Two Meson Scattering Amplitudes and their Resonances from Chiral Symmetry and the N / D Method ∗

We study the vector and scalar meson-meson amplitudes up to √ s . 1.4 GeV and their associated spectroscopy. The study has been done considering jointly the N/D method, Chiral Symmetry and implications from large Nc QCD [1]. The N/D method provides us with the way to unitarize the tree level amplitudes constructed in agreement with Chiral Symmetry and its breaking (explicit and spontaneous). These amplitudes are calculated making use of the lowest order Chiral Perturbation Theory (χPT ) Lagrangians [2] and the exchanges of resonances compatible with Chiral Symmetry as given in [3]. On the other hand the large Nc considerations allow us to distinguish between elementary (as elementary as the pions, for instance) and compound (meson-meson) states. Making use of this formalism one observes that the σ, κ and a0(980) resonances are meson-meson states originating from the unitarization of the lowest order χPT amplitudes. On the other hand, the f0(980) is a combination of a strong S-wave meson-meson unitarity effect and of a preexisting singlet resonance with a mass around 1 GeV. For the vector resonances we reproduce the well known features of Vector Meson Dominance (VMD) and the KSFR relation [4]. The much more important role that unitarity plays in the scalar sector as compared with the vector one is also stressed. In particular, it is clear from our study that the σ and the ρ resonances are states completely different in nature. The σ is a two pion resonance originated from the interaction of the pions whereas the ρ is a state as elementary as the pions themselves whose origin has nothing to do with the interaction between pions.