Strong Isospin Breaking and NonleptonicKDecays

Abstract

Assuming (a) an exactly $\left|\Delta I\right|=\frac{1}{2}$ weak Lagrangian and (b) the existence of an isospin-breaking term, ${\epsilon }_3{u}_3$, in the strong Hamiltonian, the ratios of reduced decay rates for $K\to 3\pi$ and $K\to 2\pi$ decays, observed experimentally to vary from the $\left|\Delta I\right|=\frac{1}{2}$ predictions by ∼10%, are well explained if ${\epsilon }_3\sim 0.05$. Rare $K$-decay modes involving two photons are estimated.