# Beyond integrability: Baryon-baryon backward scattering in the massive Gross-Neveu model

## TL;DR

This paper investigates how adding a mass term to the Gross-Neveu model breaks its integrability, leading to backward and inelastic baryon-baryon scattering, analyzed through a combination of analytical and numerical methods near the non-relativistic limit.

## Contribution

It provides the first detailed study of baryon-baryon scattering in the massive Gross-Neveu model, demonstrating the emergence of backward scattering due to broken integrability.

## Key findings

- Backward elastic scattering occurs when integrability is broken.
- The study confirms inelastic reactions in the massive model.
- Analytical and numerical methods successfully analyze the scattering processes.

## Abstract

Due to integrability, baryon-baryon scattering in the massless Gross-Neveu model at large N features only forward elastic scattering. A bare mass term breaks integrability and is therefore expected to induce backward elastic scattering as well as inelastic reactions. We confirm these expectations by a study of baryon-baryon scattering in the massive Gross-Neveu model near the non-relativistic limit. This restriction enables us to solve the time-dependent Hartree-Fock equations with controlled approximations, using a combination of analytical methods from an effective field theory and the numerical solution of partial differential equations.