### Speaker

### Description

We present results from our calculation of decays 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 the effect of u, d, s and c quarks in the sea for the first time. We use the Highly Improved Staggered Quark formulism, four values of the lattice spacing and sea u/d quarks down to their physical values. Our results are accurate at the 1-2% level and are therefore now more accurate than results from experiment. We find $\Gamma(\eta_c\to\gamma\gamma)=6.788(45)_{\mathrm{fit}}(41)_{\mathrm{syst}}$ keV, which agrees well with experimental results for $\gamma\gamma\to\eta_c\to K\overline{K}\pi$. This is in tension with the global PDG fit at the $4\sigma$ level, however, and we therefore advise this fit is revisited. We find $\Gamma(J/\psi\to\gamma\eta_c) = 2.219(17)_{\mathrm{fit}}(18)_{\mathrm{syst}}(24)_{\mathrm{expt}}(4)_{\mathrm{QED}}$ keV, which agrees well with results from CLEO. Finally, we predict $\Gamma(J/\psi\to\eta_c e^+ e^-)=0.01349(21)_{\mathrm{latt}}(13)_{\mathrm{QED}}$ keV. We compare our results with other theoretical approaches, while simple relationships between form factors and the $J/\psi$ decay constant in the nonrelativistic limit are also tested.

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