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

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 $\mathcal{O}(N_c^0)$ \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.

18 pages, 4 tables. Published version. Note that Eqs. A1, A3 and A4 contain SO(3) Clebsch-Gordan coefficients, not Wigner 3j coefficients

References in corpus (3)

• Baryonic mass formula in large $N_c$ QCD versus quark model
• Baryon Regge Trajectories in the Light of the $1/N_c$ Expansion
• The wave function of $[70,1^{-}]$ baryons in the $1/N_c$ expansion

Cited by in corpus (5)

• Magnetic moments of the low-lying {1/2}^- octet baryon resonances
• Baryon resonances in large $N_c$ QCD
• $[70,{\mathbf{\ell }}^{+}]$ baryons in large $N_c$ QCD revisited: The effect on Regge trajectories
• Negative parity baryons in the $1/N_c$ expansion: the three towers of states revisited
• Towers of positive parity excited baryons and their mixing in the large $N_c$ limit