One-loop calculation of mass dependent ${\cal O}(a)$ improvement coefficients for the relativistic heavy quarks on the lattice

TL;DR

This paper performs a one-loop perturbative calculation of mass-dependent ${ m O}(a)$ improvement coefficients for relativistic heavy quarks on the lattice, including renormalization factors for the axial-vector current, ensuring infrared finiteness with proper tuning.

Contribution

It provides the first one-loop calculation of mass-dependent ${ m O}(a)$ improvement coefficients for the relativistic heavy quark action on the lattice, including axial-vector current renormalization.

Findings

Improvement coefficients are infrared finite with proper tree-level tuning.

Calculated renormalization factors for axial-vector current at one-loop.

Validated the necessity of proper tuning for infrared finiteness.

Abstract

We carry out the one-loop calculation of mass dependent ${\cal O}(a)$ improvement coefficients in the relativistic heavy quark action recently proposed, employing the ordinary perturbation theory with the fictitious gluon mass as an infrared regulator. We also determine renormalization factors and improvement coefficients for the axial-vector current at the one-loop level. It is shown that the improvement coefficients are infrared finite at the one-loop level if and only if the improvement coefficients in the action are properly tuned at the tree level.