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 analysis described in this thesis is the search for the Higgs boson, decaying into bb pair, in the associated production with a vector boson, in the extreme Higgs boson transverse momentum region where the Higgs boson is reconstructed using the large-R jet technique. The use of the large-R jets allows to add a part of the phase space unexplored so far, which is particularly sensitive to possible new physics. The analysed data have been collected at LHC by the ATLAS detector between 2015 and 2018 at a centre-of-mass energy of √s = 13 TeV. The same dataset has been used to perform the differential pp → ZH and pp → WH cross-section measurements used to extract the information on the Higgs couplings and to put limits on Beyond the Standard Model effects. Furthermore the analysis has been re-used to perform a cross-section measurement of the diboson ZZ and WZ processes because the diboson and the Higgs processes have a similar topology. For the first time the ZZ(bb) and WZ(bb) cross-sections are measured at √s = 13 TeV and the observed cross-section measurements are consistent with the Standard Model predictions.

The discovery in 2012 of the Higgs boson at the Large Hadron Collider (LHC) represents a milestone for the Standard Model (SM) of particle physics. Most of the SM Higgs production and decay rates have been measured at the LHC with increased precision. However, despite its experimental success, the SM is known to be only an effective manifestation of a more fundamental description of nature. The scientific research at the LHC is strongly focused on extending the SM by searching, directly or indirectly, for indications of New Physics. The extensive physics program requires increasingly advanced computational and algorithmic techniques. In the last decades, Machine Learning (ML) methods have made a prominent appearance in the field of particle physics, and promise to address many challenges faced by the LHC. This thesis presents the analysis that led to the observation of the SM Higgs boson decay into pairs of bottom quarks. The analysis exploits the production of a Higgs boson associated with a vector boson whose signatures enable efficient triggering and powerful background reduction. The main strategy to maximise the signal sensitivity is based on a multivariate approach. The analysis is performed on a dataset corresponding to a luminosity of 79.8/fb collected by the ATLAS experiment during Run-2 at a centre-of-mass energy of 13 TeV. An excess of events over the expected background is found with an observed (expected) significance of 4.9 (4.3) standard deviation. A combination with results from other \Hbb searches provides an observed (expected) significance of 5.4 (5.5). The corresponding ratio between the signal yield and the SM expectation is 1.01 +- 0.12 (stat.)+ 0.16-0.15(syst.). The 'observation' analysis was further extended to provide a finer interpretation of the V H(H → bb) signal measurement. The cross sections for the VH production times the H → bb branching ratio have been measured in exclusive regions of phase space. These measurements are used to search for possible deviations from the SM with an effective field theory approach, based on anomalous couplings of the Higgs boson. The results of the cross-section measurements, as well as the constraining of the operators that affect the couplings of the Higgs boson to the vector boson and the bottom quarks, have been documented and discussed in this thesis. This thesis also describes a novel technique for the fast simulation of the forward calorimeter response, based on similarity search methods. Such techniques constitute a branch of ML and include clustering and indexing methods that enable quick and efficient searches for vectors similar to each other. The new simulation approach provides optimal results in terms of detector resolution response and reduces the computational requirements of a standard particles simulation.

The absence of new physics at the TeV scale observed thus far at the Large Hadron Collider (LHC) motivates an increasing focus on searches for weakly-coupled new particles and exotic signatures. In particular, particles with macroscopic mean proper lifetimes, known as long-lived particles (LLPs), are of significant interest due to their ability to elude the majority of searches which rely on the assumption that Beyond Standard Model particles decay close to the primary interaction point. Many models which aim to solve various issues with the Standard Model (SM) introduce new particles with lifetimes that are either unconstrained, or even shown to prefer the macroscopic regime. These theories often point to the Higgs boson as a possible portal to new physics, with exotic Higgs decays being the primary phenomenological consequence and means of discovery. It is well motivated both from theory and experimental constraints to consider the scenario in which the particles produced in these exotic decays have macroscopic proper lifetimes and give rise to unique detector signatures. This work describes a search for exotic decays of the Higgs boson to two long-lived, neutral, spin-0 particles which subsequently decay to pairs of b quarks, giving the striking signature of displaced hadronic jets in the ATLAS inner detector. Several other ATLAS searches have probed this decay topology previously, excluding branching ratios of the Higgs boson to LLPs of more than 10% for proper lifetimes greater than 100mm. These searches relied on dedicated triggers designed to select events with LLPs decaying in the ATLAS calorimeter or muon spectrometer. The lack of an equivalent trigger for LLP decays in the ATLAS inner detector has been a limiting factor in probing LLP lifetimes less than 100mm. To circumvent the difficulty of triggering on LLP decays, the search presented in this thesis exploits the ZH associated production mode, relying on leptonic trigger signatures to select interesting events. This is the first search for Higgs boson decays into LLPs to exploit this analysis methodology and additionally makes use of several novel methods for both background rejection and background estimation. No excess over Standard Model predictions is observed, and upper limits are set on the branching ratio of the Higgs boson to LLPs . Depending on the mass of the LLP, branching ratios greater than 10% are excluded for lifetimes as small as 4mm and as large as 100mm, probing an important gap in the ATLAS exotic Higgs decay programme. In comparison to the previous searches for Higgs decays to LLPs, these are among the most stringent limits placed on this scenario, and for LLPs with masses below 40 GeV these results represent the strongest existing constraints on the branching ratio of the Higgs boson to LLPs in this lifetime regime.

This Thesis describes the first measurement of, and constraints on, Higgs boson production in the vector boson fusion mode, where the Higgs decays to b quarks (the most common decay channel), at the LHC. The vector boson fusion mode, in which the Higgs is produced simultaneously with a pair of quark jets, provides an unparalleled opportunity to study the detailed properties of the Higgs, including the possibility of parity and CP violation, as well as its couplings and mass. It thus opens up this new field of study for precision investigation as the LHC increases in energy and intensity, leading the way to this new and exciting arena of precision Higgs research.

This thesis presents a study of the scalar sector in the standard model (SM), as well as various searches for an extended scalar sector in theories beyond the SM (BSM). The first part of the thesis details the search for an SM Higgs boson decaying to taus, and produced by gluon fusion, vector boson fusion, or associated production with a vector boson, leading to evidence for decays of the Higgs boson to taus. In turn, the second part highlights several searches for an extended scalar sector, with scalar boson decays to taus. In all of the analyses presented, at least one scalar boson decays to a pair of taus. The results draw on data collected by the Compact Muon Solenoid (CMS) detector during proton–proton collisions with a center-of-mass energy of 7 or 8 TeV.