Study of $\eta_c$ and $\eta_c^\prime$ decays into vector meson pairs

The processes of $\eta_c (\eta_c')\to VV$ are supposed to be suppressed by the helicity selection rule (HSR) but found to be rather important decay modes in experiment for $\eta_c$. We try to distinguish the short-distance transitions via the singly disconnected Okubo-Zweig-Iizuka (SOZI) processes and the doubly disconnected (DOZI) processes in $\eta_c (\eta_c')\to VV$. It shows that the SOZI processes can be related to the $\eta_c(\eta_c')$ wavefunctions at the origin. Therefore, a relation of the decay branching ratio fraction between these two decay channels can be established. Such a relation is similar to that for $J/\psi$ and $\psi^\prime\to VP$, where the so-called "$\rho\pi$ puzzle" has been existed for a while. We also show that the intermediate charmed meson loop transitions provide an evading mechanism for the DOZI processes. This contribution would turn out to be more important in $\eta_c^\prime\to VV$. As a consequence, it may produce significant deviations from the SOZI-dominant scenario. Future experimental measurement of the $\eta_c^\prime\to VV$ by BESIII should be able to clarify the DOZI-evading mechanisms.