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

The $K^+ to pi^0 pi^0 e^+ u$ ($K_{e4}^{00}$) 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 $K^+ to pi^+ pi^- e^+ u$ 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.