Negative parity baryons in the $1/N_c$ expansion: the quark excitation versus the meson-nucleon resonance picture

TL;DR

This paper extends the analysis of negative parity baryons in the large N_c limit to include states with orbital angular momentum , demonstrating degeneracy patterns and discussing compatibility between quark-shell and meson-nucleon resonance pictures.

Contribution

It provides a detailed proof of degeneracy patterns for a0 excited states, extending previous work on
a0 states, and discusses their compatibility with resonance models.

Findings

Identified three degenerate multiplets for a0 states.

Extended the degeneracy analysis to a0 orbital angular momentum states.

Discussed the compatibility of quark-shell and resonance pictures.

Abstract

In order to better understand the fundamental issue regarding the compatibility between the quark-shell picture and that of resonances in meson-nucleon scattering in large $N_c$ QCD we extend the work of Cohen and Lebed on mixed symmetric $\ell $ = 1 baryons to analyze excited states with $\ell $ = 3. We give an explicit proof on the degeneracy of mass eigenvalues of a simple Hamiltonian including operators up to order $\mathcal{O}(N^0_c)$ \emph{i. e.} neglecting $1/N_c$ corrections in the quark-shell picture in the large $N_c$ limit. We obtain three degenerate multiplets formed of $\ell = 3$ states, as in the case of $\ell $ = 1 baryons. The compatibility between this picture and that of resonances in meson-nucleon scattering is discussed in the light of the present results.