Evidence for factorized scattering of composite states in the Gross-Neveu model

TL;DR

This paper extends the analytical solution of baryon scattering in the large-N Gross-Neveu model to processes involving multiple composite states, providing evidence for factorized scattering of these multi-fermion states.

Contribution

The authors generalize the known two-baryon scattering solution to multi-baryon cases using a joint ansatz, supporting the concept of factorized scattering for composite states.

Findings

Analytical form for multi-baryon scattering derived

Numerical verification up to 8-baryon problems

Parameters determined by one- and two-baryon input

Abstract

Scattering of two baryons in the large-N Gross-Neveu model via the time-dependent Dirac-Hartree-Fock approach has recently been solved in closed analytical form. Here, we generalize this result to scattering processes involving any number and complexity of the scatterers. The result is extrapolated from the solution of few baryon problems, found via a joint ansatz for the scalar mean field and the Dirac spinors, and presented in analytical form. It has been verified numerically for up to 8-baryon problems so far, but a full mathematical proof is still missing. Examples shown include the analogue of proton-nucleus and nucleus-nucleus scattering in this toy model. All the parameters of the general result can be fixed by one- and two-baryon input only. We take this finding as evidence for factorized scattering, but on the level of composite multi-fermion states rather than elementary fermions.