Negative parity nonstrange baryons in large $N_c$ QCD: quark excitation versus meson-nucleon scattering

TL;DR

This paper demonstrates the compatibility of two different theoretical descriptions of large $N_c$ baryons, specifically for $ ext{SU}(4)$ baryons with orbital angular momentum $ ext{l} = 3$, using a simple Hamiltonian approach.

Contribution

It establishes the equivalence between quark excitation and meson-nucleon scattering pictures for $ ext{SU}(4)$ baryons with $ ext{l} = 3$ in large $N_c$ QCD, extending previous models.

Findings

The two pictures are compatible for $ ext{l} = 3$ SU(4) baryons.

A simple Hamiltonian including operators up to order $ ext{O}(N_c^0)$ suffices.

The proof builds on previous models used for $ ext{l} = 1$.

Abstract

We show that the two complementary pictures of large $N_c$ baryons - the single-quark orbital excitation about a symmetric core and the meson-nucleon resonance -- are compatible for $\ell$ = 3 SU(4) baryons. The proof is based on a simple Hamiltonian including operators up to order $\mathcal{O}(N^0_c)$ used previously in the literature for $\ell$ = 1.