$chi_{c1}$ decays into a pseudoscalar meson and a vector-vector molecule

We evaluate ratios of the $chi_{c1}$ decay rates to $eta$ ($eta, K^-$) and one of the $f_0(1370)$, $f_0(1710)$, $f_2(1270)$, $f_2(1525)$, $K^{*}_2(1430)$ 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.