Baryons as chiral solitons in the Nambu-Jona-Lasinio model

Alkofer, Reinhard; Reinhardt, Hugo; Weigel, H.

doi:10.1016/0370-1573(95)00018-6

Cited by 226 publications

(286 citation statements)

References 139 publications

(386 reference statements)

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“…Here it would be extremely interesting to see whether nucleons and nuclear matter can emerge as threedimensional inhomogeneities when going from quark matter to lower densities [108]. In this context it would certainly be rewarding to reconsider the chiral soliton models of the nucleon [204,205,206] and work out their relation to the domain-wall solitons in the inhomogeneous phases.…”

Section: Discussionmentioning

confidence: 99%

Inhomogeneous chiral condensates

Buballa

Carignano

2015

Progress in Particle and Nuclear Physics

232

251

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The chiral condensate, which is constant in vacuum, may become spatially modulated at moderately high densities where in the traditional picture of the QCD phase diagram a first-order chiral phase transition occurs. We review the current status of this idea, which originally dates back to Migdal's pion condensation, but recently received new momentum through studies on the nature of the chiral critical point and by the conjecture of a quarkyonic-matter phase. We discuss how these nonuniform phases emerge in generalized Ginzburg-Landau analyses as well as in specific calculations, both within effective models and in Dyson-Schwinger or large-N c approaches to QCD. Questions about the most favored shape of the modulations and its dimension, and about the effects of nonzero isospin chemical potential, strange quarks, color superconductivity, and external magnetic fields on these inhomogeneous phases will be addressed as well.

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Section: Discussionmentioning

confidence: 99%

Inhomogeneous chiral condensates

Buballa

Carignano

2015

Progress in Particle and Nuclear Physics

232

251

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“…We will not touch upon this topic here since there are excellent specialised reviews available, see e.g. [347][348][349].…”

Section: Approximations and Truncationsmentioning

confidence: 99%

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

406

530

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We review the spectrum and electromagnetic properties of baryons described as relativistic three-quark bound states within QCD. The composite nature of baryons results in a rich excitation spectrum, whilst leading to highly non-trivial structural properties explored by the coupling to external (electromagnetic and other) currents. Both present many unsolved problems despite decades of experimental and theoretical research. We discuss the progress in these fields from a theoretical perspective, focusing on nonperturbative QCD as encoded in the functional approach via Dyson-Schwinger and Bethe-Salpeter equations. We give a systematic overview as to how results are obtained in this framework and explain technical connections to lattice QCD. We also discuss the mutual relations to the quark model, which still serves as a reference to distinguish 'expected' from 'unexpected' physics. We confront recent results on the spectrum of non-strange and strange baryons, their form factors and the issues of two-photon processes and Compton scattering determined in the DysonSchwinger framework with those of lattice QCD and the available experimental data. The general aim is to identify the underlying physical mechanisms behind the plethora of observable phenomena in terms of the underlying quark and gluon degrees of freedom.

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“…The NJL model possesses solitonic solutions in the B=1 sector which can be viewed as a mean-field description of the ground-state baryons. On this basis the phenomenology of ground-state baryons could be reproduced quite well [7,8].…”

Section: Introductionmentioning

confidence: 79%

“…Since we do not perform a Wick rotation to Euclidean space-time we avoid ambiguities with the treatment of vector potentials [7]. We start from a model state given by the Dirac sea with three valence quarks on top.…”

Section: Equations Of Motion For a Relativistic System Of Fermionsmentioning

confidence: 99%

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RPA approach to the excitations of the nucleon Part I: Theory

Hardt¹,

Geiss²,

Lenske³

et al. 1997

Nuclear Physics A

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In this paper we develop a theoretical framework which allows us to study excitations of the nucleon. Assuming an effective two-body interaction as a model for low-energy QCD, we derive a relativistic TDHF equation for a many-body system of quarks. To render the Dirac-sea contribution to the mean field finite, we introduce a symmetry conserving regularization scheme. In the small amplitude limit we derive an RPA equation. The structure of the ph interaction and modifications due to the regularization scheme are discussed. We give a prescription to obtain a nucleon state with good angular momentum (J) and isospin (T ) quantum numbers on mean-field level. To study excitations, we develop a tensor-RPA approach, which is an extension of the conventional RPA techniques to systems with a nonscalar ground state. This allows us to construct excited states with good (J/T ) quantum numbers. We discuss a method to reduce the overcomplete ph-space and compute the tensor-RPA interaction matrix elements. Finally we extend our scheme to include ( 3 2 + , 32 )-states.

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Baryons as chiral solitons in the Nambu-Jona-Lasinio model

Cited by 226 publications

References 139 publications

Inhomogeneous chiral condensates

Inhomogeneous chiral condensates

Baryons as relativistic three-quark bound states

RPA approach to the excitations of the nucleon Part I: Theory

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