Wing Sheung Chan

160 Summary signal events and major background events in the models. Finally, the compatibility between the data and the models are assessed with hypothesis tests using a likelihood ratio as test statistic. Results To the author’s slight disappointment, no statistically significant evidence of LFV Z → `τ decays is found. The observed and expected neural network output distributions are shown in Figure S.3. Nonetheless, the analysis is still able to pose stringent constraints on the occurring probability of Z → `τ decays, which are meaningful in constraining BSM theory candidates. Upper limits on the LFV branching fraction (fraction of Z bosons which decay by an LFV decay mode with respect to the total number of Z bosons) are set to be 8 . 1 × 10 − 6 and 9 . 5 × 10 − 6 for the Z → eτ and Z → µτ decays, respectively, at 95% confidence level. These limits are currently the most stringent experimental limits on the decays, which superseded the formerly most stringent limits set by experiments at the Large Electron-Positron Collider (LEP) more than two decades ago. The success of the analysis is founded on both the amount of collected data and the analysis techniques used. An especially important analysis technique is the use of multiple neural network classifiers to optimally separate the signal and different backgrounds, which is a relatively novel approach that has not been exploited in similar searches before. Outlook Looking into the future, the result presented in this thesis is likely just the first of many more exciting results to come. With the current analysis techniques, the sensitivity of the search of Z → `τ decays is still primarily limited by statistical uncertainties due to the limited amount of data, instead of systematic uncertainties in the predictions of signal and background events. This implies that with more data collected in the future by the LHC and the ATLAS detector, we will be able to search for LFV Z → `τ decays with an even higher, unprecedented sensitivity. Moreover, in the present analysis, only events where the τ lepton decays into hadrons are analysed. It is possible that the analysis can be further improved by considering events where the τ lepton decays into lighter leptons as well. In fact, there are already ongoing efforts within the ATLAS collaboration to try to search for Z → `τ decays in these events. Significant improvements in sensitivity can be expected when these searches are combined with the present analysis. To conclude, we are now at the beginning of a new era, where the LHC and the ATLAS experiment have opened up new opportunities for lepton flavour violation searches. While this thesis has proudly set new stringent limits on the interesting LFV Z → `τ decays, even more exciting discoveries might be just ahead of us.