Measurement of $K^+ \to \pi^0 \pi^0 e^+ \nu$ ($K_{e4}^{00}$) decay using stopped positive kaons

TL;DR

This paper reports the measurement of the rare $K_{e4}^{00}$ decay using stopped positive kaons, determining the form factor and confirming its consistency with related decay modes, highlighting its potential for studying $mbda$-$$ scattering lengths.

Contribution

First measurement of the $K_{e4}^{00}$ decay with stopped kaons, providing form factor data and demonstrating its use in $mbda$-$$ scattering length determination.

Findings

Measured 216 decay events of $K_{e4}^{00}$.

Observed spectra consistent with Monte Carlo simulations.

Established $K_{e4}^{00}$ as a tool for $mbda$-$$ scattering length analysis.

Abstract

The $K^+ \to \pi^0 \pi^0 e^+ \nu$ ($K_{e4}^{00}$) decay has been measured with stopped positive kaons for a data sample of 216 events. A comparison of the observed spectra with a Monte Carlo simulation determined the $K_{e4}^{00}$ form factor. The results are compatible with the $K^+ \to \pi^+ \pi^- e^+ \nu$ data, as estimated from the $\Delta I=1/2$ rule. We also established that the $K_{e4}^{00}$ channel can be used to determine the $\pi$-$\pi$ scattering lengths.