Hadron spectroscopy and form factors at quark level

Abstract

The theoretical status of hadrons as quark composites is examined from the point of view of a simultaneous understanding of their on-shell (mass spectra) and off-shell (form factors, transition amplitudes) properties. To that end we first offer a perspective view of the emerging scenario in quark physics since the seventies, preceded by a quick overview of some important ideas and models in the pre-QCD phase that were to determine the shape of the subsequent (post-QCD) developments. The primary emphasis is on theoretical approaches to effective confinement (pending a formal resolution of the confinement problem within a QCD-Lagrangian framework, Lattice or otherwise), in providing a fuller perspective from high to low energy physics or vice-versa. To that end greater stress is laid on light quark systems which are more sensitive to the confinement regime, and more prone to relativistic effects than on heavy quarkonia (on which many reviews exist). Two broad theoretical approaches obeying Lorentz and gauge invariance are identified: (i) QCD sum rules as a means of extrapolation from high to low energies; and (ii) dynamical equations for providing a microcausal link in the opposite direction (from low to high energies). The latter represents the major focus of attention in this article, with the Bethe-Salpeter Equation (BSE) providing a formal plank for a comparative assessment of several models. The Null-plane ansatz which facilitates the reduction of the 4-D BSE to a covariant 3-D form also provides the language for its comparison with other covariant 3-D equations. In particular, attention is drawn to the interesting possibility of reconstructing the 4-D BS wave function from its 3-D form (in a two-tier fashion) as a practical tool for generating higher Fock-space components (qq̅ effects) in the BS wave function, and (more interestingly) for a clean separation between soft and hard QCD effects. To illustrate one such practical tool for an integrated view of different hadronic sectors within a single framework, the results of a two-tier BS model are presented in respect of qq̅ , qqq, gg, ggg, gqq̅ states and compared with experiment as well as with the results of other contemporary models. The N.R Resonating Group Method, which becomes necessary for bigger (six-quark) systems is briefly discussed from the point of view of its compatibility with a relativistic form of quark dynamics motivated from the BSE.