Mesonic states in the generalised Nambu-Jona-Lasinio theories

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.Comment: LaTeX2e, uses aipproc class, Talk given at the conference "Quark Confinement and the Hadron Spectrum VI", 21-25 September 2004, Sardinia, Italy, to appear in Proceeding

Quantum field theory approach to the vacuum replica in QCD

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.Comment: LaTeX2e, 2 EPS figures, uses ws-procs9x6 (included) and epsfig classes, Talk given at the conference "Quark Confinement and the Hadron Spectrum V", 10-14 September 2002, Gargnano, Italy, to appear in Proceeding

Chiral corrections to baryon properties with composite pions

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.Comment: 29 pages, Revtex, 4 ps figure

Parity doublers in chiral potential quark models

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.Comment: LaTeX2e, 4 pages, uses aipproc class, Talk given by A.Nefediev at the conference "Quark Confinement and the Hadron Spectrum VII", 2-7 September 2006, Acores, Portugal, to appear in Proceeding

Confinement and parity doubling in heavy-light mesons

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.Comment: RevTeX4, 21 pages, 6 Postscript figures, uses epsfig.sty, to appear in Phys.Rev.