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

Abstract

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-OZI 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 $BR({\chi }_{c1}\to \omega \varphi )$ being $10^{-7}$. Thus, we are waiting for the accurate measurements of the $BR({\chi }_{c1}\to \omega \omega )$, $BR({\chi }_{c1}\to \varphi \varphi )$ and $BR({\chi }_{c1}\to \omega \varphi )$, 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.

Comments: 6 pages, 3 figures, 1 table. Title changed, references added, typos corrected and presentation improved. We have removed the content related to the two-mixing angle scheme and only study the effect of \omega-\phi mixing on $BR({\chi }_{c1}\to \omega \varphi )$ with the one-mixing angle scheme. Accepted by Phys. Rev. D.