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We compute the hadronic matrix element relevant to the physical radiativedecay $\eta_{c}(2S)\to J/\psi\gamma$ by means of lattice QCD. We use the(maximally) twisted mass QCD action with Nf=2 light dynamical quarks and fromthe computations made at four lattice spacings we were able to take thecontinuum limit. The value of the mass ratio $m_{\eta_c(2S)}/m_{\eta_c(1S)}$ weobtain is consistent with the experimental value, and our prediction for theform factor is $V^{\eta_{c}(2S)\to J/\psi\gamma}(0)\equivV_{12}(0)=0.32(6)(2)$, leading to $\Gamma(\eta_c (2S) \to J/\psi\gamma) =(15.7\pm 5.7)$ keV, which is much larger than $\Gamma(\psi (2S) \to\eta_c\gamma)$ and within reach of modern experiments.

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