Successes and difficulties of unified quark-antiquark potential models

Abstract

We study the qualitative and quantitative properties of the spectrum of a two-body hamiltonian with relativistic kinematics. We show that this kinematics leads in a natural way to the observed features of light flavour (u, d, s) spectroscopy. After having established the basic properties of the operator (p ²+m ²)^1/2+V(r) in the cases of linear or logarithmic potentials, we show that, to first approximation, all$q_1 \bar q_2$ meson states can be reproduced with a very simple universal flavour-independent potential whose parameters are directly related to basic physical quantities: the Regge slopes of light flavours and the quasi-logarithmic coupling strength of heavy quarks. We can derive equivalent effective non-relativistic hamiltonians which justify the successes of N.R. approaches. The main difficulties encountered, in particular in incorporating spin effects, appear to be due to the fact that, in phenomenological potential models, chiral symmetry and the ensuing Goldstone nature of the pion cannot be implemented in a natural way. Hence, such an approach can take its full predictive power only if it is based on a deeper field-theoretic level.