Machine Learning Methods for Tau Lepton Identification and Search for the Supersymmetric Partner of the Tau Lepton Using CMS Run 2 Data

Gauge-mediated supersymmetry breaking models provide a compelling framework for the search for a supersymmetric partner of the tau lepton ($\widetilde{\tau}$) with a macroscopic lifetime. In such scenarios, $\widetilde{\tau}$ can decay to tau lepton displaced from the primary proton-proton interaction vertex. Standard tau reconstruction and identification techniques at the Compact Muon Solenoid (CMS) experiment are not designed for these displaced signatures, motivating the development of specialised approaches. This thesis begins by improving the existing CMS tau identification algorithms for prompt taus using modern machine learning techniques. Building on this foundation, a graph-based neural network is introduced to reliably identify displaced tau leptons, where large displacements pose unique detection challenges. Leveraging this dedicated displaced-tau identification, the first search for the direct production of moderately long-lived $\widetilde{\tau}$ particles (decaying within the tracker volume) with hadronic taus in the final state is performed using proton-proton collision data at $\sqrt{s}=13\text{ TeV}$. The analysis is based on a dataset corresponding to an integrated luminosity of $138\text{ fb}^{-1}$, collected by the CMS experiment from 2016 to 2018. This work significantly enhances sensitivity to $\widetilde{\tau}$ decay lengths of the order of centimetres or more, expanding the experimental coverage of gauge-mediated supersymmetry breaking scenarios.