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 rj 3ir 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 (rj) decay processes leading to a 3ir 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 mr final-state interactions will appear only in quadratic terms in the 3-?r final state.