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 $\mathrm{m̂}$ using full lattice QCD with three dynamical quarks combined with the experimental values for the $\pi$ and K masses. The simulations have degenerate u and d quarks with masses $m_u{=m}_d\equiv \mathrm{m̂}$ 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 $\mathcal{O}\left({\alpha }_S\right).\mathrm{}$ Our results are $m_s^{\overline{\mathrm{MS}}}\left(2\mathrm{}\mathrm{GeV}\right)=76\mathrm{}\left(0\right)\mathrm{}\left(3\right)\mathrm{}\left(7\right)\mathrm{}\left(0\right)\mathrm{}\mathrm{MeV},$ $m^{\overline{\mathrm{MS}}}\left(2\mathrm{}\mathrm{GeV}\right)=2.8\mathrm{}\left(0\right)\mathrm{}\left(1\right)\mathrm{}\left(3\right)\mathrm{}\left(0\right)\mathrm{}$ MeV, and $m_s/\mathrm{m̂}=27.4\mathrm{}\left(1\right)\mathrm{}\left(4\right)\mathrm{}\left(0\right)\mathrm{}\left(1\right),$ where the errors are from statistics, simulation, perturbation theory, and electromagnetic effects, respectively.