Three triplets, paraquarks, and "colored" quarks

We investigate the interconnection between various "nine-quark" models of hadrons: paraquarks of order 3, tri-"color" Gell-Mann quarks, our distinguishable three triplets with SU(3)′ × SU(3)″ symmetry, and another version with SU(3)′ × SO(3) symmetry. A natural framework in which to distinguish one model from another is provided by a recent theorem by Ohnuki and Kamefuchi on the equivalence relation between a para-Fermi field of order $p$ and a Fermi field with a hidden variable which takes on $p$ different values. Owing to the difference in charge assignment that is natural to each model, the $e^{+}{e}^{-}$ annihilation ratio $R [=\frac{\sigma (e^{+}{e}^{-}\to \mathrm{hadrons})}{\sigma (e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-})}]$ is equal to 2, 4, and 8 for para-(color) quarks, our triplets, and (fractionally charged) triplets with SU(3)′ × SO(3) symmetry, respectively. The experimental data may be interpreted to favor distinguishable triplet models. We then study the dynamics of superstrong interactions implied by the two versions of distinguishable triplet models, and find the SU(3)″ variety to be favored. Assuming integral charge and baryon-number assignment, we discuss the gross mass spectrum of hadrons. Single quarks will have a mass of ∼2 GeV, and decay into ordinary baryons or antibaryons.