  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.
