Charmonium properties from lattice QCD + QED: hyperfine splitting, $J/\psi$ leptonic width, charm quark mass and $a_{\mu}^c$

Understand

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 $M_{J/\psi}$ and including the effect of the $c$ quark's electric charge through quenched QED.
• We obtain $M_{J/\psi}-M_{\eta_c}$ (connected) = 120.3(1.1) MeV and interpret the difference with experiment as the impact on $M_{\eta_c}$ of its decay to gluons, missing from the lattice calculation.
• This allows us to determine $\Delta M_{\eta_c}^{\mathrm{annihiln}}$ =+7.3(1.2) MeV, giving its value for the first time.