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 \(J/\psi \rightarrow \phi (\omega ) f_0(1370) [f_0(1710)]\), \(J/\psi \rightarrow \phi (\omega ) f_2(1270) [f'_2(1525)]\), and \(J/\psi \rightarrow K^{*0} {\bar{K}}^{*0}_2(1430)\) 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 fair 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 which test the nature of these resonances as dynamically generated.

中文翻译：

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$$ J / \ psi $$ J /ψ衰减为$$ \ phi（\ omega）$$ ϕ（ω）和矢量矢量分子态

基于图片，\（f_0（1370），f_0（1710），f_2（1270），f'_2（1525），{\ bar {K}} ^ {* 0} _2（1430）\）共振从矢量-矢量交互动态生成的图像中，我们研究衰减\（J / \ psi \ rightarrow \ phi（\ omega）f_0（1370）[f_0（1710）] \），\（J / \ psi \ rightarrow \ phi （\ omega）f_2（1270）[f'_2（1525）] \）和\（J / \ psi \ rightarrow K ^ {* 0} {\ bar {K}} ^ {* 0} _2（1430） \）并预测其中可以完成的七个独立比率。起始机制是\（J / \ psi \）衰减为三个向量，然后是两个向量的最终状态相互作用。从以下三个基本假设获得不同的三个向量主信道的权重：\（J / \ psi \）（\（c {\ bar {c}} \））是SU（3）单线态。通过仅使用一个自由参数，我们就可以与实验公平地预测出四个比率，对尚未测得的速率进行两个额外的预测，并且在仅报告上限的一个数据上存在分歧。欢迎进一步测量以完成这些比率所需的信息，以测试动态生成的这些共振的性质。