A measurement of $K^{0}, \overline{K^{0}} \rightarrow 3\pi^{0}$ and an improved test of CPT

The CPLEAR experiment at CERN is aimed to study CP-, T- and CPT-symmetries in the neutral-kaon system. The neutral kaons are produced in $p \overline{p}$ annihilations at rest : \begin{center} $p øverline{p} \rightarrow øverline{K^0} K^+ \pi^-$, $K^0 K^- \pi^+$ . \end{center} The observation of the sign of the accompanying charged kaon allows one to determine for each event, whether the neutral kaon is a $\overline{K^0}$ or a $K^0$. This gives to CPLEAR the capacity of extracting relevant physical parameters through time-dependent asymmetries between the rates of initially pure $K^0$ and $\overline{K^0}$ decaying into various final states. \vspace{5mm} In this work an analysis of $K^0,\overline{K^0} \rightarrow \pi^0 \pi^0 \pi^0$ decays is presented. This analysis has lead to the determination of the real and imaginary part of the CP-violation parameter $\eta_{000}$ which are measured to be : \begin{eqnarray*} Re(\eta_{000}) & = & 0.18 \pm 0.14(stat) \pm 0.06(syst) \\ Im(\eta_{000}) & = & 0.15 \pm 0.20(stat) \pm 0.03(syst) . \end{eqnarray*} These values, although still compatible with CP-conservation, represent the best sensitivity to CP-violation in this decay mode; they lead to an upper limit $|\eta_{000}| < 0.58$ at $90 \%$ confidence level. Using the result on $Re(\eta_{000})$ and $Im(\eta_{000})$ together with unitarity relations in the neutral-kaon system, the imaginary part of the CPT-violation parameter $\delta$ is found to be : \begin{eqnarray*} Im(\delta) & = & (1.3 \pm 3.6) \cdot 10^{-5} . \end{eqnarray*} This value is in agreement with CPT-invariance; it leads to a mass difference between the neutral kaon and its antiparticle : \begin{eqnarray*} M_{K^0} - M_{øverline{K^0}} & = & (1.8 \pm 5.1) \cdot 10^{-19} GeV/c^2 . \end{eqnarray*} The limit on this mass difference is of the order of the inverse of the Planck scale and experimentally confirms the CPT-invariance in the neutral-kaon system up to these scales.