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

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.