Fermion Bag Solitons in the Massive Gross-Neveu and Massive Nambu-Jona-Lasinio Models in 1+1 Dimensions: Inverse Scattering Analysis

TL;DR

This paper analyzes fermion bag solitons in 1+1 dimensional massive Gross-Neveu and Nambu-Jona-Lasinio models using inverse scattering, revealing reflectionless configurations and providing explicit formulas for their profiles and masses.

Contribution

It demonstrates that extremal static bag configurations are reflectionless in the massive models and derives explicit formulas for soliton profiles and masses.

Findings

Extremal static bag configurations are reflectionless.

Explicit formulas for soliton profiles and masses are provided.

Self-consistent reflectionless solitons are identified in the massive Nambu-Jona-Lasinio models.

Abstract

Formation of fermion bag solitons is an important paradigm in the theory of hadron structure. We report here on our non-perturbative analysis of this phenomenon in the 1+1 dimensional massive Gross-Neveu model, in the large $N$ limit. Our main result is that the extremal static bag configurations are reflectionless, as in the massless Gross-Neveu model. Explicit formulas for the profiles and masses of these solitons are presented. We also present a particular type of self-consistent reflectionless solitons which arise in the massive Nambu-Jona-Lasinio models, in the large-N limit.