Global Color Symmetry Model Research Articles

The Effect of Quark Mass and α-α Term on Condensation in QCD Vacuum**The project supported in part by National Natural Science Foundation of China (19875002)

Beginning with the QCD Lagrangian in the global color symmetry model, we have derived a Hamiltonian including the lowest order current-current coupling. Taking instantaneous quadratic interaction kernel and using the Bogoliubov–Valatin transformation, we have got an effective Hamiltonian for computation. This Hamiltonian is similar to that introduced by Le Yaouanc et al., except that the α-α term has been considered here. We calculated the condensation in the BCS type of vacuum with quark mass and α-α term included. Our calculation shows that the value of condensation has increased by at least 10% with the α-α term included.

Calculation of Some Properties of Vacuum and π, σ Mesons in the Global Color Symmetry Model**The project supported in part by National Natural Science Foundation of China and Nanjing University Talent Development Foundation

Based on the quark propagator derived in the instanton dilute liquid approximation, the quark condensate , the mixed quark gluon condensate , the four-quark condensate and tensor, pion vacuum susceptibilities have been calculated at the mean-field level in a nonperturbative QCD model. The numerical results are compatible with the values obtained within other nonperturbative approaches. The calculated masses and decay constants of π and σ mesons are close to the experimental values. These results show that the instanton medium might be a good approximation of the QCD vacuum.

Pion Susceptibilities of the Vacuum in a Modified Global Colour Symmetry Model**The project supported in part by National Natural Science Foundation of China and Nanjing University Talent Development Foundation

Based on a modified version of the global color symmetry model, the pion susceptibilities of vacuum needed in the QCD sum rule external-field method for the coupling of pseudoscalar current to hadron have bean calculated beyond the vacuum saturation approximation. Comparison with the previous estimations has been given.

Vacuum Condensates from the Modification of Global Color Symmetry Model**The project supported in part by National Natural Science Foundation of China and Nanjing University Talent Development Foundation

Based on the quark propagator in the instanton dilute liquid approximation, we have determined the quark condensate , the mixed quark gluon condensate and the four-quark condensate at the mean-field level in the framework of global color symmetry model. The numerical calculation shows that our result is compatible with the range obtained within other nonperturbative approaches. In particular, we have found that even at the mean-field level the naive vacuum saturation approximation is not a good approximation when we consider nonlocal four-quark condensate.

Nonlocal Four-Quark Condensate and Vacuum Susceptibilities**The project supported in part by National Natural Science Foundation of China

Based on the quark propagator in the instanton dilute liquid approximation, we have determined the nonlocal four-quark condensate at the mean-field level in the framework of global color symmetry model. By making use of this formula, the vacuum susceptibility (pionsusceptibility) was calculated in this paper. The theoretical analysis and numerical calculation show that even at the mean-field level the naive vacuum saturation approximation is not a good approximation when we consider nonlocal four-quark condensate.

The Effective Gluon Propagator in the Global Color Symmetry Model**The project partially supported by National Natural Science Foundation of China

It is shown that the effective gluon propagator in the global color symmetry model can be calculated in the instanton dilute liquid approximation. The calculated effective gluon propagator is consistent with the general command on the qualitative features of the gluon propagator, i.e., (i) the gluon propagator is significantly enhanced at small space-like and (ii) for the perturbative results are quantitatively reliable.

Vacuum condensates in the global color symmetry model

Based on the quark propagator in the instanton dilute liquid approximation, we calculate analytically the quark condensate $<\bar{q}q>$, the mixed quark gluon condensate $g_{s}<\bar{q}G_{\mu\nu}\sigma^{\mu\nu}q>$ and the four quark condensate $<\bar{q} \Gamma q\bar{q} \Gamma q>$ at the mean field level in the framework of global color symmetry model. The numerical calculation shows that the values of these condensates are compatible with the ranges determined by other nonperturbative approaches. Moreover, we find that for nonlocal four quark condensate the previous vacuum saturation assumption is not a good approximation even at the mean field level.

Quark-Quark Interaction with Confinement Terms in a QCD-Based Model Field Theory**The project partly supported by National Natural Science Fountion of China

Based on the determined bilocal field in the global color symmetry model, the effective quark-quark interaction is deduced explicitly in this letter. The result shows that, except for the normal one-π and one-σ exchange terms, the confinement terms with screening factors can automatically be obtained.

Calculation of some properties ofπandσmesons in the global color symmetry model

It is shown in this paper that the vacuum configuration of the bilocal field in the global color symmetry model (GCM) can be calculated in the instanton dilute liquid approximation. As only the excitation of Goldstone bosons is taken into account, the relative motion against the vacuum is equivalent to the dynamical mass of a quark. The bilocal field generating the mesons a and a in the GCM is then determined. With the determined bilocal field and the effective action, the masses and the decay constants of the mesons a and a, and the decay width of sigma --> pi pi are calculated in the GCM. The calculated results agree with experimental data quite well.

Gauge invariance and the electromagnetic current of composite pions.

The Global Color-symmetry Model of QCD is extended to deal with a background electromagnetic field and the associated conserved current is identified for the finite size q\ifmmode\bar\else\textasciimacron\fi{}q pion modes at tree level. We work within a well-defined truncation that factorizes the bilocal pion field into a local field variable and a hadronic form factor having a ladder Bethe-Salpeter content. The associated pion charge form factor is formulated. These developments are used to provide an illustration of how an effective hadronic action containing form factors may be electrmagnetically coupled in a gauge invariant way that is accountable to its field substructure. In particular, the Ward-Takahashi identity for the photon vertex appropriate to the localized pion fields is seen to contain the hadronic form factors. In this context, gauge invariance of the effective hadronic action also requires recognition of the fact that the free inverse propagator for the localized pion field gauge transforms due to the substructure field content that has been absorbed into it.

Confining quark condensate model of the nucleon.

We obtain a mean-field solution for the nucleon as a quark-meson soliton obtained from the action of the global color-symmetry model of QCD. All dynamics is generated from an effective interaction of quark currents. At the quark-meson level there are two novel features: (1) absolute confinement is produced from the space-time structure of the dynamical self-energy in the vacuum quark propagator; and (2) the related scalar meson field is an extended q\ifmmode\bar\else\textasciimacron\fi{}q composite that couples nonlocally to quarks. The influence of these features upon the nucleon mass contributions and other nucleon properties is presented.

QCD bosonization and the meson effective action

A bosonization of quantum chromodynamics (QCD) is employed to derive a meson effective action, thus providing a direct link between QCD and meson phenomenology. As an example of this approach expressions are obtained for the meson parameters associated with the analysis of \ensuremath{\omega}\ensuremath{\rightarrow}3\ensuremath{\pi} decay. The bosonization also directly motivates a divergence-free, global color-symmetry model for mesons, which is seen to be a generalization of various phenomenological models. Good estimates are obtained for the values of several of the meson parameters.