Abstract
We study the excited baryon states for an arbitrary number of colors ${N}_{c}$ 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 parametrizing 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 $1/{N}_{c}$ 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.
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