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

摘要

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 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 ( connected ) = 120.3 ( 1.1 ) ? ? 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 Δ M η c annihiln = + 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 ˉ c ( 3 ? ? GeV ) = 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 hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon. We obtain a μ c = 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 ? → hadrons ) . This value for a μ c includes our determination of the effect of QED on this quantity, δ a μ c = 0.0313 ( 28 ) × 10 ? 10 .