Measurement of neutral kaon decays with electrons in the final state

In this thesis the analysis of neutral kaon decays with electrons in the final state is described. The data analysed were collected by the CPLEAR detector at CERN. In the first part the analysis of semileptonic decays is described. The crucial part of event selection is electron identification. In this analysis the calorimeter identification is used in addition to the standard CPLEAR particle identification tools. This yields a much cleaner semileptonic sample but at a large loss of statistics. Such a sample is appropriate for the measurement of the parameter $\Re (x)$ that is very sensitive to the accuracy of background description. The parameter $x$ measures the violation of the $\Delta S= \Delta Q$ rule. The result of this measurement is: $\Re (x) = (1.0\pm 5.6\pm4.3)\times 10^{-3}$, by a factor of $\approx $3 more precise that the current world average. In the second part, the search for the rare decay $K_S\rightarrow e^+e^-$ is described. This decay is not allowed in the first order of the weak interaction. The process via the combination of weak and electromagnetic coupling is believed to dominate the decay amplitude. Considering only the decay over a two real photon intermediate state a magnitude of the branching ratio of Br($K_S\rightarrow e^+e^-)\approx 10^{-14}$ is predicted. A much larger value would point to some unknown phenomena which is not included in the Standard Model. Full event reconstruction together with $e/\pi $ separation allow for a powerful background rejection and high signal acceptance. The analysis of the complete set of data yields a new upper limit of the branching ratio: Br$(K_S\rightarrow e^+e^-) < 1.4 \times 10^{-7}$ (90% CL), an improvement on the current experimental limit by a factor of 20.