An Experimental Triptych with the ATLAS Detector in the LHC and HL-LHC Era: Geometry Simulations, Upgrade Performances and the Pursuit of Higgs Boson Pairs.

The Large Hadron Collider (LHC), with a plethora of experiments lying strategically around its perimeter, has provided invaluable datasets that can be analysed to interpret our Universe at its most fundamental level. In this work, we utilise the Run 2 (2015-2018) and part of Run 3 (2022-2025) data recorded by the ATLAS detector and collected from proton-proton collisions at centre-of-mass energies of $\sqrt{s} = 13$ and $13.6$ TeV, respectively. One of the main physics goals of the LHC and its forthcoming High-Luminosity upgrade (HL-LHC) is to test the properties of the Higgs boson, discovered in 2012, and of the field responsible for the generation of particle masses. In particular, its self-coupling, $\lambda$, is of special interest, as it directly influences the associated potential and the underlying processes connected to the origin and evolution of the Universe. This thesis includes an effort to constrain it through a search for Higgs boson pair ($HH$) production in the $b\bar b\gamma\gamma$ final state. The presented analysis constitutes the first one using ATLAS Run 3 data up to 2024 and the best single-channel measurement to date. While no excess of events is observed with respect to the Standard Model (SM) background, we set an observed (expected) upper limit on the signal strength of $HH$ production at $\mu_{HH} < 3.7$ ($\mu_{HH} < 2.6$) with 95% confidence level (C.L.), assuming that it does not exist in nature. The expected limit becomes $\mu_{HH} < 3.7$ at 95% C.L. in the case that SM $HH$ production is assumed. These excluded values translate to observed (expected) constraints on the self-coupling strength, $\kappa_\lambda$, which we measure to be $-1.6 < \kappa_\lambda < 6.6$ ($-1.8 < \kappa_\lambda < 6.9$) at 95% C.L. The quartic vertex coupling strength, $\kappa_{2V}$, can also be uniquely probed with the Vector-Boson-Fusion production mode of $HH$ pairs. The derived observed (expected) limits are $-0.5 < \kappa_{2V} < 2.6$ ($-0.4 < \kappa_{2V} < 2.6$). These measurements are enabled by two additional and complementary experimental components. On one side are detector performance studies, focusing on the primary ATLAS Phase-I upgrade, the New Small Wheel (NSW). This detector, responsible for triggering and tracking muon candidates, was installed to mitigate high fake rates from background particles and to withstand the extreme radiation expected in the HL-LHC era. Using Run 3 data, we determine the background rates and assess whether they exceed the design thresholds. On the other side is the detector description of high-energy physics experiments. Specifically, we report the new software architecture for the Muon Spectrometer geometry developed in preparation for the upcoming Run 4. Lastly, these two sides can be combined into a case study linking different detector configuration scenarios with performance. We materialise this using the major ATLAS Phase-II upgrade, the Inner Tracker (ITk), testing its limits under variations in detector material and multiple proton-proton interactions per bunch crossing (pileup). Taken together, detector performance studies and geometry simulations both support and are guided by physics analyses, forming an experimental triptych.