In this work, we discuss the contribution of the mesonic loops to the decay rates of $\chi_{ c1}\to \phi\phi,\,\omega\omega$ which are suppressed by the helicity selection rules and $\chi_{ c1}\to \phi\omega$ which is a double-OZI forbidden process. We find that the mesonic loop effects naturally explain the clear signals of $\chi_{ c1}\to \phi\phi,\,\omega\omega$ decay modes observed by the BES collaboration. Moreover, we investigate the effects of the $\omega-\phi$ mixing which may result in the order of magnitude of the branching ratio $BR(\chi_{ c1} \to \omega \phi)$ being $10^{ -7}$. Thus, we are waiting for the accurate measurements of the $BR(\chi_{ c1} \to \omega \omega)$, $BR(\chi_{ c1} \to \phi \phi)$ and $BR(\chi_{ c1} \to \omega \phi)$, which may be very helpful for testing the long-distant contribution and the $\omega-\phi$ mixing in $\chi_{ c1}\to\phi\phi,\,\omega\omega,\,\omega\phi$ decays.
Categories: hep-ph hep-ex