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Physical Review D

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

Cintia Willemyns and Carlos Schat

Departamento de Física, FCEyN, Universidad de Buenos Aires and IFIBA, CONICET, Ciudad Universitaria, Pabellón 1, 1428 Buenos Aires, Argentina

Phys. Rev. D 93, 034007 – Published 5 February, 2016

DOI: https://doi.org/10.1103/PhysRevD.93.034007

Abstract

We match the nonrelativistic quark model, with both flavor-dependent and flavor-independent effective quark-quark interactions, to the spin-flavor operator basis of the $1 / N_{c}$ expansion for the $L = 1$ nonstrange baryons. We obtain analytic expressions for the coefficients of the $1 / N_{c}$ 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.

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