Cusps in K→3π decays

Abstract

Abstract The pion mass difference generates a pronounced cusp in K → 3 π decays. As has recently been pointed out by Cabibbo and Isidori, an accurate measurement of the cusp may allow one to pin down the S-wave ππ scattering lengths to high precision. Here, we present and illustrate an effective field theory framework that allows one to determine the structure of this cusp in a straightforward manner. The strictures imposed by analyticity and unitarity are respected automatically.