  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
$\Gamma(J/\psi \to e^+e^-)$.
