Search of Higgs Boson Pair Production in the bbtautau Channel with Run 2 and partial Run 3 data at the ATLAS experiment and MEDI-Net: Development of Ultra-Fast Machine Learning Algorithms for Trigger Upgrade in the HL-LHC regime

The measurement of Higgs boson pair production constitutes a central objective of the Large Hadron Collider (LHC) physics programme, as it provides direct access to the Higgs boson self-coupling and to the structure of the Higgs scalar potential. Among the experimentally accessible final states, the channel where the Higgs bosons decay into a pair of bottom quarks (b¯b) and a pair of tau leptons offers a favourable compromise between signal branching fraction and background controllability. At the same time, it remains experimentally challenging due to its complex event topology and the presence of large backgrounds. This thesis presents several developments aimed at improving the sensitivity of the ATLAS search for Higgs boson pair production in the HH -> b¯b tau+ tau- , the final state in which both tau leptons decay hadronically. On the physics analysis side, new trigger strategies are developed for the early Run 3 data-taking period, namely corresponding here to the 2022→ 2023 proton-proton collision data at \sqrt{s} = 13.6 TeV, and the analysis is updated to maximise their impact. An improved event selection and categorisation strategy is introduced, leading to a significant enhancement in the expected sensitivity with respect to the previous Run 2-only analysis. In particular, after accounting for the increase in integrated luminosity, an additional improvement of 24% is observed in the expected upper limit on the signal strength µHH , and can be attributed to the methodological developments implemented in this work. In parallel, dedicated studies are performed in view of future iterations of the analysis using the full Run 3 dataset. These include the optimisation and evaluation of the GNtau algorithm as a candidate next-generation method for hadronic tau -lepton identification in ATLAS, as well as the development of a new combined b + tau trigger configuration. The latter was studied as an alternative trigger strategy relying only on the combined presence of b-jet and hadronic-tau signatures, without requiring the full set of complementary triggers used in the early Run 3 analysis. Its effciency, evaluated after the offine event selection relevant for the analysis, is found to be comparable to that of the complete trigger strategy adopted during early Run 3 operation, motivating its central role in the forthcoming b¯b tau+ tau- analysis. The thesis also addresses challenges related to real-time event selection at the High-Luminosity LHC. A prototype hardware-oriented neural network (MEDI-Net) is developed as a candidate architecture for machine-learning-based triggering in the ATLAS Muon Spectrometer. While the achieved fake-muon rate does not yet satisfy the target requirement of 0.2%, the model exhibits competitive performance, with a latency of 347 ns, an FPGA resource occupancy of approximately 5%, and a plateau effciency of about 99%. In addition, an exploratory research activity investigates the use of memristive devices (non-volatile electronic components whose resistance depends on the history of the current that has flowed through them, enabling the storage and processing of information within the same physical element) for analog in-memory computing as a potential solution for ultra-low-power inference at trigger level. As a proof of principle, a 3-bit logic encoding is successfully implemented and characterised on memristor devices. Overall, this work contributes to both the methodological and technological aspects of Higgs boson pair searches at ATLAS, providing incremental improvements to current analyses while maintaining a common focus on trigger-related developments. These range from the optimisation of Run 3 trigger strategies and effciency studies, to the exploration of future machine-learning techniques for real-time event selection at the HL-LHC, and to the investigation of memristive devices as a possible ingredient of next-generation readout and trigger systems.