Soliton Bag Model Research Articles

Geometric Confinement in Gauge Theories

In 1978, Friedberg and Lee introduced the phenomenological soliton bag model of hadrons, generalizing the MIT bag model developed in 1974 shortly after the formulation of QCD. In this model, quarks and gluons are confined due to coupling with a real scalar field ρ, which tends to zero outside some compact region S⊂R3 determined dynamically from the equations of motion. The gauge coupling in the soliton bag model runs as the inverse power of ρ, already at the semiclassical level. We show that this model arises naturally as a consequence of introducing the warped product metric dsM2+ρ2dsG2 on the principal G-bundle P(M,G)≅M×G with a non-Abelian group G over Minkowski space M=R3,1. Confinement of quarks and gluons in a compact domain S⊂R3 is a consequence of the collapse of the bundle manifold M×G to M outside S due to shrinking of the group manifold G to a point. We describe the formation of such regions S as a dynamical process controlled by the order parameter field ρ.

A variational study of some hadron bag models

Quantum chromodynamics (QCD) is the theory of strong interaction and accounts for the internal structure of hadrons. Physicists introduced phe- nomenological models such as the M.I.T. bag model, the bag approximation and the soliton bag model to study the hadronic properties. We prove, in this paper, the existence of excited state solutions in the symmetric case and of a ground state solution in the non-symmetric case for the soliton bag and the bag approximation models thanks to the concentration compactness method. We show that the energy functionals of the bag approximation model are Gamma -limits of sequences of soliton bag model energy functionals for the ground and excited state problems. The pre- compactness, up to translation, of the sequence of ground state solutions associated with the soliton bag energy functionals in the non-symmetric case is obtained combining the Gamma -convergence theory and the concentration-compactness method. Finally, we give a rigorous proof of the original derivation of the M.I.T. bag equations done by Chodos, Jaffe, Johnson, Thorn and Weisskopf via a limit of bag approximation ground state solutions in the spherical case. The supersymmetry property of the Dirac operator is the key point in many of our arguments.

Soliton solutions of an improved quark mass density-dependent model at finite temperature

The improved quark mass density-dependent model (IQMDD) based on soliton bag model is studied at finite temperature. Applying the finite temperature field theory, the effective potential of the IQMDD model and the bag constant $B(T)$ have been calculated at different temperatures. It is shown that there is a critical temperature ${T}_{C}\ensuremath{\simeq}110\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$. We also calculate the soliton solutions of the IQMDD model at finite temperature. It turns out that when $T<{T}_{C}$, there is a bag constant $B(T)$ and the soliton solutions are stable. However, when $T>{T}_{C}$ the bag constant $B(T)=0$ and there is no soliton solution, therefore, the confinement of quarks are removed quickly.

On the parameters of the Friedberg-Lee soliton model

It is pointed out that in using the Friedberg-Lee nontopological soliton bag model to study the properties of hadrons, caution should be exercised in choosing the parameters of the model. Arbitrary choice of parameters may lead to a mathematically acceptable solution to a problem, but such a solution may have little or no physical significance.

AN ESTIMATE OF CENTRE-OF-MASS EFFECTS IN QUARK POTENTIAL MODELS

The correction to the mass for the spurious centre-of-mass motion in a three-quark system is calculated exactly in the nonrelativistic constituent quark model for the Cornell potential. The result is somewhat higher than MIT bag model estimates but similar to that of a soliton bag model and a relativistic oscillator model.

Soliton Solutions of F-L Model in the Whole Range of Temperature and Deconfinement Transition

The non-topological soliton bag model of Friedberg and Lee (F-L model), whichis developed by Goldflam and Wilets and others, has been much successful indescribing phenomenologically the static properties of hadrons and their behavior atlow energy. Particularly, with the finding of the numerical soliton solution for thespecial case of temperature being zero and bag constant B=0~+, the model affordsus a very intuitive physical explanation of the color confinement in QCD theory.For other different values of B, especially for non-trivial temperature, someinvestigation on the deconfinement transition has been made in Ref.[3], etc. byanalyzing the variation condition in which soliton solutions exist, but it remains to besettled to find the concrete solutions. In this note, we will solve directly the soliton

Excited states of the nucleon within the Friedberg-Lee model

The radially excited even-parity as well as odd-parity states of the nucleon are studied within the framework of the Friedberg-Lee nontopological soliton bag model for hadrons. The one-gluon exchange term of the model is iterated self-consistently, together with the quark and the soliton fields. The parameters of the model were determined earlier by fitting the masses of the nucleon and delta. It is found that the solutions to the excited states exist only for a limited range of the parameters. It is also found that the calculated masses of the even-parity state is larger than that of the odd-parity state, which is contrary to their experimental values.

Nontopological solitons

The use of nontopological solitons to model the quark structure of hadrons is reviewed. The soliton bag, chiral quark-meson and colour-dielectric models are described and the connections and differences between the chiral quark-meson, Nambu-Jona-Lasinio and Skyrme models are outlined. The models fall into two basic classes: those in which hidden chiral symmetry plays a major role, and those in which confinement dominates. The latter include colour-dielectric models and their chiral extensions involving mesons.

Vertex Decoupling and Quark Deconfinement in Soliton Bag Model at Finite Temperature

By means of the Matsubara Green's function method, we investigate the temperature dependence of coupling constant gqqσ in soliton bag model. We find gqqσ will decrease as temperature increases in high temperature region and will approach zero at critical temperature. Tc. The quark deconfinement phase transition in soliton bag model is discussed.

Soliton bag model and the EMC effect

Based on the Friedberg-Lee soliton bag model with consideration of the Fermi motion (including the effect of nucleon’s binding) we study mainA-dependence of the ratio of the structure function for bound and free nucleons in terms of a model in which bound nucleons have a slightly larger size than free nucleons. With our improved model, the theoretical curves are in good agreement with the experimental data. An empirical formula has been given about the effective radius of the quarks’ confinement region of a bound nucleonR A with atomic weightA and we also have discussed the influence of the masses of quarks upon the EMC effect.

Nonsymmetric Kaluza-Klein and Jordan-Thiry theory in a general non-Abelian case

This paper is devoted to an (n+4)-dimensional unification of NGT (nonsymmetric gravitation theory) and Yang-Mills theory in a Jordan-Thiry manner. We find “interference effects” between gravitational and Yang-Mills fields which appear to be due to the skew-symmetric part of the metric on the (n+4)-dimensional manifold (nonsymmetrically metrized principal fiber bundle). Our unification, called the nonsymmetric-non-Abelian Jordan-Thiry theory, becomes classical if the skew-symmetric part of the metric is zero. We find the Yang-Mills field Lagrangian up to the second order of approximation inh μν =g μν −η μν . We also deal with the Lagrangian for the scalar field (connected to the “gravitational constant”). We consider the spin content of the theory and a relationship between the cosmological constant and the coupling constant between the skewon field and the gauge field in the first order of approximation. We show how to derive a dielectric model of a confinement from “interference effects” in these theories. We underline some similarities between the nonsymmetric Jordan-Thiry Lagrangian in the flat space limit and the soliton bag model Lagrangian.

Soliton Matter

Although quantum chromodynamics is generally accepted as the fundamental theory of the strong interactions, there exist no solutions to the theory which describe the binding of quarks to form the observed particles of nuclear physics. Soliton bag models of hadronic matter attempt to capture the main features of quark confinement, while remaining amenable to calculation. In the context of the non-topological soliton model, nuclear matter is regarded as a collection of quark clusters arranged on a regular lattice in bag-like soliton structures. The conjectured phase transition of nuclear matter to quark plasma at high densities is then modelled as the melting of the soliton crystal under compression. This paper reviews some recent results on multi-soliton solutions of the linear sigma model in one space and one time dimension. Remarkably, exact periodic soliton solutions can be derived in terms of complete Jacobi elliptic integrals for arbitrarily large lattices. The conditions for a phase transition in the model, and implications for more realistic calculations are discussed.

Translational invariance in the color dielectric model

So far we have utilized the mean-field approximation (MFA) in order to obtain solutions of the hadron self-consistently and numerically from the soliton bag model lagrangian. Since the solutions are static and localized, they break the translational symmetry. We employ the color dielectric model, which gives a picture of a hadron with an absolute confinement of quarks. In order to restore this symmetry, we apply the projection method with the coherent-state approximation for the soliton field, and the effects of the quantum fluctuations are estimated to the lowest order of the gaussian moments expansion (VAP). The solution of the equations of motion derived from the approximate expression for the mass is reentered into the exact expression. Since we neglect the higher-order terms of the gaussian moments expansion, a further variation is needed, which we characterize by one parameter (VAVAP). The final solution gives the same value for the static mass and the dynamical mass. We also investigate how the values of the physical quantities change when the variation is done before and after the momentum projection.

Deconfinement phase transition and disappearance of the soliton solution in a nontopological soliton bag model.

Based on the nontopological soliton model, a new picture for the deconfinement phase transition is proposed. The relation between the existence of the soliton solution and the nonlinearity of the potential function is analyzed. The effective potential and the equation satisfied by its extrema are given at finite temperature. It turns out that, in this model, at a critical temperature ${T}_{c}$ the physical vacuum is transformed into a perturbative vacuum, the soliton solution disappears, and the deconfinement transition occurs.

Self-consistent mean-field wavefunctions of nucleon and delta for the cranked Chiral soliton bag

The mean-field equations of the chiral soliton bag model are solved numerically on a full three-dimensional grid by solving the corresponding finite difference equations self-consistently. The spherical hedgehog configuration is found to be the ground state even if deformation degrees of freedom for all fields are allowed for. Individual states describing the nucleon and the delta resonance are obtained using the cranking formalism in isospace. The classical instability of the pion field, which occurs as soon as the angular frequency is larger than the pion mass, is taken into account by an explicit treatment of the asymptotic meson tails for smaller frequencies. A comparison with the perturbative approach used by other authors is given. As an alternative approach we present calculations for baryon states built up from single-quark states of sharp spin and isospin coupled to the corresponding total quantum numbers. As a consequence of the wrong spin-isospin dependence of the short-range qq interaction mediated by the chiral meson fields a negative mass splitting between nucleon and delta is found. Implications on other approaches are discussed.

The spin structure of the proton

The spin dependent structure function g p 1( x) and g n 1( x) are calculated using a momentum projected version of the soliton bag model. The results are evolved to high Q 2 using QCD perturbation theory for the nonsinglet distribution g p 1( x)− g n 1( x). Following Jaffe, we assume that the isosinglet contribution to g 1( x) is negligible at high Q 2, enabling us to compare our calculation with recent EMC data. We find remarkable agreement between experiment and the model, which lends support to the idea that the flavor singlet distribution g s 1( x) is very small.

Valence quark distributions in the soliton bag model

Valence quark distributions are calculated in a momentum projected version of the soliton bag model. These distributions are evolved to Q 2=15 GeV 2 using QCD perturbation theory, where they are compared with experiment. Substantial agreement is achieved.

CRANKING THE CHIRAL SOLITON BAG MODEL: GLUONIC EFFECTS

The nucleon-delta mass difference is computed in the chiral soliton bag model with soft confinement of gluons by the cranking method. The resulting value of the effective strong fine structure constant is αs≃0.7.

Chiral colour dielectric model of the nucleon

Abstract We apply the colour dielectric model to the nucleon including the chiral symmetry by the linear sigma model. The results of numerical calculations show that as the quark-meson coupling becomes stronger, the chiral symmetry breaking phase inside the bag changes to the restoring phase. The hedgehog solution is projected onto the spin-isospin eigenstate by means of the collective coordinate method, and we study some static properties of the nucleon. Except for the proton magnetic moment, the observed static properties favour strong quark-meson coupling and light glueball mass (∼1 GeV) giving a “chiral bag” like solution. The calculated values of the observables are similar to those of the chiral soliton bag model with the topological number: Z = 1.

A Vibrational Bag Model for Baryons

Surface monopole vibration of baryons is investigated on the basis of the soliton bag model. We derive a relativistic Lagrangian for the surface motion whose mass parameter is proportional to square of the bag radius. With the use of the WKB approximation, the energy spectra of P11 and P33 resonances are reproduced by our model fairly well. The static properties of the nucleon are also studied in our vibrational bag model and compared with those of the static bag model. Our model predicts that the nucleon consists of the central high-density part and the surounding low-density part. It is also shown that our model is capable to predict the experimental data as well as the static bag model.