Scattering of mesons and emergence of tetraquarks in two-dimensional QCD

Abstract

Scattering of two mesons is considered in the framework of two-dimensional QCD in the large-$N_c^{}$ limit with four different quark flavors. The scattering takes place through two coupled channels, corresponding to direct and quark-exchange processes, which are of order $O(N_c^{-2})$ and $O(N_c^{-1})$, respectively. Finiteness of the scattering amplitudes to order $N_c^{-2}$ is pointed out. The theory reduces, at low energies, to an effective theory of mesons, interacting by a quark-exchange process, by means of a contact term. The unitarization of the scattering amplitudes leads to the emergence of a tetraquark bound state, located very close to the lowest two-meson elastic threshold.