[Formula Presented] corrections to the [Formula Presented] symmetry for [Formula Presented] baryons: The three towers

In the large [Formula Presented] limit, the mass spectrum of the [Formula Presented] orbitally excited baryons [Formula Presented] has a very simple structure, with states degenerate in pairs of spins [Formula Presented] corresponding to irreducible representations (towers) of the contracted [Formula Presented] symmetry group. The mixing angles are completely determined in this limit. Using a mass operator approach, we study [Formula Presented] corrections to this picture, pointing out a fourfold ambiguity in the correspondence of the observed baryons with the large [Formula Presented] states. For each of the four possible assignments, we fit the coefficients of the quark operators contributing to the mass spectrum to [Formula Presented] We comment on the implications of our results for the constituent quark model description of these states.