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Title: 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:
 [1];  [2];  [3]
  1. Department of Physics, University of Haifa at Oranim, Tivon 36006 (Israel)
  2. (Israel)
  3. 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}
}
  • The results for the spectrum of bound states and of solitons first deduced by Dashen, Hasslacher, and Neveu for a model of interacting fermions by techniques of functional integration are obtained here by methods based on Heisenberg field mechanics analogous to those applied previously to models of self-interacting bosons. The method of solution is suggested by a simplified physical picture of the bound states: These are computed in a Hartree approximation in which the self-consistent potential is a sum of contributions from the fermions (and antifermions) occupying orbitals in the conventional many-body picture and from the vacuum fluctuations of single-closed-loopmore » type. In the same approximation the self-consistent field generated by the heavy soliton is a result of the vacuum fluctuations alone. As the main new technical contribution, we deduce and solve directly equations determining the self-consistent fields as well as the amplitudes (''wave functions'') from which these are constructed. We comment on the degeneracy of the heavy soliton state. (AIP)« less
  • The two-dimensional four-fermion theory with arbitrary number of spinor field multiplets is considered in the leading order of the 1/N expansion. This model is asymptotically free, dynamical breaking of chiral invariance occurs in it, and the fermions acquire masses. In the particular case of two multiplets, it is shown that there exist at least two different phases with massive fermions. The conditions under which the theory does not have ghosts are found. In the case of equal fermion masses, the masses of the bosonic states are calculated.
  • We consider the massive Euclidean Gross-Neveu model. Thanks to the Pauli principle the bare perturbation expansion for the model with an ultraviolet cutoff is convergent in a disk whose radius corresponds by asymptotic freedom to a small finite renormalized coupling constant. The theory constructed in this way is physical (it satisfies Osterwalder and Schrader's axioms) in contrast with the planar theories obtained by similar perturbative expansions.
  • We study the thermodynamics of massive Gross-Neveu models with explicitly broken discrete or continuous chiral symmetries for finite temperature and fermion densities. The large [ital N] limit is discussed, paying attention to the no-go theorems for symmetry breaking in two dimensions which apply to the massless cases. The main purpose of the study is to serve as an analytical orientation for the more complex problem of the chiral transition in four-dimensional QCD with quarks. For any nonvanishing fermion mass, we find, at finite densities, lines of first-order phase transitions. For small mass values, traces of would-be second-order transitions and amore » tricritical point are recognizable. We study the thermodynamics of these models, and in the model with broken continuous chiral symmetry we examine the properties of the pionlike state.« less
  • We perform a 1/N expansion of the partition function of the massive Gross-Neveu model in 1+1 dimensions. The procedure allows for the inclusion of the contribution of scalar and pseudoscalar composites (of order 1/N) to the equation of state. The naive expectation that the bosonic fluctuations significantly correct the mean field approximation at low temperatures is confirmed by our calculations. Actually the relevant degrees of freedom of hadronic matter at low temperatures are found to be pionlike excitations, rather than the fundamental constituents. {copyright} {ital 1997} {ital The American Physical Society}