The Octet Model and its Clebsch-Gordan Coefficients

TLDR

The octet model provides a mathematical framework for strong interactions. The study applies the Wigner–Eckart theorem to derive a general mass formula for octet particles. The authors derive SU(3) Clebsch–Gordan coefficients, symmetry relations, and Yukawa couplings, and use the Wigner–Eckart theorem to obtain mass formulas. The derived Gell‑Mann–Okubo mass relation is well satisfied by vector mesons when the K* is taken as the 730‑MeV resonance. C.E.S.

Abstract

The Clebsch-Gordan (CG) coefficients of SU(3) are derived for the products of the most important irreducible representations. Useful symmetry relations for the CG coefficients are derived. The Wigner-Eckart theorem for this group is given and applied to derive a general mass formula for the octets. The Gell-Mann-Okubo mass relation and a mass relation foi the octets that is very well satisfied by the vector mesons, if one takes as the K/sup */ the 730-Mev (K- pi ) resonance, are given. The Yukawa couplings between baryons and mesons are considered. The mathematical framework of the octet model for strong interactions is examined. (C.E.S.)