Chiral symmetry breaking solutions for QCD in the truncated Coulomb gauge

In this paper we study the power-like confining potentials r^alpha. The region of allowed alphas is identified, the mass-gap equation is constructed for an arbitrary alpha and solved for several values of the latter, and the vacuum energy and the chiral condensate are calculated. The question of replica solutions to the mass-gap equation for such potentials is addressed and it is demonstrated that the number of replicas is infinite for any alpha, as a consequence of the peculiar behaviour of the quark self-energy in the infrared domain.Comment: RevTeX4, 18 pages, 3 Postscript figures, uses epsfig.sty, to appear in Phys.Rev.

f [N pi N]: from quarks to the pion derivative coupling

We study the N pi N coupling, in the framework of a QCD-inspired confining Nambu-Jona-Lasinio model. A simple relativistic confining and instantaneous quark model is reviewed. The Salpeter equation for the nucleon and the boosted pion is solved. The f [n pi n] and f[n pi Delta] couplings are calculated and they turn out to be reasonably good. The sensibility of f[n pi n] and f[n pi Delta] to confinement, chiral symmetry breaking and Lorentz invariance is briefly discussed.Comment: 30 pages in LaTex RevTex, 6 postscript figure

Analytical approach to chiral symmetry breaking in Minkowsky space

The mass gap equation for spontaneous chiral symmetry breaking is studied directly in Minkowsky space. In hadronic physics, spontaneous chiral symmetry breaking is crucial to generate a constituent mass for the quarks, and to produce the Partially Conserved Axial Current theorems, including a small mass for the pion. Here a class of finite kernels is used, expanded in Yukawa interactions. The Schwinger-Dyson equation is solved with an analytical approach. This improves the state of the art of solving the mass gap equation, which is usually solved with the equal-time approximation or with the Euclidean approximation. The mapping from the Euclidean space to the Minkowsky space is also illustrated.Comment: 7 pages, 3 figure

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

Field theory description of vacuum replicas

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.Comment: RevTeX4, 23 pages, 4 Postscript figures, uses epsfig.sty, to appear in Phys.Rev.

Vacuum replicas in QCD

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.Comment: RevTeX4, 26 pages, 8 EPS figures, extended references, corrected some typos, to appear in Phys.Rev.

Chirally symmetric quark description of low energy \pi-\pi scattering

Weinberg's theorem for \pi-\pi scattering, including the Adler zero at threshold in the chiral limit, is analytically proved for microscopic quark models that preserve chiral symmetry. Implementing Ward-Takahashi identities, the isospin 0 and 2 scattering lengths are derived in exact agreement with Weinberg's low energy results. Our proof applies to alternative quark formulations including the Hamiltonian and Euclidean space Dyson-Schwinger approaches. Finally, the threshold \pi-\pi scattering amplitudes are calculated using the Dyson-Schwinger equations in the rainbow-ladder truncation, confirming the formal derivation.Comment: 10 pages, 7 figures, Revtex