Semi-relativistic quark-antiquark potential models

The qualitative and quantitative properties of the spectrum of a two-body hamiltonian with relativistic kinematics are studied. One shows 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 √p2 + m2 + V(r) in the cases of linear or logarithmic potentials, one shows that, to first approximation, all q1 antiq2 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. One can derive equivalent effective non-relativistic hamiltonians which justify the successes of NR 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