Study of the di-tau Drell-Yan process with the ATLAS experiment: a probe for new physics in the Standard Model flavour sector

The ATLAS experiment at the Large Hadron Collider (LHC) has recorded $140~\mathrm{fb}^{−1}$ of proton-proton (pp) collisions at $\sqrt{s} = 13$ TeV in the years $2015$-$2018$. This dataset is fully exploited in this thesis to perform a search for leptoquark particles in di-tau Drell-Yan final states. The main aspects of the analysis are outlined, with particular attention to the estimate of the background of hadronic jets misidentified as hadronic taus. Part of the thesis is also devoted to the ATLAS L0Muon barrel trigger upgrade project, which is ongoing in view of the upcoming High-Luminosity LHC program, with focus on the Sector Logic readout firmware design and implementation.