Revisit the radiative decays of $J/\psi$ and $\psi'\to \gamma\eta_c (\gamma\eta_c^\prime)$

With the new measurements of $J/\psi$ and $\psi^\prime\to \gamma\eta_c \ (\gamma\eta_c^\prime)$ from CLEO and BES-III Collaboration, we re-investigate the intermediate meson loop (IML) contributions to these radiative decays in association with the quark model M1 transitions in an effective Lagrangian approach. It shows that the "unquenched" effects due to the intermediate hadron loops can be better quantified by the new data for $J/\psi\to \gamma\eta_c$. Although the IML contributions are relatively small in $J/\psi\to \gamma\eta_c$, they play a crucial role in $\psi^\prime\to \gamma\eta_c \ (\gamma\eta_c^\prime)$. A prediction for the IML contributions to $\psi(3770)\to \gamma\eta_c \ (\gamma\eta_c^\prime)$ is made. Such "unquenched" effects allow us to reach a coherent description of those three radiative transitions, and gain some insights into the underlying dynamics.