Tests on the molecular structure of $f_2(1270)$, $f'_2(1525)$ from $\psi (nS)$ and $\Upsilon (nS)$ decays

Abstract

Based on previous studies that support the vector-vector molecular structure of the $f_2(1270)$, $f'_2(1525)$, $\bar{K}^{*\,0}_2(1430)$, $f_0(1370)$ and $f_0(1710)$ resonances, we make predictions for $\psi (2S)$ decay into $\omega(\phi) f_2(1270)$, $\omega(\phi) f'_2(1525)$, $K^{*0}(892) \bar{K}^{*\,0}_2(1430)$ and radiative decay of $\Upsilon (1S),\Upsilon (2S), \psi (2S)$ into $\gamma f_2(1270)$, $\gamma f'_2(1525)$, $\gamma f_0(1370)$, $\gamma f_0(1710)$. Agreement with experimental data is found for three available ratios, without using free parameters, and predictions are done for other cases.