Statistical interpretations of the null result of the KARMEN 2 experiment

Several possible statistical interpretations of the null result of the KARMEN 2 neutrino oscillation experiment are discussed with the aim of clarifying the implications of the fact that KARMEN 2 did not observe any of the expected background events. The formalism that allows to take into account the error of the expected mean background in a Poisson process with background is presented and applied to the statistical analysis of the KARMEN 2 null result. The possibility of ignoring the expected mean background calculated for the KARMEN 2 experiment is discussed and it is shown that the resulting exclusion curves are ultra-conservative, but may be a safe choice in such a controversial case. It is also shown that the sensitivity curves of neutrino oscillation experiments cannot be considered as exclusion curves. The implications of the different statistical analyses of the KARMEN 2 null result for the compatibility of the results of the KARMEN 2 and LSND experiments is discussed.