Abstract
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.
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Data Availability Statement
This manuscript has no associated data or the data will not be deposited. [Authors’ comment: We do not have data associated to this article, the only data we have is from well known Particle Data Group.]
Notes
We obtain \(\chi ^2=5.99\) inside the \(90\%\) CI [0.6, 6.3]. Thus, the \(\chi ^2/\nu =1.99\). If we include the ratio \(R_2\) in the fit, then, the fit does not pass the Pearson test, the total \(\chi ^2\) increases around three units, \(\simeq 9.4\), and \(\chi ^2/\nu \simeq 2.35\). However, the value of \(\beta \) obtained barely changes, we still obtain \(\beta \simeq 0.320\) (before we obtained \(\beta =0.323\)).
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Acknowledgements
L.R.D. and L.S.G acknowledge supports from the National Natural Science Foundation of China (Grant Nos. 11975009, 11575076, 11735003, 11975041). R.M. and E.O. acknowledge the hospitality of Beihang University where this work was initiated. This work is partly supported by the Talento Program of the Community of Madrid and the Complutense University of Madrid, under the project with Ref. 2018-T1/TIC-11167, and by the Spanish Ministerio de Economia y Competitividad and European FEDER funds under Contracts No. FIS2017-84038-C2-1-P B and No. FIS2017-84038-C2-2-P B, and the Generalitat Valenciana in the program Prometeo II-2014/068, and the project Severo Ochoa of IFIC, SEV-2014-0398 (EO).
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Molina, R., Dai, L.R., Geng, L.S. et al. \(J/\psi \) decay into \(\phi (\omega )\) and vector-vector molecular states. Eur. Phys. J. A 56, 173 (2020). https://doi.org/10.1140/epja/s10050-020-00176-y
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DOI: https://doi.org/10.1140/epja/s10050-020-00176-y