Study of $\hat{I}{\cdot }_c$ and $\hat{I}{\cdot }_c^{\prime }$ decays into vector meson pairs

Abstract

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

10 pages and 6 eps figures