Unitary Triplets and the Eightfold Way

Abstract

In order to explain the eightfold way, four elementary baryon fields are introduced. Three of them form a unitary triplet and the fourth is a unitary singlet. In this approach, triplets, sextets, etc., are possible multiplets as well as singlets, octets, decuplets, etc. This model has a new quantum number, "hypercharge center." Assuming that the symmetry-breaking interactions transform like components of a triplet, selection rules in the production and decay of the triplets are derived. It is proposed that the isodoublet $\ensuremath{\kappa}(725)$ along with the isosinglet ${z}^{+}(Y=2)$ or ${\ensuremath{\eta}}^{\ensuremath{'}}(Y=0)$ forms a unitary triplet. If the symmetry-breaking interaction transforms like a component of the octet, the following baryon lepton symmetry suggested by Gell-Mann ${\ensuremath{\nu}}_{e}\ensuremath{\leftrightarrow}p''cos\ensuremath{\theta}+Z''sin\ensuremath{\theta},$ ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\leftrightarrow}\ensuremath{-}p''sin\ensuremath{\theta}+Z''cos\ensuremath{\theta}$ ${e}^{\ensuremath{-}}\ensuremath{\leftrightarrow}n''{cos\ensuremath{\theta}}^{\ensuremath{'}}+{\ensuremath{\Lambda}}^{\ensuremath{'}}''{sin\ensuremath{\theta}}^{\ensuremath{'}},$ ${\ensuremath{\mu}}^{\ensuremath{-}}\ensuremath{\leftrightarrow}\ensuremath{-}n''{sin\ensuremath{\theta}}^{\ensuremath{'}}+{\ensuremath{\Lambda}}^{\ensuremath{'}}''{cos\ensuremath{\theta}}^{\ensuremath{'}},$ between four leptons and four elementary baryon fields is shown to be possible.