First determination of the strange and light quark masses from full lattice QCD

We compute the strange quark mass ${m}_{s}$ and the average of the u and d quark masses $\mathrm{m\ifmmode \hat{}\else \^{}\fi{}}$ using full lattice QCD with three dynamical quarks combined with the experimental values for the $\ensuremath{\pi}$ and K masses. The simulations have degenerate u and d quarks with masses ${m}_{u}{=m}_{d}\ensuremath{\equiv}\mathrm{m\ifmmode \hat{}\else \^{}\fi{}}$ as low as ${m}_{s}/8,$ and two different values of the lattice spacing. The bare lattice quark masses obtained are converted to the $\overline{\mathrm{MS}}$ scheme using perturbation theory at $\mathcal{O}({\ensuremath{\alpha}}_{S}).$ Our results are ${m}_{s}^{\overline{\mathrm{MS}}}(2\mathrm{GeV})=76(0)(3)(7)(0)\mathrm{MeV},$ ${m}^{\overline{\mathrm{MS}}}(2\mathrm{GeV})=2.8(0)(1)(3)(0)$ MeV, and ${m}_{s}/\mathrm{m\ifmmode \hat{}\else \^{}\fi{}}=27.4(1)(4)(0)(1),$ where the errors are from statistics, simulation, perturbation theory, and electromagnetic effects, respectively.