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

TL;DR

This paper analyzes vector and scalar meson-meson scattering amplitudes up to 1.4 GeV using the N/D method, Chiral Symmetry, and large N_c QCD, revealing the nature of various resonances.

Contribution

It combines the N/D unitarization method with Chiral Perturbation Theory and large N_c analysis to distinguish between elementary and meson-meson states in meson resonances.

Findings

sigma, kappa, and a_0(980) are meson-meson states from unitarized ext{ChPT} amplitudes.

f_0(980) is a mix of meson-meson unitarity effects and a preexisting resonance.

The approach clarifies the nature of scalar resonances in meson scattering.

Abstract

We study the vector and scalar meson-meson amplitudes up to \sqrt{s}\lesssim 1.4 GeV and their associated spectroscopy. The study has been done considering jointly the N/D method, Chiral Symmetry and implications from large N_c QCD. 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 (\chiPT) Lagrangians and the exchanges of resonances compatible with Chiral Symmetry as given in. On the other hand the large N_c 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 \sigma, \kappa and a_0(980) resonances are meson-meson states originating from the unitarization of the lowest order \chiPT amplitudes. On the other hand, the f_0(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.