Searching for new physics with tau leptons and silicon tracker upgrades in the ATLAS detector

This thesis discusses an analysis searching for new physics beyond the Standard Model, particularly for heavy neutral resonances such as additional $H\textrm{/}A$ Higgs bosons proposed by the Minimal Supersymmetric Standard Model, as well as heavy $Z^{\prime}$ bosons. The search is conducted through the di-tau lepton final state, with focus in this thesis on the leptonic-hadronic decay channel. The analysed data was collected by the ATLAS detector, recording 139 fb$^{-1}$ integrated luminosity of proton-proton collisions within the Large Hadron Collider at 13 TeV during its Run-2. The analysis also incorporates the latest Athena Release 21 software for event reconstruction, delivering significant improvements to tau lepton identification and electron rejection algorithms which are also studied in this thesis. The result of the analysis finds no significant excess beyond the Standard Model, but sets record exclusion limits on the proposed models, in the mass range of 0.2 to 2.5 TeV, extending the result by 4 to 5 times that of previous analyses. The outlook to the ATLAS Phase-2 upgrade is also discussed, through the installation of a new all-silicon Inner Tracker. Prototype barrel strip detector modules are assembled and tested throughout this research programme, with focus on developing improvements to the construction tooling and procedures, whilst transitioning to the testing of fully electrical components.