Search for the Higgs boson produced in association with a top quark using $\tau$ leptons with ATLAS

This thesis presents the search for a Higgs boson produced in association with a single top quark ($tHq$) in the final state characterised by two light leptons and one hadronically decaying tau ($2\ell+\tau_{\text{had}}$). The measurement $tHq$ production is the only way to simultaneously determine the magnitude and relative sign of the Yukawa coupling between the Higgs boson and the top quark. Utilising 140 $\text{fb}^{-1}$ of proton-proton collision data at $\sqrt{s}=13$ TeV from LHC's Run 2 collected by the ATLAS detector, this research faces the challenge of the $tHq$ process's extremely small cross-section, especially in the $2\ell+\tau_{\text{had}}$ final state channel, which accounts for only 3.5% of total $tHq$ production. Moreover, the significant presence of background processes that can mimic the signal in the detector further complicates the selection of a pure dataset for analysis. Therefore, machine learning techniques, employing boosted decision trees, are used to both reconstruct the events and distinguish $tHq$ signal events from background events.