Effective Q-Q Interactions in Constituent Quark Models

Abstract

We study the performance of some recent potential models suggested as effective interactions between constituent quarks. In particular, we address constituent quark models for baryons with hybrid Q-Q interactions stemming from one-gluon plus meson exchanges. Upon recalculating two of such models we find them to fail in describing the N and \Delta spectra. Our calculations are based on accurate solutions of the three-quark systems in both a variational Schr\"odinger and a rigorous Faddeev approach. It is argued that hybrid {Q-Q} interactions encounter difficulties in describing baryon spectra due to the specific contributions from one-gluon and pion exchanges together. In contrast, a chiral constituent quark model with a Q-Q interaction solely derived from Goldstone-boson exchange is capable of providing a unified description of both the N and \Delta spectra in good agreement with phenomenology.