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We determine the charm and strange quark masses in the MS scheme, using n f = 2 + 1 + 1 lattice QCD calculations with highly improved staggered quarks (HISQ) and the RI-SMOM intermediate scheme to connect the bare lattice quark masses to continuum renormalisation schemes. Our study covers analysis of systematic uncertainties from this method, including nonperturbative artefacts and the impact of the non-zero physical sea quark masses. We find m MS c (3 GeV) = 0.9896(61) GeV and m MS s (3 GeV) = 0.08536(85) GeV, where the uncertainties are dominated by the tuning of the bare lattice quark masses. These results are consistent with, and of similar accuracy to, those using the current-current correlator approach coupled to high-order continuum QCD perturbation theory, implemented in the same quark formalism and on the same gauge field configurations. This provides a strong test of the consistency of methods for determining the quark masses to high precision from lattice QCD. We also give updated lattice QCD world averages for c and s quark masses.arXiv:1805.06225v1 [hep-lat]

We have performed the first n f ¼ 2 þ 1 þ 1 lattice QCD computations of the properties (masses and decay constants) of ground-state charmonium mesons. Our calculation uses the Highly Improved Staggered Quark (HISQ) action to generate quark-line connected two-point correlation functions on MILC gluon field configurations that include u=d quark masses going down to the physical point, tuning the c-quark mass from M J=ψ and including the effect of the c quark's electric charge through quenched QED. We obtain M J=ψ − M η c ðconnectedÞ ¼ 120.3ð1.1Þ MeV and interpret the difference with experiment as the impact on M η c of the η c decay to gluons, missing from the lattice calculation. This allows us to determine ΔM annihiln η c ¼ þ7.3ð1.2Þ MeV, giving its value for the first time. Our result of f J=ψ ¼ 0.4104ð17Þ GeV gives ΓðJ=ψ → e þ e − Þ ¼ 5.637ð49Þ keV, in agreement with, but now more accurate than, experiment. At the same time we have improved the determination of the c-quark mass, including the impact of quenched QED to givem c ð3 GeVÞ ¼ 0.9841ð51Þ GeV. We have also used the time moments of the vector charmonium current-current correlators to improve the lattice QCD result for the c quark hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon. We obtain a c μ ¼ 14.638ð47Þ × 10 −10 , which is 2.5σ higher than the value derived using moments extracted from some sets of experimental data on Rðe þ e − → hadronsÞ. This value for a c μ includes our determination of the effect of QED on this quantity, δa c μ ¼ 0.0313ð28Þ × 10 −10 .