Unitary chiral dynamics in J/Ψ decays into V PP and the role of the scalar mesons

We make a theoretical study of the J/Ψ decays into ωππ, φππ, ωKK̄ and φKK̄ using the techniques of the chiral unitary approach stressing the important role of the scalar resonances dynamically generated through the final state interaction of the two pseudoscalar mesons. We also discuss the importance of new mechanisms with intermediate exchange of vector and axial-vector mesons and the role played by the OZI rule in the J/Ψφππ vertex, quantifying its effects. The results nicely reproduce the experimental data for the invariant mass distributions in all the channels considered. The J/Ψ decay into a pseudoscalar meson pair and a vector meson has been claimed to be one of the most suited reactions to study the long controversial nature of the scalar mesons, on which the interpretation as qq̄ mesons or as meson-meson molecules has mainly centered the discussion. In the last years, a chiral unitary coupled channel approach [1] has proved to be successful in describing meson-meson interactions in all channels up to energies ∼ 1.2 GeV, far beyond the natural limit of applicability of the standard Chiral Perturbation Theory (ChPT), which is ∼ 500 MeV where the pole of the lightest resonance, the σ meson, appears. In this approach the scalar mesons rise up naturally as dynamically generated resonances, in the sense that, without being included as explicit degrees of freedom, they appear as poles in the s-wave meson-meson scattering amplitudes. The aim of the present work 1 is to make a consistent and comprehensive description of the J/Ψ → V PP decays, including all the mechanisms able to influence the region of pseudoscalar pair invariant masses up to ∼ 1.1 GeV, addressing the role played by the scalar mesons and the OZI rule. Following the framework of the chiral unitary approach, we will implement the final meson-meson state interaction in order to generate dynamically the scalar resonances involved. The first mechanisms considered are those involving a direct coupling of the J/Ψ to the two pseudoscalars and the vector, implementing the final state interaction of the pseudoscalars pair, as is depicted in Fig. 1 for the J/Ψ → ωππ channel. The thick dot in Fig. 1 means that one is considering the full ππ(KK̄) → ππ t-matrix, involving the loop resummation of the BetheSalpeter equation and no just the lowest order ππ(KK̄) → ππ amplitude. Actually this loop resummation is what dynamically generates the scalar resonances. The J/ΨV PP vertex can be constructed using SU(3) arguments to relate the different isospin channels and parameterizing the amplitudes in a way which clearly manifest the role played by the OZI rule in this direct vertex, accounted for by means of a parameter λφ such that, if the OZI rule would be exact, then λφ would be zero. In analogy with the approach in Ref. [3] (and in some sense to [4]), we consider next the mechanisms involving the sequential exchange of a vector or axial-vector meson as depicted in All the details of the model can be found in [2], on which the present contribution is based