Hadronic loop contributions to $J/\psi$ and $\psi^\prime$ radiative decays into $\gamma\eta_c$ or $\gamma\eta_c^\prime$

Intermediate hadronic meson loop contributions to $J/\psi$, $\psi^\prime \to \gamma\eta_c$ ($\gamma\eta_c^\prime$) are studied apart from the dominant M1 transitions in an effective Lagrangian approach. Due to the property of the unique antisymmetric tensor coupling in $V\to VP$, the hadronic loop transitions provide explicit corrections to the M1 transition amplitudes derived from the naive "quenched" $c\bar{c}$ transitions via the coupling form factors. This mechanism interfering with the M1 transition amplitudes naturally accounts for the deviations from the Godfrey-Isgur model predictions in $J/\psi$ and $\psi^\prime\to \gamma\eta_c$. It also predicts a small branching ratio of $\psi^\prime\to \gamma\eta_c^\prime$, which can be examined by experimental measurements at BES and CLEO-c.