Unitary Triplets and the Eightfold Way

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 $\kappa \mathrm{}\left(725\right)\mathrm{}$ along with the isosinglet $z^{+}\mathrm{}(Y=2\mathrm{})\mathrm{}$ or ${\eta }^{\prime }\mathrm{}(Y=0\mathrm{})\mathrm{}$ 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 ${\nu }_e\leftrightarrow p\text{'}\text{'}cos\theta +Z\text{'}\text{'}sin\theta ,$ ${\nu }_{\mu }\leftrightarrow -p\text{'}\text{'}sin\theta +Z\text{'}\text{'}cos\theta$ $e^{-}\leftrightarrow n\text{'}\text{'}{cos\theta }^{\prime }+{\Lambda }^{\prime }\text{'}\text{'}{sin\theta }^{\prime },$ ${\mu }^{-}\leftrightarrow -n\text{'}\text{'}{sin\theta }^{\prime }+{\Lambda }^{\prime }\text{'}\text{'}{cos\theta }^{\prime },$ between four leptons and four elementary baryon fields is shown to be possible.