Charmonium properties from lattice QCD+QED : Hyperfine splitting, J/ψ leptonic width, charm quark mass, and aμc

We have performed the first n f = 2 + 1 + 1 lattice QCD computations of the properties (masses and decay constants) of ground-state charmonium mesons. Our calculation uses the 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 (connected) = 120.3(1.1) MeV and interpret the difference with experiment as the impact on M η c of its decay to gluons, missing from the lattice calculation. This allows us to determine Δ M a n n i h i l n η c =+7.3(1.2) MeV, giving its value for the first time. Our result of f J / ψ = 0.4104(17) GeV, gives Γ ( J / ψ → e + e − ) =5.637(49) 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 give m c ( 3 G e V ) = 0.9841(51) 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 HVP contribution to the anomalous magnetic moment of the muon. We obtain a c μ = 14.638 ( 47 ) × 10 − 10 , which is 2.5 σ higher than the value derived using moments extracted from some sets of experimental data on R ( e + e − → h a d r o n s ) . This value for a c μ includes our determination of the effect of QED on this quantity, δ a c μ = 0.0313 ( 28 ) × 10 − 10 .