$J/\psi$ decay into $\phi (\omega)$ and vector-vector molecular states
Based on the picture that the $ f_0(1370), f_0(1710), f_2(1270), f'_2(1525), \bar{K}^{*0}_2(1430)$ resonances are dynamically generated from the vector-vector interaction, we study the decays $J/\psi \to \phi (\omega) f_0(1370) [f_0(1710)]$, $J/\psi \to \phi (\omega) f_2(1270) [f'_2(1525)]$, and $J/\psi \to K^{*0} \bar{K}^{*0}_2(1430)$ and make predictions for seven independent ratios that can be done among them. The starting mechanism is that the $J/\psi$ decays into three vectors, followed by the final state interaction of a pair of them. The weights of the different three vector primary channels are obtained from the basic assumption that the $J/\psi$ ($c \bar c$) is an SU(3) singlet. By means of only one free parameter we predict four ratios in good agreement with experiment, make two extra predictions for rates yet unmeasured, and disagree on one data for which only upper bounds are reported. Further measurements are most welcome to complete the information required for these ratios that are testing the nature of these resonances as dynamically generated.