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

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.

18 pages, 13 figures

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Cited by in corpus (5)

• Time-Dependent Hartree-Fock Solution of Gross-Neveu models: Twisted Kink Constituents of Baryons and Breathers
• Full time-dependent Hartree-Fock solution of large N Gross-Neveu models
• Nambu-Jona Lasinio and Nonlinear Sigma Models in Condensed Matter Systems
• Breathers and their interaction in the massless Gross-Neveu model
• Detecting inhomogeneous chiral condensation from the bosonic two-point function in the $(1+1)$-dimensional Gross-Neveu model in the mean-field approximation