Experimental study of 30 000Ke4decays

An experiment on the decay $K^{+}\to {\pi }^{+}{\pi }^{-}{e}^{+}\nu$ was performed at the CERN proton synchrotron with spark-chamber and counter techniques. The $K_{e4\mathrm{}}$ branching ratio has been measured relative to the $\tau$ decay. The $\pi \pi$ phase-shift difference ${\delta }_0^0 - {\delta }_1^1$ and the form factors of the hadronic current have been determined as functions of the $\pi \pi$ energy. The $\pi \pi$ scattering length $a_0^0$ has been evaluated from the phase shifts with a phenomenological model. The results are compared with the theoretical predictions of current algebra and other models.