# Meson-meson scattering in two-dimensional QCD

## TL;DR

This paper extends the analysis of meson-meson scattering in two-dimensional QCD using the 't Hooft model, deriving analytic amplitudes and numerically exploring potential tetra-quark states near thresholds.

## Contribution

It provides new analytic expressions for meson-meson scattering amplitudes and numerical evidence suggesting possible tetra-quark states in 2D QCD.

## Key findings

- Analytic expressions for scattering amplitudes derived.
- Near-threshold enhancement observed in some channels.
- Possible indication of tetra-quark states below two-meson threshold.

## Abstract

We extend the formalism pioneered by Callan, Coote and Gross to investigate the meson-meson scattering within the framework of 't Hooft model, i.e., the two-dimensional QCD in the $N_c\to \infty$ limit. We derive the analytic expressions for various two-body meson-meson scattering amplitudes, concentrating on those quark diagrams which may be identified as the meson-meson contact interaction vertex in the context of the mesonic effective lagrangian in $1/N_c$ expansion. We also carry out a detailed numerical study for the meson-meson scattering for various quark flavors, and observe the near-threshold enhancement in some channels. This may be viewed as the hint of the existence of the tetra-quark state below two-meson threshold.