Charmonium rescattering effects in psi(2S) rightarrow gamma eta_{c}^{} decay

Charmonium rescattering effects in the M1 transition of $ psi$ (2S) $ rightarrow$ $ gamma$ $ eta_{c}^{}$ are investigated by modeling a $ chi_{{cJ}}^{}$ or J/ $ psi$ rescattering into a $ eta_{c}^{}$ final state. The absorptive and dispersive part of the transition amplitudes for the rescattering loops of $ eta$ $ psi$ ( $ gamma^{{ast}}_{}$ ) and $ gamma$ $ chi$ ( $ psi$ ) are separately evaluated. The numerical results show that the contribution from the $ gamma$ $ chi$ ( $ psi$ ) rescattering process is negligible. Compared with the virtual D $ bar{{D}}$ (D ^*) rescattering processes, the $ eta$ $ psi$ ( $ gamma^{{ast}}_{}$ ) process may be regarded as the next-leading order of the hadronic loop mechanism, which only offers the partial decay width of ～ 0.045 keV to the $ psi$ (2S) $ rightarrow$ $ gamma$ $ eta_{c}^{}$ .