A Transformer and Novel Triggers for the Search for Higgs Boson Pair Production in the $b\bar{b}\tau^{+}\tau^{-}$ Final State with the ATLAS Detector

The Higgs boson self-interaction is a direct probe of the shape of the Higgs potential, one of the last predictions of the Standard Model awaiting experimental confirmation. A major goal of the ATLAS Experiment for the ongoing Run 3 of the LHC is to investigate the self-interaction via searches for Higgs boson pair production ($HH$). The $HH \to b\bar{b}\tau^+\tau^-$ analysis targets one of the most sensitive channels for this search but necessitates refining its strategy for Run 3. Two such refinements are presented in this thesis. In the first study, novel trigger chains are examined to improve the signal efficiency in data-taking, comparing them to baseline triggers used for the Run 2 analysis. The research considers new di-$\tau$ triggers with lower transverse momentum thresholds, the jet-only Delayed stream trigger from the $HH \to b\bar{b}b\bar{b}$ analysis, and proposed $b+\tau$ triggers. Together, the total trigger efficiency can be improved from $55\%$ in Run 2 to up to $85\%$ in Run 3. In the second study, a state-of-the-art machine learning algorithm, a transformer, is employed to separate ggF and VBF $HH$ events. The study achieved a significant enhancement compared to the Run 2 analysis, based on a boosted decision tree. A $15\%$ increase in VBF efficiency for the same ggF contamination, and a $100\%$ increase in ggF rejection (inverted false positive rate) for the same VBF efficiency are found.