${\chi }_{c1}$ decays into a pseudoscalar meson and a vector-vector molecule

Abstract

We evaluate ratios of the ${\chi }_{c1}$ decay rates to $\eta$ (${\eta }^{\prime },K^{-}$) and one of the $f_0(1370)$, $f_0(1710)$, $f_2(1270)$, $f_2^{\prime }(1525)$, $K_2^{\ast }(1430)$ resonances, which in the local hidden gauge approach are dynamically generated from the vector-vector interaction. With the simple assumption that the ${\chi }_{c1}$ is a singlet of SU(3), and the input from the study of these resonances as vector-vector molecular states, we describe the experimental ratio $\mathcal{B}({\chi }_{c1}\to \eta f_2(1270))/\mathcal{B}({\chi }_{c1}\to {\eta }^{\prime }{f}_2^{\prime }(1525))$ and make predictions for six more ratios that can be tested in future experiments.

12 pages, 2 figures, 1 table

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• $J/\psi$ decay to $\varphi ,\omega ,K^{\ast 0}$ plus $f_0(1370)$, $f_0(1710)$, $K_0^{\ast }(1430)$, $f_2(1270)$, $f_2^{\prime }(1525)$ and $K_2^{\ast }(1430)$: role of the $D$-wave for tensor production
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