SU(6) [70,1−][{\bf 70},1^-] baryon multiplet in the 1/Nc1/N_c expansion

The masses of excited states of mixed orbital symmetry of nonstrange and strange baryons belonging to the lowest $[{\bf 70},1^-]$ multiplet are calculated in the $1/N_c$ expansion to order $1/N_c$ with a new method which allows to considerably reduce the number of linearly independent operators entering the mass formula. This study represents an extension to SU(6) of our work on nonstrange baryons, the framework of which was SU(4). The conclusion regarding the role of the flavor operator, neglected in previous SU(6) studies, is reinforced. Namely, both the flavor and spin operators contribute dominantly to the flavor-spin breaking.Comment: 26 pages, 11 tables, to be published in PR

Negative parity baryons in the 1/Nc1/N_c expansion: the quark excitation versus the meson-nucleon resonance picture

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

Baryon resonances in large NcN_c QCD

The baryon spectra are discussed in the context of the $1/N_c$ expansion approach, with emphasis on mixed symmetric states. The contributions of the spin dependent terms as a function of the excitation energy are shown explicitly. At large energies these contributions are expected to vanish.Comment: 6 pages, based on a talk given by Fl. Stancu at the Miniworkshop "Progress in Quark Models" Bled, Slovenia, July 10-17, 2006, to be published in Bled Workshops in Physics, vol. 7 no.

Highly Excited Baryons in Large NcN_c QCD

We use the $1/N_c$ expansion of QCD to analyse the spectrum of positive parity resonances with strangeness $S = 0, -1, -2$ and -3 in the 2--3 GeV mass region, supposed to belong to the $[\textbf{56},4^+]$ multiplet. The mass operator is similar to that of $[\textbf{56},2^+]$, previously studied in the literature. The analysis of the latter is revisited. In the $[\textbf{56},4^+]$ multiplet we find that the spin-spin term brings the dominant contribution and that the spin-orbit term is entirely negligible in the hyperfine interaction, in agreement with constituent quark model results. More data are strongly desirable, especially in the strange sector in order to fully exploit the power of this approach. We discuss possibilities of extending the calculations to other excited baryons belonging to the N=2 or the N=4 band.Comment: 10 pages, Prepared for the Workshop "Three Days of Hadronics Physics", Joint Meeting Heidelberg-Liege-Paris-Rostock, December 16-18, 2004, Spa, Belgium, to be published in AIP Proceedings. One reference adde

Updated 1/Nc1/N_c expansion analysis of [56,2+][{\bf 56, 2^+}] and [70,ℓ+][{\bf 70, \ell^+}] baryon multiplets

The mass spectra of the $[{\bf 56, 2^+}]$ and $[{\bf 70, \ell+}]$ multiplets, both belonging to the $N$ = 2 band, is reviewed in the $1/N_c$ expansion method. Previous studies, separately made for each multiplet, are presently updated to the 2014 Particle Data Group. The mass formula including corrections up to $\mathcal{O}(1/N_c)$ and first order in SU(3) flavor symmetry breaking, has the same independent operator basis in both cases. A special emphasis is made on the role of the SU(3) symmetry breaking operators $B_i$ $(i = 1,2,3)$. This can allow for multiplet assignment of $\Lambda$ and $\Sigma$ hyperons, which generally is quite difficult to make. Tentative assignments of hyperons with two- and one-star resonances are made to the $[{\bf 70, \ell+}]$ multiplet. Another important aim is to find out whether or not a common value of the coefficient $c_1$ of the dominant operator in the mass formula, can well fit the present data in both multiplets. A negative answer, which is here the case, implies distinct Regge trajectories for symmetric and mixed symmetric states.Comment: 25 pages, to appear in Phys.Rev.

Excited [70,ℓ+][{\bf 70},\ell^+] baryon resonances in large NcN_c QCD

We summarize results obtained in the $1/N_c$ expansion method for the masses of baryon resonances belonging to the $[{\bf 70},\ell^+]$ multiplet. They represent an extension of our previous studies from two to three flavors. A better approach to mixed symmetric states of any angular momentum and parity is also outlined.Comment: 4 pages, 1 figure, uses espcrc2.sty (included), based on a talk given by N. Matagne at the 13th International QCD Conference, QCD06, Montpellier, France, 3-7th July 200

Excited Baryons in the 1/N_c Expansion

We review results for the mass spectrum of orbitally excited baryons obtained in the $1/N_c$ expansion. We show the dependence of various contributions to the mass operator as a function of the excitation energy.Comment: 4 pages, 2 figures, based on a talk given by N. Matagne at the Workshop on the Physics of Excited Baryons (NSTAR 2005), Tallahassee, Florida, 12-15 October 200

Mixed symmetric baryon multiplets in large NcN_c QCD: two and three flavours

We propose a new method to study mixed symmetric multiplets of baryons in the context of the $1/N_c$ expansion approach. The simplicity of the method allows to better understand the role of various operators acting on spin and flavour degrees of freedom. The method is tested on two and three flavours. It is shown that the spin and flavour operators proportional to the quadratic invariants of SU$_S$(2) and SU$_F$(3) respectively are dominant in the mass formula.Comment: 7 pages, 2 tables, talk given by Fl. Stancu at Mini-Workshop "Dressing Hadrons", Bled, Slovenia, July 4-11, 201

Excited [70,ℓ+][{\bf 70, \ell^+}] baryons in large NcN_c QCD

The masses of the positive parity $[{\bf 70},0^+]$ and $[{\bf 70},2^+]$ non-strange baryons are calculated in large $N_c$ QCD by considering the most dominant operators in an $1/N_c$ expansion. The approach is based on the introduction of an excited core, obtained after the last particle (an excited quark) has been removed. Configuration mixing is neglected, for simplicity. Although being a sub-leading $1/N_c$ order, we find that the spin-spin interaction plays a dominant role in describing the data. The role of $N_c^ 0$ operators is also pointed out. We show how the contribution of the linear term in $N_c$, of the spin-spin and spin-orbit terms vary with the excitation energy.Comment: 11 pages, 3 figures, LaTeX, uses espcrc1.sty (included), correspond with the published versio

Baryon resonances in large NcN_c QCD

We review the current status and present open challenges of large $N_c$ QCD baryon spectroscopy. After introducing the $1/N_c$ expansion method we first shortly revisit the latest achievements for the ground state properties. Next we discuss the applicability of this method to excited states, presenting two different approaches with their advantages and disadvantages. Selected results for the spectrum and strong and electromagnetic decays are described. We also show further developments supported by the qualitative compatibility between the quark excitation picture and the meson-nucleon scattering picture. We give a quantitative comparison between results obtained from the mass formula of the $1/N_c$ expansion method and quark models and shortly discuss the implications of different large $N_c$ limits.Comment: 45 pages, 5 figures, accepted for publication in Reviews of Modern Physic