Baryons as non-topological chiral solitons

TL;DR

This work presents a comprehensive account of baryons in the Nambu–Jona-Lasinio framework, treating baryons as non-topological chiral solitons formed by Nc valence quarks coupled to a polarized Dirac sea within both SU(2) and SU(3) flavors. The approach rests on bosonization, large-Nc mean-field, and a chiral-circle constraint, linking the physics to the instanton-vacuum description of QCD and yielding predictions for a wide range of baryon properties, including electromagnetic, axial, scalar, and strange observables, with good overall agreement around a constituent mass M ≈ 420 MeV. It highlights the crucial role of chiral symmetry breaking and quark–Goldstone interactions, while noting limitations from confinement absence and missing meson-loop effects. The results provide a unified, semiclassical picture of the nucleon and hyperons that connects to both Skyrme-type topological solitons and constituent quark models, and offers predictions for strange form factors and tensor charges that can guide future experiments and lattice studies.

Abstract

The present review gives a survey of recent developments and applications of the Nambu--Jona-Lasinio model with $N_f=2$ and $N_f=3$ quark flavors for the structure of baryons. The model is an effective chiral quark theory which incorporates the SU(N$_f$)$_L\otimes$SU(N$_f$)$_R\otimes$U(1)$_V$ approximate symmetry of Quantum chromodynamics. The approach describes the spontaneous chiral symmetry breaking and dynamical quark mass generation. Mesons appear as quark-antiquark excitations and baryons arise as non-topological solitons with three valence quarks and a polarized Dirac sea. For the evaluation of the baryon properties the present review concentrates on the non-linear Nambu--Jona-Lasinio model with quark and Goldstone degrees of freedom which is identical to the Chiral quark soliton model obtained from the instanton liquid model of the QCD vacuum. In this non-linear model, a wide variety of observables of baryons of the octet and decuplet is considered. These include, in particular, electromagnetic, axial, pseudoscalar and pion nucleon form factors and the related static properties like magnetic moments, radii and coupling constants of the nucleon as well as the mass splittings and electromagnetic form factors of hyperons. Predictions are given for the strange form factors, the scalar form factor and the tensor charge of the nucleon.

Figures (27)

• Figure 1: Diagram representation of the gap equation. The thin line corresponds to "bare" quarks whereas the thick line represents the constituent "dressed" quarks.
• Figure 2: Cutoff $\Lambda$ on the left and the quark condensate $\langle\bar{u}u\rangle$ (solid line) and current quark mass $m_0$ (dashed line) on the right in the case of the proper-time regularization as a function of the constituent quark mass $M$.
• Figure 3: Quark spectrum of the one-particle hamiltonian $h$ for an exponential profile form $\Theta (r) = - \pi \exp (- r/ R )$ as a function of the profile size $R$. Both the energies $\epsilon_n$ and $R$ are given in scaled units: ($\epsilon_n \over M$ and $MR$).
• Figure 4: Classical soliton energy $M_{cl}$ split in Dirac sea and valence parts in the case of an exponential profile form. The energies are given in unit of the constituent quark mass $M$ and the size of the soliton $R$ is given in terms of the scaled unit $MR$.
• Figure 5: Classical energy $M_{cl}$ of the selfconsistent soliton split in sea and vacuum contributions as a function of the constituent quark mass $M$.