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

The processes of $η_c (η_c')\to VV$ are supposed to be suppressed by the helicity selection rule (HSR) but found to be rather important decay modes in experiment for $η_c$. We try to distinguish the short-distance transitions via the singly disconnected Okubo-Zweig-Iizuka (SOZI) processes and the doubly disconnected (DOZI) processes in $η_c (η_c')\to VV$. It shows that the SOZI processes can be related to the $η_c(η_c')$ 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 $J/ψ$ and $ψ^\prime\to VP$, where the so-called "$ρπ$ 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 $η_c^\prime\to VV$. As a consequence, it may produce significant deviations from the SOZI-dominant scenario. Future experimental measurement of the $η_c^\prime\to VV$ by BESIII should be able to clarify the DOZI-evading mechanisms.

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