Spectrum ofP-wave baryonic excitations in a model with field confinement

Abstract

We investigate the spectrum of $P$-wave excitations of three quarks confined within a baryon by a uniform external pressure (a hadronic bag). We develop a formalism to take into account the dynamical effects of the motion of the boundary of the bag, and we find that this induces a collective coupling of the quarks, which resolves a degeneracy otherwise present among the energy levels. We find that the lowest states of excitation are those that can be grouped into the (70, $L=1\mathrm{}$) representation of $\mathrm{SU}\mathrm{}\left(6\right)\mathrm{}\times \mathrm{O}{\mathrm{}\left(3\right)\mathrm{}}_L$, and that the states of the (56, $L=1\mathrm{}$) representation should be expected at a definitely higher energy.