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

Gerald V. Dunne^*

Christian Fitzner^† and Michael Thies^‡

Department of Physics, University of Connecticut, Storrs, Connecticut 06269, USA

Institut für Theoretische Physik III, Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany

^*dunne@phys.uconn.edu
^†fitzner@theorie3.physik.uni-erlangen.de
^‡thies@theorie3.physik.uni-erlangen.de

Phys. Rev. D 84, 105014 – Published 10 November, 2011

DOI: https://doi.org/10.1103/PhysRevD.84.105014

Abstract

The scattering of two Dashen-Hasslacher-Neveu 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 Dashen-Hasslacher-Neveu baryons is sensitive to the backreaction 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.

Synopsis

When Two Baryons Scatter

Published 10 November, 2011

The time-dependent solution of one of the most basic models in field theory has applications from nuclear to condensed-matter physics.

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Article Text

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