A Perturbative Determination of Mass Dependent $O(a)$ Improvement Coefficients in a Relativistic Heavy Quark Action

TL;DR

This paper calculates mass-dependent improvement coefficients for a relativistic heavy quark action to reduce discretization errors in lattice QCD simulations involving heavy quarks.

Contribution

It provides a perturbative method to determine key improvement coefficients for heavy quark actions, extending on-shell $O(a)$ improvement to large quark masses.

Findings

Coefficients are free from infrared divergences after proper tuning.

Parameters are computed as functions of $m_Q a$ for various gauge actions.

Results help improve accuracy in heavy quark lattice simulations.

Abstract

We present the results for a perturbative determination of mass dependent improvement coefficients $\nu$, $r_s$, $c_E$ and $c_B$ in 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 $m_Q \gg \Lambda_{\rm QCD}$, where $m_Q$ is the heavy quark mass. The parameters $\nu$ and $r_s$ are determined from the quark propagator and $c_E$ and $c_B$ are from the on-shell quark-quark scattering amplitude. We show that all the parameters, together with the quark wave function and the mass renormalization factors, are determined free from infrared divergences once their tree level values are properly tuned. Results of these parameters are shown as a function of $m_Q a$ for various improved gauge actions.