Unitary Symmetry and Weak Interactions. III. Nonleptonic Hyperon Decay

Abstract

It is shown that B. W. Lee's relation for nonleptonic hyperon decay can be derived from $T-L$ invariance and $\Delta T=\frac{1}{2}$, and that the vanishing of $\alpha ({\Sigma }^{+}\to n{\pi }^{+})$ requires the additional assumption of $R$ invariance. The vanishing of $\alpha ({\Sigma }^{-}\to n{\pi }^{-})$ cannot be derived from these symmetries, and since there are no others applicable to weak interactions in $\mathrm{SU}\left(3\right)\mathrm{}$, it must result from weak-interaction dynamics. A comparison is made between this theory and those of Cabibbo and Coleman, Glashow and Lee. Mathematical aspects of $T-L$ invariance are discussed in an appendix.