Precise determination of decay rates for ${\eta }_c\to \gamma \gamma$, $J/\psi \to \gamma {\eta }_c$ and $J/\psi \to {\eta }_c{e}^{+}{e}^{-}$ from lattice QCD

Abstract

We calculate the decay rates for ${\eta }_c\to \gamma \gamma$, $J/\psi \to \gamma {\eta }_c$ and $J/\psi \to {\eta }_c{e}^{+}{e}^{-}$ in lattice QCD with $u$, $d$, $s$ and $c$ quarks in the sea for the first time. We improve significantly on previous theory calculations to achieve accuracies of 1--2\%, giving lattice QCD results that are now more accurate than the experimental values. In particular our results transform the theoretical picture for ${\eta }_c\to \gamma \gamma$ decays. We use gluon field configurations generated by the MILC collaboration that include $n_f=2+1+1$ flavours of Highly Improved Staggered (HISQ) sea quarks at four lattice spacing values from 0.15 fm to 0.06 fm and with sea u/d masses down to their physical value. We also implement the valence $c$ quarks using the HISQ action. We find $\Gamma ({\eta }_c\to \gamma \gamma )=6.788(45{)}_{\text{fit}}(41{)}_{\text{syst}}\mathrm{keV}$, in good agreement with experimental results using $\gamma \gamma \to {\eta }_c\to K\overline{K}\pi$ but in 4$\sigma$ tension with the Particle Data Group global fit result; we suggest this fit is revisited. We also calculate $\Gamma (J/\psi \to \gamma {\eta }_c)=2.219(17{)}_{\text{fit}}(18{)}_{\text{syst}}(24{)}_{\text{expt}}(4{)}_{\text{QED}}\mathrm{keV}$, in good agreement with results from CLEO, and predict the Dalitz decay rate $\Gamma (J/\psi \to {\eta }_c{e}^{+}{e}^{-})=0.01349(21{)}_{\text{latt}}(13{)}_{\text{QED}}\mathrm{keV}$. We use our results to calibrate other theoretical approaches and to test simple relationships between the form factors and $J/\psi$ decay constant expected in the nonrelativistic limit.

Comments: 26 pages, 19 figures. Updated Figure 7, added 3 references and made further small changes to clarify the presentation. Further small changes to text, version accepted by Physical Review D