Sum Rules forK-Meson Decays withCPNonconservation

Abstract

The well-known isospin relations for $K\to 2\pi$ and $K\to 3\pi$ decays with $\mathrm{CP}$ conservation are generalized to include the case of $\mathrm{CP}$-nonconserving weak interaction, but keeping $\mathrm{CPT}$ invariance and $\left|\Delta \mathrm{I}\right|<~\frac{3}{2}$. Specifically the amplitude relation $2(K^{+}\to {\pi }^{+}{\pi }^0)=({K_1}^0\to {\pi }^{+}{\pi }^{-})-2({K_1}^0\to {\pi }^0{\pi }^0)$ is generalized and found to be in agreement with experiment.