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Revisit the radiative decays of $J/ψ$ and $ψ'\to γη_c (γη_c^\prime)$

With the new measurements of $J/ψ$ and $ψ^\prime\to γη_c \ (γη_c^\prime)$ 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 $J/ψ\to γη_c$. Although the IML contributions are relatively small in $J/ψ\to γη_c$, they play a crucial role in $ψ^\prime\to γη_c \ (γη_c^\prime)$. A prediction for the IML contributions to $ψ(3770)\to γη_c \ (γη_c^\prime)$ 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.