Light quark masses from lattice quark propagators at large momenta

We compute nonperturbatively the average up-down and strange quark masses from the large momentum (short-distance) behavior of the quark propagator in the Landau gauge. This method, which has never been applied so far, does not require the explicit calculation of the quark mass renormalization constant. Calculations were performed in the quenched approximation, by using $\mathcal{O}(a)$ improved Wilson fermions. The main results of this study are ${m}_{l}^{\mathrm{RI}}(2\mathrm{GeV})=5.8(6)\mathrm{MeV}$ and ${m}_{s}^{\mathrm{RI}}(2\mathrm{GeV})=136(11)\mathrm{MeV}.$ Using the relations between different schemes, obtained from the available four-loop anomalous dimensions, we also find ${m}_{l}^{\mathrm{RGI}}=7.6(8)\mathrm{MeV}$ and ${m}_{s}^{\mathrm{RGI}}=177(14) \mathrm{MeV},$ and the modified minimal subtraction scheme $(\overline{\mathrm{MS}})$ masses ${m}_{l}^{\overline{\mathrm{MS}}}(2 \mathrm{GeV})=4.8(5) \mathrm{MeV}$ and ${m}_{s}^{\overline{\mathrm{MS}}}(2 \mathrm{GeV})=111(9)\mathrm{MeV}.$