Stable Fermion Bag Solitons in the Massive Gross-Neveu Model: Inverse Scattering Analysis

TL;DR

This paper analyzes fermion bag solitons in the massive Gross-Neveu model using inverse scattering, revealing that stable static configurations are reflectionless and can support multiple bound states, extending previous variational results.

Contribution

It demonstrates that extremal static bag configurations are reflectionless with arbitrary bound states and identifies the stability conditions for these multi-bound state solitons.

Findings

Reflectionless static bag configurations support multiple bound states.

Only configurations with a single pair of bound states are stable.

Stable configurations form an O(2N) antisymmetric tensor multiplet.

Abstract

Formation of fermion bag solitons is an important paradigm in the theory of hadron structure. We study this phenomenon non-perturbatively in the 1+1 dimensional Massive Gross-Neveu model, in the large $N$ limit. We find, applying inverse scattering techniques, that the extremal static bag configurations are reflectionless, as in the massless Gross-Neveu model. This adds to existing results of variational calculations, which used reflectionless bag profiles as trial configurations. Only reflectionless trial configurations which support a single pair of charge-conjugate bound states of the associated Dirac equation were used in those calculations, whereas the results in the present paper hold for bag configurations which support an arbitrary number of such pairs. We compute the masses of these multi-bound state solitons, and prove that only bag configurations which bear a single pair of bound states are stable. Each one of these configurations gives rise to an O(2N) antisymmetric tensor multiplet of soliton states, as in the massless Gross-Neveu model.