# Stable fermion bag solitons in the massive Gross-Neveu model: Inverse scattering analysis

## Abstract

Formation of fermion bag solitons is an important paradigm in the theory of hadron structure. We study this phenomenon nonperturbatively 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 multibound 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.

- Authors:

- Department of Physics, University of Haifa at Oranim, Tivon 36006 (Israel)
- (Israel)
- Department of Physics, Technion, Haifa 32000 (Israel)

- Publication Date:

- OSTI Identifier:
- 20711588

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 72; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.72.105009; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AXIOMATIC FIELD THEORY; BAG MODEL; BOUND STATE; DIRAC EQUATION; FERMIONS; HADRONS; INVERSE SCATTERING PROBLEM; O GROUPS; ONE-DIMENSIONAL CALCULATIONS; RELATIVISTIC RANGE; REST MASS; SOLITONS; TENSORS; VARIATIONAL METHODS

### Citation Formats

```
Feinberg, Joshua, Department of Physics, Technion, Haifa 32000, and Hillel, Shlomi.
```*Stable fermion bag solitons in the massive Gross-Neveu model: Inverse scattering analysis*. United States: N. p., 2005.
Web. doi:10.1103/PhysRevD.72.105009.

```
Feinberg, Joshua, Department of Physics, Technion, Haifa 32000, & Hillel, Shlomi.
```*Stable fermion bag solitons in the massive Gross-Neveu model: Inverse scattering analysis*. United States. doi:10.1103/PhysRevD.72.105009.

```
Feinberg, Joshua, Department of Physics, Technion, Haifa 32000, and Hillel, Shlomi. Tue .
"Stable fermion bag solitons in the massive Gross-Neveu model: Inverse scattering analysis". United States.
doi:10.1103/PhysRevD.72.105009.
```

```
@article{osti_20711588,
```

title = {Stable fermion bag solitons in the massive Gross-Neveu model: Inverse scattering analysis},

author = {Feinberg, Joshua and Department of Physics, Technion, Haifa 32000 and Hillel, Shlomi},

abstractNote = {Formation of fermion bag solitons is an important paradigm in the theory of hadron structure. We study this phenomenon nonperturbatively 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 multibound 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.},

doi = {10.1103/PhysRevD.72.105009},

journal = {Physical Review. D, Particles Fields},

number = 10,

volume = 72,

place = {United States},

year = {Tue Nov 15 00:00:00 EST 2005},

month = {Tue Nov 15 00:00:00 EST 2005}

}