Three-Triplet Model with Double<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>SU</mml:mi><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>)</mml:mo><mml:mn/></mml:math>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 $U(3)$ scheme of triplets with integral charges, one is naturally led to three triplets located symmetrically about the origin of ${I}_{3}\ensuremath{-}Y$ diagram under the constraint that the Nishijima-Gell-Mann relation remains intact. A double $\mathrm{SU}(3)$ symmetry scheme is proposed in which the large mass splittings between different representations are ascribed to one of the $\mathrm{SU}(3)$, while the other $\mathrm{SU}(3)$ is the usual one for the mass splittings within a representation of the first $\mathrm{SU}(3)$.