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In this work, we discuss the contribution of the mesonic loops to the decayrates of $\chi_{c1}\to \phi\phi,\,\omega\omega$ which are suppressed by thehelicity selection rules and $\chi_{c1}\to \phi\omega$ which is a double-OZIforbidden process. We find that the mesonic loop effects naturally explain theclear signals of $\chi_{c1}\to \phi\phi,\,\omega\omega$ decay modes observed bythe BES collaboration. Moreover, we investigate the effects of the$\omega-\phi$ mixing which may result in the order of magnitude of thebranching ratio $BR(\chi_{c1} \to \omega \phi)$ being $10^{-7}$. Thus, we arewaiting 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 bevery helpful for testing the long-distant contribution and the $\omega-\phi$mixing in $\chi_{c1}\to\phi\phi,\,\omega\omega,\,\omega\phi$ decays.

Understanding the branching ratios of \chi_{c1}\to\phi\phi, \omega\omega, \omega\phi observed at BES-III