Extended non-chiral quark models confronting QCD

We discuss the low energy effective action of QCD in the quark sector. When it is built at the CSB (chiral symmetry breaking) scale by means of perturbation theory it has the structure of a generalized Nambu-Jona-Lasinio (NJL) model with CSB due to attractive forces in the scalar channel. We show that if the lowest scalar meson state is sufficiently lighter than the heavy pseudoscalar $\pi'$ then QCD favors a low-energy effective theory in which higher dimensional operators (of the Nambu-Jona-Lasinio type) are dominated and relatively strong. A light scalar quarkonium ($m_\sigma = 500 \div 600$ MeV) would provide an evidence in favor to this NJL mechanism. Thus the non-chiral Quasilocal Quark Models (QQM) in the dynamical symmetry-breaking regime are considered as approximants for low-energy action of QCD. In the mean-field (large-N_c) approach the equation on critical coupling surface is derived. The mass spectrum of scalar and pseudoscalar excited states is calculated in leading-log approach which is compatible with the truncation of the QCD effective action with few higher-dimensional operators. The matching to QCD based on the Chiral Symmetry Restoration sum rules is performed and it helps to select out the relevant pattern of CSB as well as to enhance considerably the predictability of this approach.Comment: 10 pages, Latex, talk at the Workshop HADRON 99, Coimbra, Portuga

Spontaneous parity violation in extreme conditions: an effective lagrangian analysis

We investigate how large baryon densities (and possibly high temperatures) may induce spontaneous parity violation in the composite meson sector of vector-like gauge theory (presumably QCD or techni-QCD) . The analysis at intermediate energy scales is done by using an extended $\sigma$-model lagrangian that includes two scalar and two pseudoscalar multiplets and fulfills low-energy constraints for vector-like gauge theories. We elaborate on a novel mechanism of parity breaking based on the interplay between lightest and heavier meson condensates, which therefore cannot be realized in the simplest $\sigma$ model. The results are relevant for an idealized homogeneous and infinite nuclear (quark or techniquark) matter where the influence of density can be examined with the help of a constant chemical potential. The model is able to describe satisfactorily the first-order phase transition to stable nuclear matter, and predicts a second-order phase transition to a state where parity is spontaneously broken. We argue that the parity breaking phenomenon is quite generic when a large enough chemical potential is present. Current quark masses are explicitly taken into account in this work and shown not to change the general conclusions.Comment: 24 pages, substantial revisio

Meson mass spectrum and OPE: matching to the large-N_c QCD

The relations between masses and decay constants of variety of meson resonances in the energy range 0--3 GeV are verified from the string-like, linear mass spectrum for vector, axial-vector, scalar and pseudoscalar mesons with a universal slope. The way to match the universality with the Operator Product Expansion (OPE) is proposed. The necessity of small deviations from linearity in parameterization of the meson mass spectrum and their decay constants is proven from matching to OPE.Comment: 4 pages, more refs added, Talk at V Int. Conference "Quark Confinement and the Hadron Spectrum", 10-14 Sept. 2002, Garda Lake, Ital

Searching for P- and CP-odd effects in heavy ion collisions

In this talk we will summarize the main results from our recent work concerning the possibility that a new metastable phase occurs in some heavy ion collisions (HIC). This phase would be characterized by the breaking of two characteristic symmetries of strong interactions; namely P and CP. We investigate the experimental consequences of parity breaking in such a situation and propose suitable observables to elucidate the presence this phenomenon.Comment: Talk presented at the XI Conference on Quark Confinement and Hadron Spectrum, Saint Petersburg, September 201

Intertwined isospectral potentials in an arbitrary dimension

The method of intertwining with n-dimensional (nD) linear intertwining operator L is used to construct nD isospectral, stationary potentials. It has been proven that differential part of L is a series in Euclidean algebra generators. Integrability conditions of the consistency equations are investigated and the general form of a class of potentials respecting all these conditions have been specified for each n=2,3,4,5. The most general forms of 2D and 3D isospectral potentials are considered in detail and construction of their hierarchies is exhibited. The followed approach provides coordinate systems which make it possible to perform separation of variables and to apply the known methods of supersymmetric quantum mechanics for 1D systems. It has been shown that in choice of coordinates and L there are a number of alternatives increasing with $n$ that enlarge the set of available potentials. Some salient features of higher dimensional extension as well as some applications of the results are presented.Comment: 14 pages, Latex fil