A Search for Lepton Flavour Violation in $Z\to\tau\mu$ decays at $\sqrt{s} = 13$ TeV with the ATLAS Detector

Violation of lepton flavour number conservation is forbidden at tree-level in the Standard Model and highly suppressed at higher orders. While violation of lepton flavour has been observed via neutrino oscillations, it has not yet been measured among charged leptons. The discovery of such processes is therefore a direct sign of new physics beyond the Standard Model. In this thesis, a strategy for analysing the presence of a lepton flavour violating $Z \to \tau_{\mathrm{had}}\mu$ signature in LHC proton-proton collision data is presented. The analysis is based on $\sqrt{s} = 13$ TeV data collected by the ATLAS Detector corresponding to an integrated luminosity of $\mathcal{L} = 11.8~ \mathrm{fb}^{-1}$. A selection of kinematic cuts are tested in order to locate a phase space region that is enhanced in signal. Two such signal regions are defined, yielding a combined statistical significance of 1.6. Monte Carlo simulated events are normalised to data by scale factors derived in normalisation regions. Backgrounds that contribute due to misidentification of tau leptons are estimated from data in control regions using a fake factor method. This results in a background model that is agreement with data at preselection level. Once the proper validation tests have been carried out, the presence of a signal will be evaluated with a likelihood fit in order to detect a signal or set a new upper limit.