Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2011-06-24
Phys.Rev.D84:056013, 2011
Physics
High Energy Physics
High Energy Physics - Phenomenology
18 pages, 4 tables. Published version. Note that Eqs. A1, A3 and A4 contain SO(3) Clebsch-Gordan coefficients, not Wigner 3j c
Scientific paper
10.1103/PhysRevD.84.056013
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.
Matagne Nicolas
Stancu Fl.
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