Parity-Violating Nonleptonic Decay and the Cabibbo Current

In a current×current theory of weak interactions, the use of a Cabibbo-type current endows parity-violating nonleptonic decay with certain specific properties. These properties do not include octet dominance, but they are sufficient to forbid all $K\to 2\pi$ decays in the limit of $\mathrm{SU}\left(3\right)\mathrm{}$-conserving strong interactions. When electromagnetic corrections are taken into account, the decay modes $K_1^{}{}_{}{}^0\to {\pi }^{+}{\pi }^{-}$ and $K^{+}\to {\pi }^{+}{\pi }^0$ are allowed, but $K_1^{}{}_{}{}^0\to 2{\pi }^0$ is still forbidden. Consequently the smallness of the rate for $K^{+}\to {\pi }^{+}{\pi }^0$ relative to both modes of $K_1^{}{}_{}{}^0$ decay can be explained only by an appeal to medium-strong, $\mathrm{SU}\left(3\right)\mathrm{}$-breaking interactions. In the case of nonleptonic hyperon decay, the Cabibbo current×current interaction predicts two sum rules for parity-violating amplitudes. The recent results obtained by Sugawara and Suzuki from current commutation relations can be understood in terms of these sum rules, together with one simple constraint upon the effective Hamiltonian.