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

TL;DR

This paper analyzes mesonic loop contributions and omega-phi mixing effects to the decay rates of _{1} into , , and , explaining observed signals and predicting small branching ratios.

Contribution

It introduces a detailed analysis of mesonic loop effects and - mixing in _{1} decays, providing explanations for observed decay modes and predictions for unmeasured ones.

Findings

Mesonic loops explain observed _{1} and  decay signals.

- mixing may lead to _{1} decay branching ratio around 10^{-7}.

Predictions highlight the importance of future measurements for testing long-distance effects.

Abstract

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.