The hypercentral Constituent Quark Model and its application to baryon properties

The hypercentral Constituent Quark Model (hCQM) for the baryon structure is reviewed and its applications are systematically discussed. The model is based on a simple form of the quark potential, which contains a Coulomb-like interaction and a confinement, both expressed in terms of a collective space coordinate, the hyperradius. The model has only three free parameters, determined in order to describe the baryon spectrum. Once the parameters have been fixed, the model, in its non relativistic version, is used to predict various quantities of physical interest, namely the elastic nucleon form factors, the photocouplings and the helicity amplitudes for the electromagnetic excitation of the baryon resonances. In particular, the $Q^2$ dependence of the helicity amplitude is quite well reproduced, thanks to the Coulomb-like interaction. The model is reformulated in a relativistic version by means of the Point Form hamilton dynamics. While the inclusion of relativity does not alter the results for the helicity amplitudes, a good description of the nucleon elastic form factors is obtained.