Cusp effects in meson decays

TL;DR

This paper develops a non-relativistic effective field theory framework to analyze cusp effects in meson decays, enabling precise extraction of pion-pion scattering lengths and applying the method to various decay channels.

Contribution

It introduces a novel EFT approach to model cusp phenomena in meson decays, including radiative corrections, and extends the analysis to eta and eta' decay channels.

Findings

Framework accurately describes cusp structures in meson decays.

Allows high-precision determination of pion-pion scattering lengths.

Applicable to multiple decay processes, including eta and eta' decays.

Abstract

The pion mass difference generates a pronounced cusp in the pi0 pi0 invariant mass distribution of K+ --> pi0 pi0 pi+ 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 eta and eta' decays, are also discussed.