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

• Received 26 December 2009

DOI:https://doi.org/10.1103/PhysRevD.81.074006