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 [SU(2)SU(2)]×T₉. This new representation is suitable for accommodating the $Y=0$ hyperon isobars and has the spin-isospin content J=I±1/2=1/2, 3/2, 5/2, ⋯. We obtain Γ(Y₁*→Σπ)Γ(Y₁*→Λπ)=12% [SU(3) prediction 16%; observed ratio 11%]. The ratio of (Y₁*→Λπ) to (Σ→Λπ) coupling and the isovector magnetic moments come out in agreement with SU(6), while the ratio of ΣΣπ to ΣΛπ coupling comes out having the SU(3) sign and approximately the SU(3) magnitude corresponding to D/F=3/2.