Lattice QCD study of the radiative decays $J/\psi\to \eta_c\gamma$ and $h_c\to \eta_c\gamma$

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We present the results of our lattice QCD study of the hadronic matrix elements relevant to the physical radiative $J/\psi\to \eta_c\gamma$ and $h_c\to \eta_c\gamma$ decays.

• We used the twisted mass QCD action with $N_{\rm f}=2$ light dynamical quarks and from the computations made at four lattice spacings we were able to take the continuum limit.
• Besides the form factors parameterizing the above decays we also computed: (i) the hyperfine splitting and obtained $\Delta = 112\pm 4$ MeV, (ii) the annihilation constant $f_{J/\psi}$ which agrees with the one inferred from the measured $\Gamma(J/\psi \to e^+e^-)$.