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

Abstract

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

Comments: 19 pages, 4 figs