In this work, the interaction between the Higgs boson and the top quark is studied with the proton-proton collisions at 13 TeV provided by the LHC at the CMS detector at CERN (Geneva). At the LHC, these particles are produced simultaneously via the associate production of the Higgs boson with one top quark (tH process) or two top quarks (ttH process). Compared to many other possible outcomes of the proton-proton interactions, these processes are very rare, as the top quark and the Higgs boson are the heaviest elementary particles known. Hence, identifying them constitutes a significant experimental challenge. A high particle selection efficiency in the CMS detector is therefore crucial. At the core of this selection stands the Level-1 (L1) trigger system, a system that filters collision events to retain only those with potential interest for physics analysis. The selection of hadronically decaying τ leptons, expected from the Higgs boson decays, is especially demanding due to the large background arising from the QCD interactions. The first part of this thesis presents the optimization of the L1 τ algorithm in Run 2 (2016-2018) and Run 3 (2022-2024) of the LHC. It includes the development of a novel trigger concept for the High-Luminosity LHC, foreseen to start in 2027 and to deliver 5 times the current instantaneous luminosity. To this end, sophisticated algorithms based on machine learning approaches are used, facilitated by the increasingly modern technology and powerful computation of the trigger system. The second part of the work presents the search of the tH and ttH processes with the subsequent decays of the Higgs boson to pairs of τ lepton, W bosons or Z bosons, making use of the data recorded during Run 2. The presence of multiple particles in the final state, along with the low cross section of the processes, makes the search an ideal use case for multivariant discriminants that enhance the selectivity of the signals and reject the overwhelming background contributions. The discriminants presented are built using state-of-the-art machine learning techniques, able to capture the correlations amongst the processes involved, as well as the so-called Matrix Element Method (MEM), which combines the theoretical description of the processes with the detector resolution effects. The level of sophistication of the methods used, along with the unprecedented amount of collision data analyzed, result in the most stringent measurements of the tH and ttH cross sections up to date.

The work presented in this thesis spans a wide range of experimental particle physics subjects, starting from level-1 trigger electronics to the final results of the search for Higgs boson decay and to tau lepton pairs. The thesis describes an innovative reconstruction algorithm for tau decays and details how it was instrumental in providing a measurement of Z decay to tau lepton pairs. The reliability of the analysis is fully established by this measurement before the Higgs boson decay to tau lepton pairs is considered. The work described here continues to serve as a model for analysing CMS Higgs to tau leptons measurements.

The book gives a quite complete and up-to-date picture of the Standard Theory with an historical perspective, with a collection of articles written by some of the protagonists of present particle physics. The theoretical developments are described together with the most up-to-date experimental tests, including the discovery of the Higgs Boson and the measurement of its mass as well as the most precise measurements of the top mass, giving the reader a complete description of our present understanding of particle physics.

This thesis presents a 5.5 standard deviation observation of the Higgs boson decaying to fermions using the data collected at the LHC at 13 TeV center-of-mass energy. The studied dataset corresponds to an integrated luminosity of 35.9 inverse femtobarns. The best fit signal strength for the H to tau tau process is measured to be mu = 1.24 ^{+0.29}/{-0.27}, consistent with standard model predictions. Unique event categories are used targeting the leading Higgs boson production processes, gluon fusion, vector boson fusion, and associated production. This provides signal regions sensitive to Higgs boson couplings to both fermions and vector bosons. These two Higgs boson couplings are measured and are consistent with standard model predictions within one standard deviation. This 5.5 standard deviation observation of the H to tau tau process and the consistency of the Higgs boson couplings with the standard model provide confirmation of the Higgs boson Yukawa couplings to fermions. This is evidence that the Higgs field provides mass for the tau lepton in addition to the vector bosons.

This thesis presents a search for long-lived particles decaying into displaced electrons and/or muons with large impact parameters. This signature provides unique sensitivity to the production of theoretical lepton-partners, sleptons. These particles are a feature of supersymmetric theories, which seek to address unanswered questions in nature. The signature searched for in this thesis is difficult to identify, and in fact, this is the first time it has been probed at the Large Hadron Collider (LHC). It covers a long-standing gap in coverage of possible new physics signatures. This thesis describes the special reconstruction and identification algorithms used to select leptons with large impact parameters and the details of the background estimation. The results are consistent with background, so limits on slepton masses and lifetimes in this model are calculated at 95% CL, drastically improving on the previous best limits from the Large Electron Positron Collider (LEP).