Two-loop matching factors for light quark masses and three-loop mass anomalous dimensions in the RI/SMOM schemes

TL;DR

This paper computes two-loop corrections and three-loop anomalous dimensions for light quark mass schemes, improving the precision of quark mass determinations by reducing systematic uncertainties in lattice QCD calculations.

Contribution

It provides the first two-loop matching factors and three-loop anomalous dimensions for RI/SMOM schemes, enhancing the accuracy of quark mass conversions from lattice to continuum schemes.

Findings

Two-loop matching coefficients are about 0.6-2% of leading order.

Results enable significant reduction of systematic uncertainties.

Provides tensor operator results as a by-product.

Abstract

Light quark masses can be determined through lattice simulations in regularization invariant momentum-subtraction(RI/MOM) schemes. Subsequently, matching factors, computed in continuum perturbation theory, are used in order to convert these quark masses from a RI/MOM scheme to the MS-bar scheme. We calculate the two-loop corrections in quantum chromodynamics(QCD) to these matching factors as well as the three-loop mass anomalous dimensions for the RI/SMOM and RI/SMOM_gamma_mu schemes. These two schemes are characterized by a symmetric subtraction point. Providing the conversion factors in the two different schemes allows for a better understanding of the systematic uncertainties. The two-loop expansion coefficients of the matching factors for both schemes turn out to be small compared to the traditional RI/MOM schemes. For nf=3 quark flavors they are about 0.6-0.7% and 2%, respectively, of the leading order result at scales of about 2 GeV. Therefore, they will allow for a significant reduction of the systematic uncertainty of light quark mass determinations obtained through this approach. The determination of these matching factors requires the computation of amputated Green's functions with the insertions of quark bilinear operators. As a by-product of our calculation we also provide the corresponding results for the tensor operator.