The ATLAS experiment comprises one of the largest scientific collaborations in the history of the natural sciences, exploring physical phenomena at the smallest probed scales. The known elementary particles and their fundamental interactions are described by the Standard Model (SM). This theory makes exceptionally precise predictions, but also has compelling shortcomings, such as the origin of Dark Matter or the naturalness problem of the Higgs boson mass. ATLAS performs precision measurements to deepen our understanding of the SM, along with searches for hints of new physics.

The Trigger system is an essential component of the ATLAS detector. It selects which collision events are recorded by performing real-time analysis of detector signals. Trigger decisions reduce the event rate from almost 40 MHz to roughly 3 kHz. This significant reduction must preserve maximal efficiency for relevant physics events. In this thesis, a novel trigger methodology is implemented: the fast b-tagging preselection, filtering events containing b-jets in early stages of the High-Level Trigger (HLT). This approach relies on a Machine Learning algorithm, which analyses coarse tracks to tag jets. This preselection was deployed in HLT for the beginning of Run 3, optimising computing resources and allowing looser thresholds for event discrimination. An efficiency enhancement of nearly 50% is achieved for key physics signatures, such as HH → bbbb decays. Furthermore, implementing jet flavour tagging in early stages of the HLT allowed the introduction of b-tagging in the Trigger-level analysis data stream.

Supersymmetry (SUSY) provides a rich framework for new physics, extending the SM. In SUSY theories, the Higgs naturalness problem vanishes, and new DM candidate particles are allowed. This thesis scrutinised the full Run 2 ATLAS dataset in a search for resonant decays of heavy SUSY particles. Decay channels through R-parity violating couplings were considered, which lead to less-constrained fully-hadronic final states. To deal with the challenging background arising from strong interactions, two alternative approaches were used: an improved cut-and-count method and a new technique that leverages ML algorithms. Both approaches led to significant sensitivity improvements compared to previous analyses. No excesses were found with respect to the expected background, and cross-section limits were set on several SUSY models. Furthermore, the results obtained with the cut-and-count were interpreted in the context of alternative theories, constraining an extended portion of the SUSY parameter space.