Cusps in eta' --> eta pi pi decays

TL;DR

This paper predicts a significant cusp effect in eta' --> eta pi pi decays using a generalized non-relativistic effective field theory, offering a new way to study pi pi interactions but not pi eta parameters.

Contribution

It extends the non-relativistic effective field theory framework to eta' decays, predicting a measurable cusp effect and analyzing its implications for scattering length extraction.

Findings

Cusp effect exceeds 8% in decay spectrum below pi+ pi- threshold

The cusp effect can be used to extract pi pi S-Wave scattering lengths

Current data does not allow extraction of pi eta threshold parameters

Abstract

The discovery of the cusp effect in the decay K+ --> pi+ pi0 pi0 has spurred the search for other decay channels, where this phenomenon, which is generated by strong final-state interactions, should also occur. A very promising candidate is eta' --> eta pi0 pi0. The cusp effect offers an excellent opportunity to experimentally extract pi pi S-Wave scattering lengths. We adapt and generalize the non-relativistic effective field theory framework developed for K --> 3 pi decays to eta' --> eta pi pi. The cusp effect is predicted to have an effect of more than 8 % on the decay spectrum below the pi+ pi- threshold. We also show that with our current theoretical information about eta' --> eta pi pi decays, it is not possible to extract pi eta threshold parameters.