The Isgur-Karl model revisited

TL;DR

This paper revisits the Isgur-Karl model by connecting it to the 1/Nc spin-flavor operator expansion, deriving parameter-free mass relations and highlighting the model's limitations compared to recent operator basis proposals.

Contribution

It demonstrates how to match the Isgur-Karl model with the 1/Nc expansion without assuming specific spatial wave functions and shows the incompleteness of recent alternative operator bases.

Findings

Derives parameter-free mass relations for excited baryons.

Shows the Isgur-Karl model with harmonic oscillator wave functions is a counterexample.

Highlights limitations of recent operator basis proposals.

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.