Precise MS-bar light-quark masses from lattice QCD in the RI/SMOM scheme

Abstract

We compute the conversion factors needed to obtain the MS-bar and RGI up, down, and strange-quark masses at next-to-next-to-leading order from the corresponding parameters renormalized in the recently proposed RI/SMOM and RI/SMOM_gamma_mu renormalization schemes. This is important for obtaining the MS-bar masses with the best possible precision from numerical lattice-QCD simulations, because the customary RI(')/MOM scheme is afflicted with large irreducible uncertainties both on the lattice and in perturbation theory. We find that the smallness of the known one-loop matching coefficients is accompanied by even smaller two-loop contributions. From a study of residual scale dependences, we estimate the resulting perturbative uncertainty on the light-quark masses to be about 2% in the RI/SMOM scheme and about 3% in the RI/SMOM_gamma_mu scheme. Our conversion factors are given in fully analytic form, for general covariant gauge and renormalization point. We provide expressions for the associated anomalous dimensions.

arXiv commentAdded results for the RI/SMOM_gamma_mu scheme and anomalous dimensions; typos fixed (results unchanged); added references

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