Understanding the branching ratios of χ_{c1}\toϕϕ, ωω, ωϕobserved at BES-III

Abstract

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

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 ω-ϕmixing on $BR(χ_{c1}\to ωϕ)$ with the one-mixing angle scheme. Accepted by Phys. Rev. D.