Lie Group of the Strong-Coupling Theory. II. Equivalence with Static Bootstrap Theory and Application to Pion-Hyperon Scattering

The mathematical equivalence of the Lie-group approach of Cook, Goebel, and Sakita to strong-coupling theory and certain conventional static bootstrap models is established. This equivalence is exploited to explicitly exhibit a new irreducible representation of the strong-coupling group $\mathrm{}\left[SU\right(2\mathrm{})\mathrm{}\otimes \mathrm{SU}(2\left)\right]\times T_9$. This new representation is suitable for accommodating the $Y=0\mathrm{}$ hyperon isobars and has the spin-isospin content $J=I\pm \frac{1}{2}=\frac{1}{2}, \frac{3}{2}, \frac{5}{2}, \cdots$. We obtain $\frac{\Gamma ({Y_1}^{*}\to \Sigma \pi )}{\Gamma ({Y_1}^{*}\to \Lambda \pi )}=12\%$ [$\mathrm{SU}\left(3\right)\mathrm{}$ prediction 16%; observed ratio 11%]. The ratio of (${Y_1}^{*}\to \Lambda \pi$) to ($\Sigma \to \Lambda \pi$) coupling and the isovector magnetic moments come out in agreement with $\mathrm{SU}\left(6\right)\mathrm{}$, while the ratio of $\Sigma \Sigma \pi$ to $\Sigma \Lambda \pi$ coupling comes out having the $\mathrm{SU}\left(3\right)\mathrm{}$ sign and approximately the $\mathrm{SU}\left(3\right)\mathrm{}$ magnitude corresponding to $\frac{D}{F}=\frac{3}{2}$.