Global Color Symmetry Model Research Articles

Temperature dependence of the effective bag constant and the radius of a nucleon in the global color symmetry model of QCD

We study the temperature dependence of the effective bag constant, the mass, and the radius of a nucleon in the formalism of the simple global color symmetry model in the Dyson-Schwinger equation approach of QCD with a Gaussian-type effective gluon propagator. We obtain that, as the temperature is lower than a critical value, the effective bag constant and the mass decrease and the radius increases with the temperature increasing. As the critical temperature is reached, the effective bag constant and the mass vanish and the radius tends to infinity. At the same time, the chiral quark condensate disappears. These phenomena indicate that the deconfinement and the chiral symmetry restoration phase transitions can take place at high temperature. The dependence of the critical temperature on the interaction strength parameter in the effective gluon propagator of the approach is given.

Non-perturbative Aspects of QCD and Parameterized Quark Propagator

Based on the Global Color Symmetry Model, the non-perturbative QCD vacuum is investigated in the parameterized fully dressed quark propagator. Our theoretical predictions for various quantities characterized the QCD vacuum are in agreement with those predicted by many other phenomenological QCD inspired models. The successful predictions clearly indicate the extensive validity of our parameterized quark propagator used here. A detailed discussion on the arbitrariness in determining the integration cut-off parameter of μ in calculating QCD vacuum condensates and a good method, which avoided the dependence of calculating results on the cut-off parameter is also strongly recommended to readers.

Baryon structure in the global color symmetry model of QCD

Baryons are considered as solitons in the global color symmetry model (GCM) of QCD. With both the scalar and pseudoscalar chiral fields being included and the Hedgehog approximation being taken, we obtain a GCM soliton profile whose mass and radius are quite close to the experimental data of a nucleon. We then quantize the angular momentum and isospin with the collective quantization method and obtain a nucleon-Delta mass split comparable with experimental data.

Study of Strange Quark Mass in CFL Phase

In this paper we introduce bilocal fields in the globalcolor symmetry model and consider color and electricalneutrality conditions simultaneously to study the effect of strangequark mass MS for the momentum-dependent condensate ofcolor-flavor locked phase. Consequently we find thatthere will be a quantum phase transition occurring.

Quark Loop Effects on Dressed Gluon Propagator inFramework of Global Color Symmetry Model

Based on the global color symmetry model (GCM), a method forobtaining the quark loop effects on the dressed gluon propagatorin GCM is developed. In the chiral limit, it is found that thedressed gluon propagator containing the quark loop effectsin the Nambu–Goldstone and Wigner phases are quite different.In solving the quark self-energy functions in the two differentphases and subsequent study of bag constant one should use the abovedressed gluon propagator as input. The above approach forobtaining the current quark mass effects on the dressedgluon propagator is quite general and can also be used to calculatethe chemical potential dependence of the dressed gluonpropagator.

Soliton with a pion field in the global color symmetry model

We calculate the property of the global color symmetry model soliton with the pion field being included explicitly. The calculated results indicate that the pion field provides a strong attraction so that the eigen-energy of a quark and the mass of a soliton reduce drastically, in contrast to those with only the sigma field.

Mixed tensor susceptibility of the QCD vacuum from effective quark–quark interactions

We calculate the mixed tensor susceptibility of QCD vacuum in the framework of the global color symmetry model. In our calculation, the functional integration over gluon fields can be performed and the gluonic vacuum observable can be expressed in terms of the quark operators and the effective gluon correlator. The mixed tensor susceptibility was obtained with the subtraction of the perturbative contribution which is evaluated by the Wigner solution of the quark gap equation. Using several different effective quark–quark interaction models, we find the values of the mixed tensor susceptibility are very small.

Density dependence of nucleon radius and mass in the global color symmetry model of QCD with a sophisticated effective gluon propagator

Making use of the global color symmetry model (GCM) at finite chemical potential and with a sophisticated effective gluon propagator, the density dependence of the bag constant, the total energy and the radius of a nucleon in nuclear matter is investigated. A maximal nuclear matter density for the existence of the bag with three quarks confined within is given as about 8 times the normal nuclear matter density. The calculated results indicate that, before the maximal density is reached, the bag constant and the total energy of a nucleon decrease, and the radius of a nucleon increases, with the increasing of the nuclear matter density. As the maximal nuclear matter density is reached, the mass and the bag constant of the nucleon vanish and the radius becomes infinite suddenly. It manifests that a phase transition from nucleons to quarks takes place. Meanwhile, shortening the interaction range among quarks can induce the phase transition to happen easier.

Mixed quark–gluon condensate at finite temperature and density in the global color symmetry model

We study the properties of mixed quark–gluon condensate at finite temperature and chemical potential in the framework of global color symmetry model. In comparing with the quark condensate, we confirm that both of these condensates give the same information about chiral phase transition. We also find that the ratio of these two condensates is insensitive to the temperature T and the chemical potential μ, which supports the conclusion obtained recently by the authors using quenched lattice QCD.

Quark condensates in nuclear matter in the global color symmetry model of QCD

With the global color symmetry model being extended to finite chemical potential, we study the density dependence of the local and nonlocal scalar quark condensates in nuclear matter. The calculated results indicate that the quark condensates increase smoothly with the increasing of nuclear matter density before the critical value (about 12$\rho_0$) is reached. It also manifests that the chiral symmetry is restored suddenly as the density of nuclear matter reaches its critical value. Meanwhile, the nonlocal quark condensate in nuclear matter changes nonmonotonously against the space-time distance among the quarks.

Reevaluation of the density dependence of nucleon radius and mass in the global color symmetry model of QCD

With the global color symmetry model (GCM) at finite chemical potential, the density dependence of the bag constant, the total energy and the radius of a nucleon in nuclear matter is investigated. A relation between the nuclear matter density and the chemical potential with the action of QCD being taken into account is obtained. A maximal nuclear matter density for the existence of the bag with three quarks confined within is given. The calculated results indicate that, before the maximal density is reached, the bag constant and the total energy of a nucleon decrease, and the radius of a nucleon increases slowly, with the increasing of the nuclear matter density. As the maximal nuclear matter density is reached, the mass of the nucleon vanishes and the radius becomes infinite suddenly. It manifests that a phase transition from nucleons to quarks takes place.

Calculation of vacuum properties from the global color symmetry model

A modified method for calculating the non-perturbative quark vacuum condensates from the global color symmetry model is derived. Within this approach it is shown that the vacuum condensates are free of ultraviolet divergence which is different from previous studies. As a special, the two-quark condensate and the mixed quark-gluon condensate are calculated. A comparision with the results of the other nonperturbative QCD approaches is given.

Tensor susceptibility of the QCD vacuum from an effective quark–quark interaction

With an effective quark–quark interaction in the global color symmetry model, the tensor susceptibility of QCD vacuum is calculated. The values we obtained are much smaller than the estimations from QCD sum rules and from chiral constituent quark model.

QCD Sum Rule External Field Approach and Vacuum Susceptibilities**The project supported in part by National Natural Science Foundation of China under Grant Nos. 19975062, 10175033, and 10135030

Based on QCD sum rule three-point and two-point external field formulas respectively, the vector vacuum susceptibilities are calculated at the mean-field level in the framework of the global color symmetry model. It is shown that the above two approaches of determination of the vector vacuum susceptibility may lead to different results. The reason of this contradiction is discussed.

The Mixed Quark-Gluon Condensate from the Global Color Symmetry Model**The project supported in part by National Natural Science Foundation of China under Grant Nos 19975062, 10175033 and 10135030

The mixed quark-gluon condensate from the global color symmetry model is derived. It is shown that the mixed quark-gluon condensate depends explicitly on the gluon propagator. This interesting feature may be regarded as an additional constraint on the model of gluon propagator. The values of the mixed quark-gluon condensate from some ansatz for the gluon propagator are compared with those determined from QCD sum rules.

The π and Tensor Vacuum Susceptibilities from the Global Color Symmetry Model**The project supported in part by National Natural Science Foundation of China under Grant Nos. 19975062, 10175033, and 10135030

A modified method for calculating the nonperturbative quark vacuum condensates from the global color symmetry model is derived. Within this approach it is shown that the treatment of quark vacuum condensates is different from that in the previous studies. As a special case we calculate the π and tensor vacuum susceptibilities. A comparison with the results of the other nonperturbative QCD approaches is given.

Nonperturbative aspects of axial vector vertex in the global color symmetry model

The relation between the axial vector current of current quark and that of constituent quark has been studied within the framework of the global color symmetry model. Gluon dressing of the axial vector vertex and the quark self-energy function are described by the inhomogeneous Bethe-Salpeter equation in the ladder approximation and the Schwinger-Dyson equation in the rainbow approximation, respectively.

Nonperturbative Aspects of Axial Vector Vertex**The project supported in part by National Natural Science Foundation of China under Grant Nos 19975062 and 10135030

It is shown how the axial vector current of current quarks is related to that of constituent quarks within the framework of the global color symmetry model. Gluon dressing of the axial vector vertex and the quark self-energy functions are described by the inhomogeneous Bethe–Salpeter equation in the ladder approximation and the Schwinger–Dyson equation in the rainbow approximation, respectively.

The Effect of Retardation on the Spontaneous Breaking of Chiral Symmetry in GCM**The project supported in part by National Natural Scirnce Foundation of China (19875002)

An effective Hamiltonian including current-current coupling from the global color symmetry model is derived. Retardation effects are introduced by the factor , instead of in the correlation kernel, from which the retardation gap equation with coupling in the vacuum is obtained, condensations of different retardation parameters with or without the term are calculated. The results show the effects of retardation,and indicate that the typical value of is about at reasonable value of condensation. And while taking typical value of of, the condensation is about 13% larger than that with no retardation effect. With the terms, the condensation is about 17% larger than that without it for all values of the parameter . This shows that the retardation effects and the terms are important for further studying in the Iow-energy region.

Density dependence of nucleon bag constant, radius and mass in an effective field theory model of QCD

With the global color symmetry model (GCM) being extended to finite chemical potential, the density dependence of the bag constant, the total energy and the radius of a nucleon, as well as the quark condensate in nuclear matter are investigated. A maximal nuclear matter density for the existence of the bag with three quarks confined within is obtained. The calculated results indicate that, before the maximal density is reached, the bag constant, the total energy of a nucleon and the quark condensate decrease gradually, and the radius of a nucleon increases, with the increasing of the nuclear matter density. Nevertheless no sudden change emerges. As the maximal nuclear matter density is reached, a phase transition from nucleons to quarks takes place and the chiral symmetry is restored.