Operator analysis of effective spin-flavor interactions for L=1 excited baryons

Abstract

We match the non-relativistic quark model, with both flavor dependent and flavor independent effective quark-quark interactions, to the spin-flavor operator basis of the 1/Nc expansion for the L=1 non-strange baryons. We obtain analytic expressions for the coefficients of the 1/Nc operators in terms of radial integrals that depend on the shape and relative strength of the spin-spin, spin-orbit and tensor interactions of the model, which are left unspecified. We obtain several new, parameter-free relations between the seven masses and the two mixing angles that can discriminate between different spin-flavor structures of the effective quark-quark interaction. We discuss in detail how a general parametrization of the mass matrix depends on the mixing angles and is constrained by the assumptions on the effective quark-quark interaction. We find that, within the present experimental uncertainties, consistency with the best values of the mixing angles as determined by a recent global fit to masses and decays does not exclude any of the two most extreme possibilities of flavor dependent (independent) quark-quark interactions, as generated by meson (gluon) exchange interactions.

36 pages, 9 figures

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• Towers of baryons of the $\mathcal{N}=2$ quark model band in the large $N_c$ limit