Using the results of our recent analysis of e + e − annihilation, we plot the curves for the diagonal and transition form factors of light hadrons in the time-like region up to the production threshold of an open charm quantum number. The comparison with existing data on the decays of J/ψ into such hadrons shows that some new resonance structures may be present in the mass range between 2 GeV and the J/ψ mass. Searching them may help in a better understanding of the mass spectrum in both the simple and a more sophisticated quark models, and in revealing the details of the three-gluon mechanism of the OZI rule breaking in KK channel.PACS numbers: 13.25. Gv, 13.40.Gp, 14.40.Cs, 14.40.Gx Typeset using REVT E X * e-mail: achasov@math.nsc.ru † e-mail: kozhev@math.nsc.ru 1 There are intentions to study the energy range of e + e − annihilation in the interval of the center-of-mass energy from 2E = 1.5 GeV up to m J/ψ using the collider VEPP-4M [1]. The BEPC e + e − collider team has also a plan to study some exclusive channels in the energy range from 2 to 5 GeV [2]. This raises the question of comparison of the results of existing analysis of the diagonal and transition form factors of light hadrons in the energy range between 1 and 2 GeV [3,4] with the data now existing at the J/ψ mass. Here we perform this task, in order to uncover possible surprises that might be revealed in future experiments. We use the following formulas expressing the cross sections through corresponding form factors.where p h is the modulus of the 3-momentum of the hadron h in the center-of-mass system of e + e − beams, whose total energy is √ s. The cross section for π + π − is given by Eq. (2.1) of the paper [3]. The cross section for K + K − is given by Eq. (2.1) of the paper [4]. If the final state is V P , wherewhere p V P is the modulus of the 3-momentum of the hadron V (or P ) in the center-of-mass system of e + e − beams. The cross section for V P final state is given by Eq. (2.1) of the paper [3]. If the final state is 2πwhere cross section for the production of 2π + 2π − is given by Eq. (2.8) of Ref.[3], andThe Okubo-Zweig-Iizuka (OZI) rule violating decays of the cc quarkonia into the light hadrons are divided into two very different classes. The isovector states π + π − , ωπ 0 , ρη and ρ 0 π + π − are produced predominantly via the one photon (γ) intermediate state. The threegluon (ggg) contribution which violates the conservation of isospin should be suppressed. Indeed, in the π + π − channel, the ratio of the coupling constant due to three gluons to that due to one photon is estimated aswhere α = 1/137, α s ≃ 0.2 is the QCD coupling constant, and f J/ψ enters the expression for the leptonic width of the J/ψ in a usual way:Inserting m d − m u ≃ 3 MeV, choosing conservatively Q ∼ m π , and taking the vectorfor the pion form factor, one gets the figure of 10 −2 for above ratio. Similar estimate holds for other isovector channels cited above. The amplitude with ggγ in intermediate state is also expected to be suppressed [5...