Soliton Bag Model Research Articles

Nuclear matter in the crystal soliton bag model.

A model for nuclear matter is introduced as consisting of an infinite number of bags placed on a spatial cubic lattice. Using the soliton bag model of Friedberg and Lee in the self-consistent mean-field approximation we study the properties of the system as a function of the lattice constant. At low densities the hadronic matter is well described by the solutions of isolated nucleons. With decreasing lattice constant the energies of the quarks spread out into bands and the quark wave functions of different bags start to overlap. At a certain critical density an abrupt phase transition to a uniform quark distribution occurs. The model yields a critical density of the order of the normal nuclear density which shows that the model cannot adequately describe the repulsive part of the nucleon-nucleon interaction at small relative distances.

Soliton bag models of hadrons from QCD.

Several phenomenological models of hadrons are derived from quantum chromodynamics (QCD). Functional-integral methods are used to obtain an approximate bilocal-field representation of the QCD generating functional. The degenerate vacuum configurations of the action for the bilocal fields have a rich topological structure arising from the dynamically broken chiral symmetry. Restricting the bilocal-field fluctuations to those of local fields results in a local-field bosonization of QCD, from which we obtain values for several meson parameters. A nontopological-soliton ansatz for hadronic states leads to a generalized bag-model action which as special cases contains the chiral-bag-model action and the MIT-bag-model action. All parameters in these actions are calculable and in particular the MIT bag constant is calculated. This work extends our previous calculation of the bag constant.

Numerical solution of soliton bag models.

We develop a new, efficient, and accurate method of obtaining numerical solutions for soliton bag models. By introducing additional differential equations to describe the integral constraints and eigenvalue conditions, and after a careful analysis of the asymptotic form of the solutions, we convert the equations of the soliton bag model in the mean-field approximation into a two-point boundary-value system, which is readily solved by standard methods. To illustrate the techniques we find solutions for a chiral model, for cases of both massless and massive pions, for a wide range of parameters, and compare our results with previous calculations.

Deconfinement phase transition of hot and dense nuclear matter in the non-topological soliton bag model

We investigate the quark deconfinement phase transition in hot and dense nuclear matter in the non-topological soliton bag model. For this purpose we study the behaviour of the nucleon (soliton) at finite temperature in a spherical Wigner-Seitz cell. We find the deconfinement transition to occur for zero temperature through a rather wide transitional region centered at about five times the nuclear matter saturation density while for zero chemical potential the transition happens rather abruptly at a critical temperature of about 112 MeV.

Quantum chromodynamics with colored Higgs mechanism.

We derive, in the context of a previously proposed chiral soliton bag model with colored Higgs mechanism, the field equations for the eight gluons and the remaining four Higgs particles. It is pointed out that the boundary condition used by Jaendel for supporting his claim about the lack of a suppression mechanism for open-color states do not follow from these highly coupled nonlinear field equations, unless nonlinearities appearing in these equations are neglected. It is also pointed out that the possible presence of a large surface energy in the proposed model does not necessarily give rise to the so-called ''fine-tuning'' problem. Finally, we also outline briefly a few additional important aspects which may be useful for further understanding the proposed model.

On the role of a recoil effect in the bag model

The electromagnetic form factors of a proton and its static characteristicsare calculated on the basis of the Friedberg-Lee soliton bag model solution obtained in the covariant perturbation theory. The contributions due to the recoil effect are separated. In particular, the correction to the magnetic moment calculated in the cavity approximation turns out to be large and positive.

QCD at large Nc-Skyrme or the bag?

A framework for extracting the low-energy dynamics of pseudoscalar mesons from QCD at large N is developed and, to leading order in the decoupling of heavy mesons, the pure pseudoscalar theory is calculated truncated to four derivatives. The soliton is found not to be manifestly stabilized by the four derivative terms. Under a plausible assumption about the classical solution for the scalar meson field, a natural realization of the previously proposed topological soliton bag model is obtained.

Gluonic interactions in the soliton bag model.

Gluonic effects are included to lowest order in calculations using the soliton bag model. The N-\ensuremath{\Delta} splitting is calculated in the one-gluon-exchange approximation, using a gluon propagator which is confined by the \ensuremath{\sigma} field. The string constant is obtained, in the Abelian approximation, from a self-consistent calculation for a cylindrical system of \ensuremath{\sigma} and gluon fields. These results are used to fix the strong coupling constant ${\ensuremath{\alpha}}_{s}$. We obtain values for ${\ensuremath{\alpha}}_{s}$ which are \ensuremath{\sim}2, similar to those in the MIT bag model. Constraints are placed on both the model parameters and the dependence of the dielectric function on the \ensuremath{\sigma} field.

Nontopological and topological chiral soliton bags as a model of the nucleon

As a possible phenomenological model of nucleons, we examine a lagrangian which combines the features of the soliton bag model of T.D. Lee et al. and the nonlinear sigma model. The lagrangian is numerically solved in the semiclassical approximation for the hedgehog ansatz without linearization. Soliton solutions with winding numbers Z = 0 and 1 are examined as functions of the pion decay constant. The Z = 0 solution is similar to the cloudy bag model, but the Z = 1 solution, despite a smaller soliton bag radius, is quite different from the little (chiral) bag model. The latter solution is found to have a lower energy for realistic parameter values.

Free Field Dominance of Deep-Inelastic Structure Functions in a Nontopological Soliton Bag Model

Free Field Dominance of Deep-Inelastic Structure Functions in a Nontopological Soliton Bag Model

Low energy QCD — an introduction

The following contribution is an invited introduction for the low energy QCD sessions at this conference. It gives a short summary of QCD inspired models for low energy particle and nuclear physics. It summarizes first bag models from Bogolioubov to the cloudy bag. Then the soliton bag model of Friedberg and Lee and the Skyrmion bubble of Skyrme, Witten, Rho, Brown and others is mentioned. In the constituent quark model we dwell especially on the nucleon-nucleon interaction. Different explanations for the EMC-effect are discussed. Open questions are pointed out in the summary.

Chiral soliton-bag models with nonlinear pion fields

We show that treating the scalar field of a chiral soliton-bag model as the chiral partner of the pion leads in practice to a situation in which the soliton field is eliminated from the model in favor of nonlinear terms in the pion field. The pion is then the sole agency of confinement, and numerical solutions processing this property are presented. To avoid having the pion as the confinement mechanism one may introduce a separate scalar soliton field for this purpose and insure chirality through nonlinear pion terms in the lagrangian.

Soliton bag model with chiral dynamics: Colored Higgs mechanism

We describe a compact scheme which allows gluons to acquire large masses outside a bag, and only outside the bag, via the Higgs mechanism of a specific kind ("colored"). The proposed mechanism does not give rise to "unwanted" massless particles and yet maintains color gauge invariance. Accordingly, we demonstrate the feasibility of constructing a renormalizable soliton bag model with (or without) SU(2)\ifmmode\times\else\texttimes\fi{}SU(2) chiral dynamics explicitly built in by hand.

Excited states in the soliton bag model

Numerical analysis of the solutions of the soliton bag model of Friedberg and Lee is performed. The recent analysis of Goldflam and Wilets is extended to include even-parity as well as odd-parity radially excited states. It is shown that the existence of the solutions (especially the odd-parity ones) restrict severely the allowed range of parameters.

Boosting the bag

The Lorentz boost transformation for the soliton bag model is constructed in the mean-field approximation. Assuming that the standard static-bag wave function is equivalent to the zero-momentum eigenstate, the Lorentz boost transformation generates quark wave functions corresponding to a moving bag. We demonstrate that the mean-field energy and momentum of such a moving bag are related to the energy of the bag at rest by the correct Lorentz-transformation formulas. The boosted quark wave functions are used to investigate relativistic recoil corrections to hadronic form factors. Electromagnetic and axial-vector form factors are discussed, as well as the pion-nucleon vertex corresponding to a hybrid chiral bag model. Various types of bags (e.g., MIT type and SLAC type) are considered. It is shown that ignoring quark binding in the boost transformation leads to an overestimate of recoil corrections to magnetic moments. Relativistic recoil generally hardens the form factors. The proton charge radius is decreased by about 15% compared to the static-approximation values. The magnetic moment is changed by less than 10%. The inclusion of recoil corrections leads to reasonable agreement with experiment for all form factors considered if the bag radius (for an MIT bag) is about 1.3 fm. A comparison is made with other works on this topic.

Chiral invariance in the soliton bag model

The soliton bag model of quark confinement is shown to give the same pionic coupling as the cloudy bag model, explicitly independent of details of the soliton field. The Goldberger-Treiman relation is satisfied in this development.

Recoil corrections in bag models

The recoil corrections to bag models are considered using a definition of the center-of-energy operator analogous to the Newtonian concept of center of mass. This definition is used to calculate corrections to bag energy, charge radius, and other properties within the framework of the soliton bag model. Some of our results also apply directly to the MIT bag model and compare favorably with other analyses.

A silicon bag model with SU(2) × SU(2) chiral dynamics

We describe a soliton bag model which incorporates explicitly SU(2) × SU(2) chiral dynamics, including the conservation of the polar vector current, the partial conservation of the axial vector current, and the SU(2) × SU(2) current algebra. This model appears to be renormalizable so that higher order effects may be treated systematically.

Soliton bag model

The soliton bag model of Friedberg and Lee is investigated. We study in detail the numerical solution of the main-field limit of the model and develop quantum corrections to this approximation. Both the MIT and SLAC bags are recovered as limiting cases of the model. The surface bag excitations coupled to quark-antiquark excitations and their relation to the virtural-meson cloud as well as other aspects of the model are discussed.