Bootstrap Model of Meson and Baryon Supermultiplets

The $\mathrm{SU}\left(6\right)\mathrm{}$-symmetric bootstrap model of the baryon supermultiplet is discussed and extended. The relation between the static limit of the model and relativistic interactions is discussed. A hypothesis is made concerning the meson-meson-meson interactions. The $V_8$ (vector octet) exchange forces in the $V_8+V_8$ states may lead to the bootstrapping of the $X_0$ meson in this model. The bootstrapping of the other mesons is discussed. It is postulated that the lightest odd-parity baryon isobars are produced by meson exchange forces in meson-baryon $S$ states. The lightest odd-parity resonances predicted from this postulate are a spin-½ singlet and a spin-$\frac{3}{2}$ octet. These may be identified with the 1405-MeV ${Y_0}^{*}$ and the "$D_{\frac{3}{2}}$" baryon-meson resonance octet. Recent data concerning the various decay amplitudes of the ${\frac{3}{2}}^{-}$ resonances are compared with the predictions of $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry.