arXiv subjects
Publications and source records attributed to J. E. F. T. Ribeiro.
Various aspects of the Generalised Nambu-Jona-Lasinio model for QCD in four dimensions are reviewed. The properties of mesonic excitations are discussed in detail, with special attention paid to the chiral pion. The spontaneous chiral symmetry breaking in the vacuum and the effective chiral symmetry restoration in the spectrum of highly excited mesons and baryons are described microscopically.
Radial excitations of the quark-antiquark string sweeping the Wilson-loop area are considered in the framework of the effective-action formalism. Identifying these excitations with the daughter Regge trajectories, we find corrections which they produce to the constituent quark mass. The energy of the quark-antiquark pair turns out to be mostly saturated by the constituent quark masses, rather than by the elongation of the quark-antiquark string. Specifically, while the constituent quark mass turns out to increase as the square root of the radial-excitation quantum number, the energy of the string increases only as the fourth root of that number.
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 Generalised Nambu-Jona-Lasinio model. It is argued that such domains, if exist in the Universe, appear dark to an external observer.
We suggest the possibility of creation in the early Universe of stable domains of radius a few kilometers wide, formed by coherently excited states of $π$-mesons. Such domains appear dark to an external observer, since the decay rate of the said coherent pionic states into photons is vanishingly small. The related thermal insulation of the domains from the outer world could have allowed them to survive till present days. The estimated maximum radius and the period of rotation of such objects turn out to be compatible with those of certain pulsars.
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.
Generalised Nambu-Jona-Lasinio model for QCD is considered at finite temperatures in the framework of a real-time formalism. The proposed approach allows one to study various properties of the model at T>0, such as chiral symmetry breaking and restoration, properties of the bound-state spectrum, and so on.
An approach to baryons in the framework of the microscopic Generalized Nambu-Jona-Lasinio chiral potential quark model is considered and quite general arguments are given in favor of effective restoration of chiral symmetry in excited baryons.
The Goldberger--Treiman relation for heavy--light systems is derived in the context of a quark model. As a paradigmatic example, the case of ${\bar D}\to {\bar D}' π$ is studied in detail. The fundamental role played by the pion two-component wave function, in the context of the Salpeter equation, is emphasized.
The effect of spontaneous breaking of chiral symmetry over the spectrum of highly excited hadrons is addressed in the framework of a microscopic chiral potential quark model (Generalised Nambu-Jona-Lasinio model) with a vectorial instantaneous quark kernel of a generic form. A heavy-light quark-antiquark bound system is considered, as an example, and the Lorentz nature of the effective light-quark potential is identified to be a pure Lorentz-scalar, for low-lying states in the spectrum, and to become a pure spatial Lorentz vector, for highly excited states. Consequently, the splitting between the partners in chiral doublets is demonstrated to decrease fast in the upper part of the spectrum so that neighboring states of an opposite parity become almost degenerate. A detailed microscopic picture of such a "chiral symmetry restoration" in the spectrum of highly excited hadrons is drawn and the corresponding scale of restoration is estimated.
In this paper, we discuss the transition to the semiclassical regime in excited hadrons, and consequently, the restoration of chiral symmetry for these states. We use a generalised Nambu-Jona-Lasinio model with the interaction between quarks in the form of the instantaneous Lorentz-vector confining potential. This model is known to provide spontaneous breaking of chiral symmetry in the vacuum via the standard selfenergy loops for valence quarks. It has been shown recently that the effective single-quark potential is of the Lorentz-scalar nature, for the low-lying hadrons, while, for the high-lying states, it becomes a pure Lorentz vector and hence the model exhibits the restoration of chiral symmetry. We demonstrate explicitly the quantum nature of chiral symmetry breaking, the absence of chiral symmetry breaking in the classical limit as well as the transition to the semiclassical regime for excited states, where the effect of chiral symmetry breaking becomes only a small correction to the classical contributions.
In this paper, we study the chiral symmetry restoration in the hadronic spectrum in the framework of generalised Nambu-Jona-Lasinio quark models with instantaneous confining quark kernels. We investigate a heavy-light quarkonium and derive its bound-state equation in the form of a Schroedingerlike equation and, after the exact inverse Foldy-Wouthuysen transformation, in the form of a Diraclike quation. We discuss the Lorentz nature of confinement for such a system and demonstrate explicitly the effective chiral symmetry restoration for highly excited states in the mesonic spectrum. We give an estimate for the scale of this restoration.
For any Nambu-Jona-Lasinio model of QCD with arbitrary nonlocal, instantaneous, quark current-current confining kernels, we use a generalised Bogoliubov technique to go beyond BCS level (in the large-Nc limit) so as to explicitly build quark-antiquark compound operators for creating/annihilating mesons. In the Hamiltonian approach, the mesonic bound-state equations appear (from the generalised Bogoliubov transformation) as mass-gap-like equations which, in turn, ensure the absence, in the Hamiltonian, of mesonic Bogoliubov anomalous terms. We go further to demonstrate the one-to-one correspondence between Hamiltonian and Bethe-Salpeter approaches to non-local NJL-type models for QCD and give the corresponding "dictionary" necessary to "translate" the amplitudes built using the graphical Feynman rules to the terms of the Hamiltonian, and vice versa. We comment on the problem of multiple vacua existence in such type of models and argue that mesonic states in the theory should be prescribed to have an extra index - the index of the replica in which they are created. Then the completely diagonalised Hamiltonian should contain a sum over this new index. The method is proved to be general and valid for any instantaneous quark kernel.
In this paper, we study generic non-local NJL models for four-dimensional QCD in the limit of a large number of colours. We diagonalise, through a Bogoliubov-type transformation, the Hamiltonian of the model completely in terms of the compound operators creating/annihilating mesons - bound states of dressed quarks and antiquarks - and demonstrate a one-to-one correspondence between the Bogoliubov diagonalisation condition and the Bethe-Salpeter equation for bound states. We conclude that, in the leading order in N_C, the nontrivial contents of the theory is entirely encoded in the chiral angle - the solution to the mass-gap equation for dressed quarks. As a consequence, we extend the statement of existence of excited solutions to the mass-gap equation, called vacuum replicas, beyond the BCS level and prescribe a new index to the mesonic operators - the label of the vacuum state in which the corresponding meson is created.
In this paper we develop a systematic quantum field theory based approach to the vacuum replica recently found to exist in effective low energy models in hadronic physics. A local operator creating the replica state is constructed explicitly. We show that a new effective quark-quark force arises in result of replica existence. Phenomenological implications of such a force are also briefly discussed.
Quantum field theory is used to describe the contribution of possible new QCD vacuum replica to hadronic processes. This sigma-like new state has been recently shown to be likely to appear for any realistic four-quark interaction kernel as a consequence of chiral symmetry. The local operator creating the replica vacuum state is constructed explicitly. Applications to physical processes are outlined.
The properties of the vacuum are addressed in the two- and four-dimensional quark models for QCD. It is demonstrated that the two-dimensional QCD ('t Hooft model) possesses only one possible vacuum state - the solution to the mass-gap equation, which provides spontaneous breaking of the chiral symmetry (SBCS). On the contrary, the four-dimensional theory with confinement modeled by the linear potential supplied by the Coulomb OGE interaction, not only has the chirally-noninvariant ground vacuum state, but it possesses an excited vacuum replica, which also exhibits SBCS and can realize as a metastable intermediate state of hadronic systems. We discuss the influence of the latter on physical observables as well as on the possibility to probe the vacuum background fields in QCD.
A calculational scheme is developed to evaluate chiral corrections to properties of composite baryons with composite pions. The composite baryons and pions are bound states derived from a microscopic chiral quark model. The model is amenable to standard many-body techniques such as the BCS and RPA formalisms. An effective chiral model involving only hadronic degrees of freedom is derived from the macroscopic quark model by projection onto hadron states. Chiral loops are calculated using the effective hadronic Hamiltonian. A simple microscopic confining interaction is used to illustrate the derivation of the pion-nucleon form factor and the calculation of pionic self-energy corrections to the nucleon and Delta(1232) masses.
We work in a chiral invariant quark model, with a condensed vacuum, characterized by only one parameter. Bound state equations for the nucleon and Delta are solved in order to obtain an updated value of their radii and masses. Nucleon-nucleon S-Wave scattering is studied in the RGM framework both for isospin T=1 and T=0. The phase shifts are calculated and an equivalent local potential, which is consistent with K-N scattering, is derived. The result is a reasonable microscopic short range repulsion in the nucleon-nucleon interaction.