Jose Emilio Fernandes T. Ribeiro

Various aspects of the generalized Nambu – Jona-Lasinio model of QCD in four dimensions are reviewed. The properties of mesonic excitations are discussed in detail, with special attention on the chiral pion. Spontaneous chiral symmetry breaking in a vacuum and effective chiral symmetry restoration in the spectrum of highly excited mesons and baryons are described microscopically.

We propose a model for the quark-antiquark interaction in Minkowski space using the Covariant Spectator Theory. We show that with an equal-weighted scalar-pseudoscalar structure for the confining part of our interaction kernel the axial-vector Ward-Takahashi identity is preserved and our model complies with the Adler-zero constraint for π-π-scattering imposed by chiral symmetry.

The quark condensate is calculated using the effective‐action formalism, by imposing an ansatz for the Wilson loop, which interpolates between the area‐law for large loops and the area‐squared law for small loops. For 3 colors and 2 light flavors, a lower bound of 460 MeV for the constituent quark mass is found to be accessible, provided an effective scale‐dependent string tension of a light quark falls off linearly with the Schwinger proper time. This behavior of the effective string tension yields the Hausdorff dimension of a light‐quark trajectory equal to 4, which shows that these trajectories are similar to branched polymers. A gluonic chain based on such trajectories provides an example of a model describing weak first‐order deconfinement phase transition, which takes place in SU(3) Yang–Mills theory.

The connection between effective‐actions and generalizations of Nambu‐Jona‐Lasinio models is discussed. We suggest the possibility of creation in the early Universe of stable domains of radius a few kilometers wide. Such domains should appear dark to an external observer. The insulation of the domains from the outer world, a consequence of the joint role played by gravity and the existence of two orthogonal Fock spaces could have allowed them to survive untill present days.

A possibility is suggested for the formation in the Universe of domains occupied by coherent‐like states of strongly correlated quark‐antiquark pairs. Only domains of the radius larger than 5 fm had a chance to survive over the entire history of the Universe, while the requirement of stability against the gravitational collapse restricts the maximum domain’s radius to 14 km. Within the Generalised Nambu–Jona‐Lasinio model, an exponential suppression with the domain’s volume is found for the overlap between the macroscopic ground‐state wavefunction of the quark‐antiquark pairs and the QCD vacuum. This finding supports, at the microscopic level, the above arguments in favour of the stability of the domains.

Formation of stable domains filled with strongly correlated coherent quark matter is discussed in general terms and is exemplified further in the framework of the generalized Nambu-Jona-Lasinio...

The quark condensate is calculated in terms of the effective string tension and the constituent quark mass. For 3 colors and 2 light flavors, the constituent mass is bounded from below by the value of 460 MeV. This value is only accessible when the string tension decreases linearly with the Schwinger proper time. For this reason, the Hausdorff dimension of a light-quark trajectory is equal to 4, indicating that these trajectories are similar to branched polymers, which can describe a weak first-order deconfinement phase transition in SU(3) Yang-Mills theory. Using this indication, we develop a gluon-chain model based on such trajectories.