Matching the quark model to the 1/Nc expansion

TL;DR

This paper connects the quark model with the 1/Nc expansion for excited baryons, showing that different interactions lead to similar dominant operators, aligning with experimental data.

Contribution

It provides a detailed calculation of effective mass operator coefficients using the Isgur-Karl model, bridging model-specific and general approaches.

Findings

Pion and gluon exchange lead to the same dominant operator.

The effective mass operator coefficients match experimental data.

Both approaches reveal similar physics behind baryon masses.

Abstract

We compute the coefficients of the effective mass operator of the 1/Nc expansion for negative parity L=1 excited baryons using the Isgur-Karl model in order to compare the general approach, where the coefficients are obtained by fitting to data, with a specific constituent quark model calculation. We discuss the physics behind the fitted coefficients for the scalar part of the most general two-body quark-quark interaction. We find that both pion exchange and gluon exchange lead to the dominance of the same operator at the level of the effective mass operator, which is also observed from data.