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

Abstract

The $K^+ \to π^0 π^0 e^+ ν$ ($K_{e4}^{00}$) 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 $K^+ \to π^+ π^- e^+ ν$ data, as estimated from the $ΔI=1/2$ rule. We also established that the $K_{e4}^{00}$ channel can be used to determine the $π$-$π$ scattering lengths.