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 ${\chi }_{c1}\to \varphi \varphi ,\omega \omega$ 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.

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 $BR({\chi }_{c1}\to \omega \varphi )$ with the one-mixing angle scheme. Accepted by Phys. Rev. D.

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Cited by in corpus (10)

• Observation of $e^{+}{e}^{-}\to {\chi }_{c0}\omega$ and missing higher charmonium $\psi (4S)$
• Explaining the anomalous ${\rm Y}(5S)\to {\chi }_{bJ}\omega$ decays through the hadronic loop effect
• Long-distant contribution and ${\chi }_{c1}$ radiative decays to light vector meson
• Observation of ${\chi }_{c1}$ decays into vector meson pairs $\varphi \varphi$, $\omega \omega$, and $\omega \varphi$
• Possible $B^{(\ast )}\bar{K}$ hadronic molecule state
• Anomalous radiative transitions between $h_b(nP)$ and ${\eta }_b(mS)$ and hadronic loop effect
• Hidden-charm decays of $X(3915)$ and $Z(3930)$ as the P-wave charmonia
• Detecting the polarization in ${\chi }_{cJ}\to \varphi \varphi$ decays to probe hadronic loop effect
• Observation of OZI suppressed decays ${\chi }_{cJ}\to \omega \varphi$
• Study the decays of ${\chi }_{cJ}(J=0,1,2)$ to light meson pairs with SU(3) flavor symmetry/breaking analysis