Higgs boson properties and tau lepton identification at the $\sqrt{s}$ = 3 TeV Muon Collider

The Higgs sector of the Standard Model (SM) is of critical importance in high energy particle physics, as the Higgs boson $H$ could couple with new particles and provide a portal to New Physics (NP). Amongst other future colliders currently under study, a Higgs factory such as the Muon Collider would allow to perform unprecedented precision measurements of the Higgs boson parameters. The goal of this thesis is to extract an estimate of the statistical uncertainty on the cross section of the $H\rightarrow \tau^+\tau^-$ process at a 3 TeV center-of-mass energy Muon Collider. In this study, the performance of the TauFinder algorithm, used to reconstruct $\tau$ leptons in their different decay modes through their decay products, is also assessed. An analysis of the pion track and particle reconstruction efficiencies is carried out to find an optimal event reconstruction configuration, aiming at balancing reconstruction efficiency and computational performance. The study of TauFinder's performance demonstrates that the reconstruction efficiency of 1-prong hadronic $\tau$ leptons decays is above 60% in the detector central region ($|\eta| < 0.5$) for 10 GeV/c $\le p_\text{T} \le$ 100 GeV/c, where most $\tau$ leptons resulting from Higgs decay are produced. The energy corrections of the $\tau$ leptons are also computed. The signal process $H \rightarrow \tau^+\tau^-$ is investigated, with a focus on the case of both $\tau$ leptons decaying hadronically ($\tau_h$). The main background processes are discussed and compared with the signal. A Multivariate Analysis technique is applied to enhance the signal-background discrimination: a Boosted Decision Tree (BDT) classifier is trained using kinematical variables of the final state $\tau_h$ leptons from signal and background samples. With the resulting BDT response distributions, histogram template fits are performed in 100k Monte Carlo toy experiments, to extract an estimate of the statistical sensitivity on the cross section of the signal process: $\Delta\sigma/\sigma (H \rightarrow \tau^+\tau^-)$ = 5.3%. Finally, further steps towards improving the sensitivity to the process are discussed.