The permutation group S_N and large Nc excited baryons

Abstract

We study the excited baryon states for an arbitrary number of colors Nc from the perspective of the permutation group S_N of N objects. Classifying the transformation properties of states and quark-quark interaction operators under S_N allows a general analysis of the spin-flavor structure of the mass operator of these states, in terms of a few unknown constants parameterizing the unknown spatial structure. We explain how to perform the matching calculation of a general two-body quark-quark interaction onto the operators of the 1/Nc expansion. The inclusion of core and excited quark operators is shown to be necessary. Considering the case of the negative parity L=1 states transforming in the MS of S_N, we discuss the matching of the one-gluon and the Goldstone-boson exchange interactions.

38 pages. Final version to be published in Physical Review D

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Cited by in corpus (15)

• Light baryon masses in different large-$N_c$ limits
• Baryon resonances in large $N_c$ QCD
• Analysis of Negative Parity Baryon Photoproduction Amplitudes in the $1/N_c$ Expansion
• Matrix elements of SU(6) generators for baryons with arbitrary $N_c$ quarks in mixed symmetric states $[N_c-1,1]$
• Highly excited negative parity baryons in the $1/N_c$ expansion
• Quark Forces from Hadron Spectroscopy
• 1/Nc expansion and the spin-flavor structure of the quark interaction in the constituent quark model
• Operator analysis of effective spin-flavor interactions for L=1 excited baryons
• The Isgur-Karl model revisited
• Configuration Mixing of Quark States in Baryons
• Negative parity baryons in the $1/N_c$ expansion: the three towers of states revisited
• $[70,{\mathbf{\ell }}^{+}]$ baryons in large $N_c$ QCD revisited: The effect on Regge trajectories
• Towers of positive parity excited baryons and their mixing in the large $N_c$ limit
• Group theoretical study of nonstrange and strange mixed symmetric baryon states $[N_c-1,1]$ in the $1/N_c$ expansion
• Excited Baryons in Large Nc QCD: Matching the 1/Nc expansion to quark models using the permutation group S_N