Color Dielectric Model Research Articles

NUCLEON PROPERTIES IN CHIRAL COLOR DIELECTRIC MODEL

The chiral extension of color dielectric model has been used to study the static properties of nucleon. In this calculation we have treated the gluon and the pion fields perturbatively. It is found that the neutron charge rms radius and the pion-nucleon coupling constant are almost insensitive to the parameters used and are in excellent agreement with the experimental values. For better fitting the proton charge rms radius, nucleon magnetic moments and axial coupling constant prefer large quark masses (~100 MeV) and small glueball masses (<1100 MeV). The strong coupling constant is found to be very sensitive to the quark and glueball masses.

Deconfinement and chiral symmetry restoration in the color-dielectric model

We investigate the structure of the vacuum and the behavior of uniform quark matter at high density in the color-dielectric model for SU (3) c. We extend the original formulation of the color-dielectric model first to take care of chiral symmetry (by use of the σ-model) and second to include negative energy orbitals. At high baryonic density the model describes the two phase transitions which are expected in QCD: deconfinement of quarks and chiral symmetry restoration.

Chiral symmetry breaking in the colour dielectric model

Approximating the long-distance gluon dynamics ofSU(3)colour by colour-dielectric block-spin variables, we obtain an effective QCD theory of a scalar colour-dielectric field and a massive colour-bleached gluon field coupled to light quarks. The massive vector field produces a strong attraction betweenq\(\bar q\) pairs, which leads toq\(\bar q\) condensation when the colour-dielectric field becomes small. We calculate\(\left\langle {\bar \psi \psi } \right\rangle\) and the pion decay constantf n as a function of the dielectric field expectation value, by evaluating the fermion determinant in a derivative expansion, and integrating out the bosonic variables. We find that the effective quark-gluon coupling,α s eff , including quark effects, is large on the surface of bags, where\(\left\langle {\bar \psi \psi } \right\rangle\) ±0, but decreases inside hadronic bags, where |\(\left\langle {\bar \psi \psi } \right\rangle\)| is decreasing.

Hyperons and the H-particle in the color dielectric model

The masses of hyperons and the H-particle are calculated in the color dielectric model within a framework of self-consistent calculation of quarks, color dielectric field and effective gluon. Reasonably good agreements are obtained concerning the masses of hyperons by adjusting a mass parameter of the strange quark. The calculated magnetic moments agree well with the observed values for octet baryons except for the nucleon. The binding energy of the H-particle is estimated to be in the range from 100 MeV to 210 MeV depending on models used. The color magnetic energy is found to give rise to a repulsive force in the ΛΛ channel, in marked contrast to the result of the MIT bag model.

Proton-neutron mass slitting in the colour-dielectric model

The isospin-symmetry breaking contribution to the proton-neutron mass difference is calculated in a chirally symmetric version of the colour-dielectric model. The basic mechanism is a small difference in the effective constituent up- and down-quark masses which originates in an explicit chiral symmetry breaking term and whose magnitude is determined by the charged-uncharged kaon mass splitting. The result for the model in which the quarks couple to the inverse of the glueball field is M n− M p=2.4±0.5 MeV, where the error reflects only the input data (the experimental value is 1.29 MeV). The baryon mass spectrum is also estimated using the same methods. The results are satisfactory for the case of inverse quark-glueball coupling. They are much less satisfactory for the case of inverse-square coupling. This provides the first example of a prediction which is able to distinguish between these two cases.

Color-dielectric-model nucleon in the nuclear medium.

The color-dielectric model has been used to study the behavior of nucleons in the nuclear medium. Assuming that the nuclear medium generates a background color-dielectric field and a scalar density of quarks, the equations of motion of the quark and the color-dielectric field are solved in the presence of the background fields. The properties of the nucleon in the nuclear medium are then calculated from these solutions. The calculations show that the nucleon swells in the nuclear medium and the quark eigenenergy decreases. It is found that when the nuclear density is more than 0.08 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}3}$, bound quark states do not exist, thus implying that the nucleon dissolves into quark matter.

Repulsive core effect of the nucleon in the color dielectric model

Bag models of hadrons inspired by quantum chromodynamics have a problem in that it is difficult to realize the hard-core repulsion between nucleons without corrections, and the nucleon collapses. We include into the color dielectric model pions, effects of one-gluon exchange and a center-of-mass correction, and investigate how they contribute to the repulsive core by comparing masses of a three-quark bag and of a six-quark bag. Results of numerical calculations show that to make the nucleon stable without zero-point energy one has to take a weak coupling for pions, which suggests a cloudy-bag-like picture rather than a chiral-bag-like one. If, however, one prefers the latter picture which is in better agreement with physical observables in this model, one then has to include the zero-point energy in some way.

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.

ACAUSALITY IN COLOR DIELECTRIC MODELS

It is shown that color dielectric models may lead to acausal behavior in the gluon sector. A solution to this problem is suggested.

Gluonic effects in color dielectric model: (II). Effective quark mass and color dielectric function

We study generalized versions of the Nielsen and Patkós color dielectric model with an effective quark mass m q(χ) = m q χ τ and a dielectric function k( χ) = χ β . Gluonic effects are studied in this model with both perturbative and self-consistent calculations. In the case of τ = 0.5 and β = 2, it is shown that the perturbative gluonic effects are too strong to obtain a reasonable description of N and Δ. The choice of τ = 2 and β = 4 is shown to give a reasonable agreement of the masses of N and Δ with their observed ones. Taking into account the results in our previous paper, it is therefore suggested that the choice of τ: β = 1:2 is superior to that of 1:4, the latter of which corresponds to the Nielsen and Patkós model.

Quark matter in the colour-dielectric model

The properties of cold, two-flavour, quark matter are considered in a simple colour-dielectric model. If the soliton solutions of the same Hamiltonian are identified with nucleons, one finds that the one relevant parameter for the quark matter problem is determined uniquely. Results for quark matter are then independent of the mass of the chi field. In addition, this observation lead to useful scaling laws in the soliton sector.

Tensor coupling of the rho meson in a chiral confining model.

Both the field current identity and universal coupling imply that the isovector part of the anomalous magnetic moment of the nucleon, {kappa}{sub {ital v}}, is equal to the tensor coupling of the {rho} meson, {kappa}{sub {rho}}. However, the empirical value of {kappa}{sub {rho}}/{kappa}{sub {ital v}} extracted through dispersion relation is 1.78. In this paper we show that a color dielectric model can explain in a natural way why the ratio {kappa}{sub {rho}}/{kappa}{sub {ital v}}{gt}1. We study a chirally invariant color dielectric model. We point out that a fractional power of the color dielectric function should be present in the quark-meson interaction term. The quark part of the {rho} meson current, modified by this factor, is {ital structurally} different from the isovector part of the electromagnetic current. Both the magnetic-moment-like quantity, {mu}{sub ({rho})}, and the {rho}-nucleon coupling constant, {ital g}{sub {rho}{ital N}{ital N}}, are modified making {kappa}{sub {rho}}=({mu}{sub ({rho}){ital p}}{minus}{mu}{sub ({rho}){ital n}})(2{ital M}/{ital g}{sub {rho}{ital N}{ital N}}){minus}1 different from {kappa}{sub {ital v}} and, indeed, larger than {kappa}{sub {ital v}}. The numerical value of the ratio {kappa}{sub {rho}}/{kappa}{sub {ital v}} is found to be 1.35, quite independent of the details of the model. It appears that some additional mechanism is needed tomore » fit the value 1.78.« less

Gluonic effects in the color dielectric model

Gluonic effects in the Nielsen and Patkós color dielectric model are studied with both perturbative and self-consistent calculations. In the perturbative calculations, the gluonic effects are found to depend sensitively on the behavior of the color dielectric field X and thus distinguish the one phase and two phase solutions found by Dodd, Williams and Thomas. The dielectric functional κ( x) = x 4 proposed by Nielsen and Patkós is shown to be too singular for the residual gluonic effects to be perturbative. It is shown by performing fully self-consistent calculation with the gluon field that κ( x) = x 2 is more favorable for this purpose.

Color-dielectric models from a lattice point of view.

We study the color-dielectric model, introduced by Nielsen and Patkos, using lattice gauge theory. We argue that the collective color-dielectric field, which is introduced by a block-spinning method, approaches zero in the vacuum for confining theories for a sufficiently large averaging size of the block-spinning box, as a consequence of the area-law behavior of Wilson loops. Increasing the box size increases the effective potential height for quarks, but decreases the resolving power of the effective theory. Estimates show that there exists an optimal choice of the size of the box suitable for a mean-field description of hadrons within the color-dielectric models with confinement. This yields a limit for the maximum momentum scales for which these models are applicable. This limit poses no difficulties for construction of phenomenological models.

Momentum projection of the nucleon in the colour-dielectric model

We use the method of Lübeck et al. to project the mean-field solutions of the colour-dielectric model onto momentum eigenstates, so removing the spurious c.m. motion. A coherent state is used to provide a quantum description of the colour-dielectric field. In addition the nucleon mass is varied after projection. A range of parameter sets is considered, but we find that this technique is only appropriate to those with a simple quadratic potential. These results show a significant improvement over the mean-field approximation, the product of the proton mass and r.m.s. radius being within 30% of its observed value. Projection of solutions for a double-minimum potential results in a mass-radius project which is an order of magnitude too small, due to the high mean-square momentum in the soliton approximation. We conclude that the MFA is not a good starting point for parameter sets of this kind.

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.

Chiral nontopological solitons with perturbative quantum pions.

We investigate chiral extensions of a broad class of nontopological soliton bag models. Chiral symmetry is restored in a nonlinear realization through the introduction of an elementary pion field. We show in particular that it is consistent to treat the pions as a perturbative quantum field, as is done in the cloudy-bag model. The cloudy-bag model is recovered as a limiting case. A careful comparison is made between predictions of chiral extensions of the Friedberg-Lee and the Nielsen-Patkos color-dielectric nontopological soliton models and the cloudy-bag model. Once the overall distance scale is fixed we find relative insensitivity to the detailed choice of nontopological soliton parameters. We investigate two versions of chiral nontopological solitons, analogous to the surface- and volume-coupled cloudy-bag model, and discuss their relation to current algebra.

Roper resonance in a color dielectric model

Radial excitations of baryons are studied in the framework of a color dielectric model. An analogue of the RPA technique is used to describe coupled vibrations of valence quarks and the background “glueball” field. The excitation energy of the Roper resonance is found to be in the range 300–350 MeV. It is also established that the solitons in the color dielectric model are classically stable with respect to radial vibrations.

Numerical study of a confining color-dielectric soliton model.

Using the numerical methods recently suggested by Dodd and Lohe, we have made an accurate and detailed study of (nontopological) soliton solutions in a particular color-dielectric model. The coupling of the quarks to the confining scalar field in this model leads to absolute confinement and strong dependence of the soliton properties on the quark masses. The nucleon is well described as a two-phase soliton over a wide range of input parameters. Single-phase soliton solutions, where the confining field is everywhere close to its vacuum value, are also presented for comparison. A striking property of this model is that over a narrow range of input parameters, where the transition from one to two phase solutions occurs, three separate solutions (close in energy) coexist. The associated fold in solution space is explored.

Nuclear binding and quark confinement.

We present a schematic solution of the color dielectric model for the nucleon and demonstrate how the nucleon can be bound in nuclear matter. The gluon field surrounding the bound nucleon is obtained from the linearized field equations of motion in the color dielectric. This schematic model of the baryon allows a comparison of the neutron and proton mass in the nucleus. We calculate the Nolen-Schiffer anomaly for several light nuclei.