Lattice artifacts proportional to the quark mass in the QCD running coupling

TL;DR

This paper analyzes and computes two-loop renormalization factors to correct lattice artifacts proportional to quark mass, enhancing the precision of strong-coupling measurements in lattice QCD with heavy quarks.

Contribution

It provides a perturbative calculation of mass-dependent lattice artifacts and improvement coefficients for Wilson fermions, enabling more accurate renormalization schemes in lattice QCD.

Findings

Derived two-loop renormalization factors for mass-dependent effects.

Provided numerical values for common gauge actions.

Ensured symmetry and consistency in the results.

Abstract

Discretization artifacts proportional to the quark mass can limit the precision of strong-coupling determinations in lattice QCD, especially in the presence of heavy quarks. In this work, we perform a lattice perturbative analysis of such $\mathcal{O}(a m)$ effects in the running coupling by computing its two-loop renormalization factor $Z_g$. Using the background field method together with clover-improved Wilson fermions and Symanzik-improved gauge actions, we determine the mass-dependent components of the relevant two-point Green's functions and obtain the improvement coefficients needed to remove $\mathcal{O}(a m)$ artifacts in mass-independent renormalization schemes. Our results are presented for general values of the number of colors $N_c$, the number of quark flavors $N_f$, and the clover coefficient $c_{\mathrm sw}$, and satisfy all symmetry and consistency constraints. Numerical values are provided for widely used instances of the above gauge actions, allowing improved control of mass-related cutoff effects in high-precision determinations of the strong coupling constant from lattice QCD. Full derivations and extended numerical results can be found in Ref. [arXiv:2503.00463].