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Within the framework of the effective Lagrangian approach, we perform athorough analysis of the $J/\psi \to P\gamma(\gamma^*)$, $J/\psi \to VP$, $V\toP\gamma(\gamma^*)$, $P\to V\gamma(\gamma^*)$ and $P\to\gamma\gamma(\gamma^*)$processes, where $V$ stand for light vector resonances, $P$ stand for lightpseudoscalar mesons, and $\gamma^*$ subsequently decays into lepton pairs. Theprocesses with light pseudoscalar mesons $\eta$ and $\eta'$ are paid specialattention to and the two-mixing-angle scheme is employed to describe theirmixing. The four mixing parameters both in singlet-octet and quark-flavor basesare updated in this work. We confirm that the $J/\psi \to\eta(\eta^{\prime})\gamma^{(*)}$ processes are predominantly dominated by the$J/\psi\to \eta_c \gamma^{*} \to \eta(\eta^{\prime})\gamma^{(*)}$ mechanism.Predictions for the $J/\psi \to P \mu^+\mu^-$ are presented. A detaileddiscussion on the interplay between electromagnetic and strong transitions inthe $J/\psi \to VP$ decays is given.

Unified study of $J/\psi \to PV$, $P\gamma^{(*)}$ and light hadron radiative processes