Regge-Daughter Hypothesis in the Quark Model

Abstract

The internal Lorentz group generated by orbital and spin transformations on a quark­ antiquark system is utilized to introduce Regge-daughter hypothesis into the quark model. Perturbation solutions of the Domokos-Suranyi type are found (to second order) to an eigen­ value equation which is assumed to determine functional form of any trajectory at the quark level. Particle spectrum in the symmetry limit with no spin-orbit couplings is described by four (five if parity doublet is counted as two) Regge families with only two unknown para­ meters in the linear approximation. The new Gell-Mann-Zweig scheme is reproduced in our model. § 1. In.troduction Within the framework of the quark model we shall develop in this paper the concept of Regge families I) for mesons. Instead of the usual nonrelativistic quark model, we shall make use of an internal space-time symmetry implied by the quark model in its full power.**) Our main assumptions are summarized as follows.