Effects of heavy meson loops on higher charmonia radiative transitions

Radiative transitions between charmonium states offer an insight into the internal structure of heavy quark bound states within QCD. In this work, we performed a systematically investigation of the radiative transitions of \(\psi (nS) \rightarrow \gamma \chi _{cJ}(mP)\) and \(\psi (nD) \rightarrow \gamma \chi _{cJ}(mP)\) via intermediate charmed meson loop with a non-relativistic effective field theory. We only focus on the line-shape behavior of the distributions via different intermediate meson loops. Our results show that the coupled-channel effects of these decays are relatively weak, while the coupled channel effects has obvious enhancement when the inial (final) states are closed to the thresholds of charmed-mesons pair.