Towers of baryons of the $\mathcal{N}=2$ quark model band in the large $N_c$ limit

Abstract

We performed a complete analysis of the spectrum of all the states in the $\mathcal{N}=2$ quark model harmonic oscillator band with $N_f=3$ in the large $N_c$ limit including the often disregarded antisymmetric multiplet $[20,1^{+}]$. We included configuration mixing effects. We found that the states in the $[56,L^{+}]$ and $[70,L^{+}]$ with $L=0,2$ fall into nine towers of degenerate states. We found that nonstrange antisymmetric states fall into three towers and respond to the same structure as the states in the $[70,1^{-}]$ multiplet. We also showed explicitly the compatibility of these results and the scattering resonance picture.

Comments: 41 pages, 7 tables, v2: minor changes to match published version, typos in Eqs. (16) and (20) corrected