Vector particles in Quasilocal Quark Models.pdf

a r X i v : h e p - p h / 0 3 0 4 1 4 0 v 1 1 5 A p r 2 0 0 3 Vector particles in Quasilocal Quark Models1 V. A. Andrianov and S. S. Afonin V. A. Fock Department of Theoretical Physics, St. Petersburg State University, 198504 St. Petersburg, Russia Abstract We consider the Quasilocal Quark Model of NJL type including vector and axial-vector four-fermion interaction with derivatives. The mass spectrum for the ground and first excited states is obtained. The chiral symmetry restoration sum rules in these channels are im- posed as matching rules to QCD at intermediate energies and a set of constraints on parameters of QQM is performed. 1. Introduction The main purpose of this paper is to describe the physics of as ground vector (V) and axial-vector (A) meson resonances at low energies as excited states with increasing masses at intermediate energies in the framework of effective action of Quasilocal Quark Models (QQM) which were introduced in [1]. We will see that these effective QCD QQM are sufficiently general and from the physical point of view evident to allow a good description of wide set of mass relations for vector and axial-vector mesons. Moreover, using properties of two-point QCD VA correlators of quark densities at high energies (asymptotic freedom and Operator Product Expansion (OPE)) and two-resonance ansatz for VA meson correlators of QQM, we will obtain a number of constraints for parameters of QQM from the so-called Chiral Symmetry Restoration (CSR) sum rules. It is well known that the effective QCD-inspired quark models with four- fermion interactions of Nambu-Jona-Lasinio (NJL) type are often applied to describe the low-energy QCD in the hadronization regime [2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. The appearance of effective quark theory is connected with one of specific property of QCD — the dynamical Chiral Symmetry Breaking (CSB). The local four-fermion interaction is involved to induce the CSB due to strong attraction in the scalar channel. As a c