The Isgur-Karl model revisited

Abstract

We show how to match the Isgur-Karl model to the spin-flavor quark operator expansion used in the 1/Nc studies of the non-strange negative parity L=1 excited baryons. Using the transformation properties of states and interactions under the permutation group S_3 we are able to express the operator coefficients as overlap integrals, without making any assumption on the spatial dependence of the quark wave functions. The general mass operator leads to parameter free mass relations and constraints on the mixing angles that are valid beyond the usual harmonic oscillator approximation. The Isgur-Karl model with harmonic oscillator wave functions provides a simple counterexample that demonstrates explicitly that the alternative operator basis for the 1/Nc expansion for excited baryons recently proposed by Matagne and Stancu is incomplete.

19 pages, 1 figure

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• Decays of Non-strange Negative Parity Baryons in the 1/Nc Expansion
• New look at the $[70,1^{-}]$ baryon multiplet in the $1/N_c$ expansion
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• The permutation group S_N and large Nc excited baryons
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Cited by in corpus (6)

• Light baryon masses in different large-$N_c$ limits
• Highly excited negative parity baryons in the $1/N_c$ expansion
• 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
• Towers of positive parity excited baryons and their mixing in the large $N_c$ limit
• Lowest negative parity baryons in the $1/N_c$ expansion