Final-State Interactions in theK→3πandη→3πDecays

Abstract

We derive an integral equation which should describe, to a good approximation, the results of any theory of the $K$ and $\eta 3\pi$ decays. We show that present experimental information implies that one subtraction in this equation is not enough; instead, we find that two subtractions are necessary in order for the equation to describe experiment correctly. We then observe the striking fact that for the weak ($K$) and electromagnetic ($\eta$) decay processes leading to a $3\pi$ final state, the subtraction constants are identical, up to an over-all normalization. A short discussion of the possible significance of this is given, although no definite conclusions are reached. Our analysis confirms the suggestion that $\pi \pi$ final-state interactions will appear only in quadratic terms in the $3\pi$ final state.