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Four-quark spectroscopy within the hyperspherical formalism

N. Barnea·J. Vijande·A. Valcarce
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Abstract

We present a generalization of the hyperspherical harmonic formalism to study systems made of quarks and antiquarks of the same flavor. This generalization is based on the symmetrization of the $N-$body wave function with respect to the symmetric group using the Barnea and Novoselsky algorithm. The formalism is applied to study four-quark systems by means of a constituent quark model successful in the description of the two- and three-quark systems. The results are compared to those obtained by means of variational approaches. Our analysis shows that four-quark systems with exotic $0^{+-}$ and non-exotic $2^{++}$ quantum numbers may be bound independently of the mass of the quark. $2^{+-}$ and $1^{+-}$ states become attractive only for larger mass of the quarks.

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N. Barnea, J. Vijande, A. Valcarce. 2006-04-03. Four-quark spectroscopy within the hyperspherical formalism. https://doi.org/10.1103/physrevd.73.054004

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