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

TL;DR

This paper analyzes the complete spectrum of ${ m N}=2$ quark model baryons in the large $N_c$ limit, revealing nine degenerate towers and clarifying their relation to scattering resonances.

Contribution

It provides a comprehensive classification of baryon states in the ${ m N}=2$ quark model, including the antisymmetric multiplet, with configuration mixing effects considered.

Findings

States form nine degenerate towers in the large $N_c$ limit

Nonstrange antisymmetric states form three towers similar to $[\mathbf{70},1^-]$

Results are compatible with the scattering resonance picture

Abstract

We performed a complete analysis of the spectrum of all the states in the ${\cal N}=2$ quark model harmonic oscillator band with $N_f=3$ in the large $N_c$ limit including the often disregarded antisymmetric multiplet $[{\bf 20},1^+]$. We included configuration mixing effects. We found that the states in the $[{\bf 56},L^+]$ and $[{\bf 70},L^+]$ 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 $[{\bf 70},1^-]$ multiplet. We also showed explicitly the compatibility of these results and the scattering resonance picture.