Cusp effects in meson decays

Helmholtz-Institut fūr Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universität Bonn, D-53115 Bonn, Germany

^a e-mail: kubis@hiskp.uni-bonn.de

Abstract

The pion mass difference generates a pronounced cusp in the π⁰ π⁰ invariant mass distribution of K⁺ → π⁰ π⁰ π⁺ decays. As originally pointed out by Cabibbo, an accurate measurement of the cusp may allow one to pin down the S-wave pion–pion scattering lengths to high precision. We present the non-relativistic effective field theory framework that permits to determine the structure of this cusp in a straightforward manner, including the effects of radiative corrections. Applications of the same formalism to other decay channels, in particular η and η′ decays, are also discussed.