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The processes of $\eta_c (\eta_c')\to VV$ are supposed to be suppressed bythe helicity selection rule (HSR) but found to be rather important decay modesin experiment for $\eta_c$. We try to distinguish the short-distancetransitions via the singly disconnected Okubo-Zweig-Iizuka (SOZI) processes andthe doubly disconnected (DOZI) processes in $\eta_c (\eta_c')\to VV$. It showsthat the SOZI processes can be related to the $\eta_c(\eta_c')$ wavefunctionsat the origin. Therefore, a relation of the decay branching ratio fractionbetween these two decay channels can be established. Such a relation is similarto 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 intermediatecharmed meson loop transitions provide an evading mechanism for the DOZIprocesses. This contribution would turn out to be more important in$\eta_c^\prime\to VV$. As a consequence, it may produce significant deviationsfrom the SOZI-dominant scenario. Future experimental measurement of the$\eta_c^\prime\to VV$ by BESIII should be able to clarify the DOZI-evadingmechanisms.

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