Development of $\tau$ selection techniques and search for the Higgs boson produced in association with top quarks with the CMS detector at the LHC

This thesis presents a study of the Higgs boson production in association with one top quark (tH) top quarks ($\mathrm{t\bar{t}H}$) with the proton-proton collisions at 13 TeV provided by the LHC at the CMS detector at CERN. These production modes are important to characterize the coupling of the Higgs boson to the top quark ($y_t$), directly accessible upon measurement of the cross sections of these processes. Additionally, the processes are sensitive to the existence of physics beyond the Standard Model, as variations of the predicted couplings result in a measurable change of the value of the cross sections. The production of these processes is very rare; hence, maximizing the selection efficiency is essential. The first part of the thesis work is devoted to the optimization of the algorithm to select tau leptons that decay into hadrons ($\tau_h$) in the Level-1 (L1) trigger of CMS. The work is focused on the improvement of the trigger during Run 2 (2016-2018) and Run 3 (2022-2024) of the LHC and to the development of a new trigger concept for the High-Luminosity LHC (HL- LHC), foreseen to start in 2027. The data collected by these triggers is pivotal to enlarge the sensitivity to the tH and $\mathrm{t\bar{t}H}$ processes. The second part of the thesis work is dedicated to the search of the tH and $\mathrm{t\bar{t}H}$ processes where the Higgs boson decays into a W, Z or tau pair making use of the data produced in Run 2, corresponding to an integrated luminosity of $137~\mathrm{fb}^{-1}$. The presence of multiple background processes makes this analysis relatively complex. For this reason, multivariate techniques are employed to extract the signal making use of machine learning algorithms and the Matrix Element Method (MEM). The measured cross sections normalized to the theoretical prediction amount to 0.92$^{+0.26}_{-0.23}$ for $\mathrm{t\bar{t}H}$ and to $5.67^{+4.05}_{-3.98}$ for tH, in agreement with the Standard Model. The value of $y_t$ normalized to the theoretical prediction is contrained to the intervals $-0.9 < y_t < -0.7$ or $0.7 < y_t < 1.1$ at 95% confidence level.