for the vector and axial vector currents with a relativistic heavy quark action, which we have designed to control $m_Qa$ errors by extending the on-shell $O(a)$ improvement program to the case of $m_Q \gg \Lambda_{\rm QCD}$ with $m_Q$ the heavy quark mass. We discuss what kind of improvement operators are required for the heavy-heavy and the heavy-light cases under the condition that the Euclidean rotational symmetry is not retained anymore because of the $m_Qa$ corrections. Our calculation is performed employing the ordinary perturbation theory with the fictitious gluon mass as an infrared regulator. We show that all the improvement coefficients are determined free from infrared divergences. Results of the renormalization factors and the improvement coefficients are presented as a function of $m_Q a$ for various improved gauge actions as well as the plaquette action.