Four-quark spectroscopy within the hyperspherical formalism

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 ${0}^{+\ensuremath{-}}$ and nonexotic ${2}^{++}$ quantum numbers may be bound independently of the mass of the quark. ${2}^{+\ensuremath{-}}$ and ${1}^{+\ensuremath{-}}$ states become attractive only for larger mass of the quarks.