The neutral kaon decays to $\pi^+ \pi^- \pi^0$: a detailed analysis of the CPLEAR data

A detailed analysis of neutral kaons decaying to \Pgpp \Pgpm \Pgpz\ is presented based on the complete data set containing half a million events. Time-dependent decay rate asymmetries are measured between initially tagged \PKz\ and \PaKz\ and for different regions of the phase space. These asymmetries, resulting from the interference between the CP-conserving decay amplitude of \PKzL\ and the decay amplitude of \PKzS\ -- either CP-violating or CP-conserving -- allow the determinationof the \PKzS\ parameters \etapmz\ (CP-violating) and \lampmz\ (CP-conserving), and also of the main i sospin components of the \PKzS\ decay amplitude. The branching ratio of \PKzS\ $\rightarrow$ \Pgpp \Pgpm \Pgpz\ (CP-conserving) is deduced directly from \lampmz . In addition, we extract the slope parameters describing the energy dependence of the $\PKzL \rightarrow \Pgpp \Pgpm \Pgpz $ Dalitz plot. The whole set of our results fits well within the current phenomenological picture of the neut ral-kaon system including CP violation and Chiral Perturbation Theory (ChPT).