Lattice QCD estimate of the ${\eta }_c(2S)\to J\mathrm{/}\psi \gamma$ decay rate

We compute the hadronic matrix element relevant to the physical radiative decay ${\eta }_c(2S)\to J\mathrm{/}\psi \gamma$ by means of lattice QCD. We use the (maximally) twisted mass QCD action with Nf=2 light dynamical quarks and from the computations made at four lattice spacings we were able to take the continuum limit. The value of the mass ratio $m_{{\eta }_c(2S)}\mathrm{/}{m}_{{\eta }_c(1S)}$ we obtain is consistent with the experimental value, and our prediction for the form factor is $V^{\eta_{c}(2S)\to J/\psi\gamma}(0)\equiv V_{12}(0)=0.32(6)(2)$,leadingto$\Gamma(\eta_c (2S) \to J/\psi\gamma) = (15.7\pm 5.7)$keV,whichismuchlargerthan$\Gamma(\psi (2S) \to \eta_c\gamma)$ and within reach of modern experiments.