Corrections to the Octuplet Spurion in the Nonleptonic Decays of the Hyperons

Corrections due to the 27-plet spurion and the second-order electromagnetic effects are calculated to the octuplet spurion in the nonleptonic hyperon decays. The 27-plet spurion predicts a relation among small deviations from the $\Delta I=\frac{1}{2}$ rule, namely $\left(〈\Lambda \right|p{\pi }^{-}〉+\sqrt{2}〈\Lambda \left|n{\pi }^0〉\right)=-\left(〈{\Xi }^{-}\right|\Lambda {\pi }^{-}〉+\sqrt{2}〈{\Xi }^0\left|\Lambda {\pi }^0〉\right)$ for the parity-violating amplitudes. This holds as it stands if the second-order electromagnetic effects are introduced on the assumption of the octuplet tadpole mechanism. A test of this relation, although still not possible with present experimental data, has a deep significance for the structure of the weak interactions.