Three-Triplet Model with Double $\mathrm{SU}\left(3\right)\mathrm{}$ Symmetry

With a view to avoiding some of the kinematical and dynamical difficulties involved in the single-triplet quark model, a model for the low-lying baryons and mesons based on three triplets with integral charges is proposed, somewhat similar to the two-triplet model introduced earlier by one of us (Y. N.). It is shown that in a $U\left(3\right)\mathrm{}$ scheme of triplets with integral charges, one is naturally led to three triplets located symmetrically about the origin of $I_3-Y$ diagram under the constraint that the Nishijima-Gell-Mann relation remains intact. A double $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry scheme is proposed in which the large mass splittings between different representations are ascribed to one of the $\mathrm{SU}\left(3\right)\mathrm{}$, while the other $\mathrm{SU}\left(3\right)\mathrm{}$ is the usual one for the mass splittings within a representation of the first $\mathrm{SU}\left(3\right)\mathrm{}$.