Baryon-baryon scattering in the Gross-Neveu model: the large N solution

TL;DR

This paper provides an exact large N solution for baryon-baryon scattering in the Gross-Neveu model, revealing complex interactions influenced by fermion back-reaction, with potential applications in conducting polymers.

Contribution

It introduces a simple ansatz for solving the complex scattering problem of DHN baryons in the large N Gross-Neveu model, extending previous kink-antikink solutions.

Findings

Exact analytic expressions for mean fields and spinors in baryon scattering

Solution accounts for fermion back-reaction effects

Applicable to scattering in conducting polymers

Abstract

The scattering of two Dashen-Hasslacher-Neveu (DHN) baryons in the large N Gross-Neveu model is solved exactly using the relativistic, time-dependent Hartree-Fock approach. Unlike the special case of kink-antikink scattering, the scattering of DHN baryons is sensitive to the back-reaction of the fermions bound inside the baryons. Correspondingly the solution is much more complicated than the kink-antikink scattering solutions, which can be expressed in terms of sinh-Gordon solitons. Nevertheless, we present a simple ansatz form that gives closed analytic expressions for both the space-time dependent mean fields and the Dirac spinors for all continuum and bound states. The solution can also be applied to the scattering of polarons and solitons in conducting polymers.