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

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.

22 pages, 5 figures

References in corpus (6)

• Solitons and AdS String Solutions
• Exact solution of N baryon problem in the Gross-Neveu model
• Kink dynamics, sinh-Gordon solitons and strings in AdS(3) from the Gross-Neveu model
• Gross-Neveu Models, Nonlinear Dirac Equations, Surfaces and Strings
• Bulk viscosity of the massive Gross-Neveu model
• Covariant boost and structure functions of baryons in Gross-Neveu models

Cited by in corpus (9)

• 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
• Integrable Gross-Neveu models with fermion-fermion and fermion-antifermion pairing
• Nambu-Jona Lasinio and Nonlinear Sigma Models in Condensed Matter Systems
• Breathers and their interaction in the massless Gross-Neveu model
• Evidence for factorized scattering of composite states in the Gross-Neveu model
• Beyond integrability: Baryon-baryon backward scattering in the massive Gross-Neveu model
• Untwisting twisted NJL${}_2$-kinks by a bare fermion mass
• Detecting inhomogeneous chiral condensation from the bosonic two-point function in the $(1+1)$-dimensional Gross-Neveu model in the mean-field approximation