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

We evaluate ratios of the ${\chi }_{c1}$ decay rates to $\eta$ (${\eta }^{\mathrm{\prime }},K^{-}$) and one of the $f_0(1370)$, $f_0(1710)$, $f_2(1270)$, $f_2^{\mathrm{\prime }}(1525)$, $K_2^{\ast }(1430)$ 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} \rightarrow \eta f_2(1270))/ $\mathcal{B}$(\chi_{c1} \rightarrow \eta’ f_2’(1525))$ and make predictions for six more ratios that can be tested in future experiments.