Study of the $f_2(1270)$, $f_2^{\prime }(1525)$, ${\overline{K}}_2^{*}(1430)$, $f_0(1370)$ and $f_0(1710)$ production from $\psi (nS)$ and $\mathrm{\Upsilon }(nS)$ decays

Based on previous studies that support the important role of the $f_2(1270)$, $f_2^{\prime }(1525)$, and ${\overline{K}}_2^{*}(1430)$ resonances in the $J/\psi [\psi (2S)]\to \varphi (\omega )VV$ decays, we make an analysis of the analogous decays of $\mathrm{\Upsilon }(1S)$ and $\mathrm{\Upsilon }(2S)$, taking into account recent experimental data. In addition, we study the $J/\psi$ and $\psi (2S)$ radiative decays and we also made predictions for the radiative decay of $\mathrm{\Upsilon }(1S)$ and $\mathrm{\Upsilon }(2S)$ into $\gamma f_2(1270)$, $\gamma f_2^{\prime }(1525)$, $\gamma f_0(1370)$ and $\gamma f_0(1710)$, comparing with the recent results of a CLEO experiment. We can compare our results for ratios of decay rates with eight experimental ratios and find agreement in all but one case, where experimental problems are discussed.

Figure 1

Production mechanism of $\omega$ and two interacting vector mesons.

Figure 2

Selection of diagrams of Fig. 1 that go into resonance formation, omitting the coupling to $VV$ without interaction.

Figure 3

Two mechanisms of the $\mathrm{\Upsilon }(1S)$ radiative decays.

Figure 4

Schematic representation of $\mathrm{\Upsilon }(1S)$ decay into a photon and one dynamically generated resonance.