S-wave $K^-\pi+$ System in $D^+\to K^-\pi^+\pi^+$ Decays from Fermilab E791

TL;DR

This paper presents a model-independent analysis of the S-wave $K ext{-}ar{ ext{K}}$ amplitude in $D^+ o K^-\pi^+\pi^+$ decays, comparing it with elastic scattering data and testing the Watson theorem's predictions.

Contribution

It introduces a new model-independent method for analyzing three-body decays and compares the $K ext{-}ar{ ext{K}}$ S-wave amplitude with elastic scattering results, testing theoretical predictions.

Findings

The $K ext{-}ar{ ext{K}}$ S-wave amplitude was obtained as a function of invariant mass.

Results suggest the Watson theorem does not fully describe the data if $I=\frac{1}{2}$ dominates.

Contributions from $I=\frac{1}{2}$ and $I=\frac{3}{2}$ are not resolved in this study.

Abstract

A new approach to the analysis of three body decays is presented. Model-independent results are obtained for the \swave $K\pi$ amplitude as a function of $K\pi$ invariant mass. These are compared with results from $\Km\pip$ elastic scattering, and the prediction of the Watson theorem, that the phase behavour be the same below $K\eta^{\prime}$ threshold, is tested. Contributions from $I=\half$ and $I={3\over 2}$ are not resolved in this study. If $I=\half$ dominates, however, the Watson theorem does not describe these data well.}