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.

This PhD thesis documents two of the highest-profile searches for supersymmetry performed at the ATLAS experiment using up to 80/fb of proton-proton collision data at a center-of-mass energy of 13 TeV delivered by the Large Hadron Collider (LHC) during its Run 2 (2015-2018). The signals of interest feature a high multiplicity of jets originating from the hadronisation of b-quarks and large missing transverse momentum, which constitutes one of the most promising final state signatures for discovery of new phenomena at the LHC. The first search is focused on the strong production of a pair of gluinos, with each gluino decaying into a neutralino and a top-antitop-quark pair or a bottom-antibottom-quark pair. The second search targets the pair production of higgsinos, with each higgsino decaying into a gravitino and a Higgs boson, which in turn is required to decay into a bottom-antibottom-quark pair. Both searches employ state-of-the-art experimental techniques and analysis strategies at the LHC, resulting in some of the most restrictive bounds available to date on the masses of the gluino,neutralino, and higgsino in the context of the models explored.

The work presented in this PhD dissertation is the first search at CMS for Higgs bosons produced in association with top quarks (ttH) in a final state consisting of only jets. The results presented in this book uncover a new class of ttH events that will help us elucidate our understanding of the Yukawa sector interactions between the Higgs boson and the top quark. Despite this being the most common decay signature for ttH, a large contamination of SM backgrounds makes it the most challenging for extracting a signal from data. The PhD thesis presents many sophisticated tools and techniques that were developed in order to overcome these challenges. These tools pave the way for future analyses to investigate other standard model and beyond-standard model physics.

This thesis provides a detailed and comprehensive description of the search for New Physics at the Large Hadron Collider (LHC) in the mono-jet final state, using the first 3.2 fb-1 of data collected at the centre of mass energy of colliding protons of 13~TeV recorded in the ATLAS experiment at LHC. The results are interpreted as limits in different theoretical contexts such as compressed supersymmetric models, theories that foresee extra-spatial dimensions and in the dark matter scenario. In the latter the limits are then compared with those obtained by other ATLAS analyses and by experiments based on completely different experimental techniques, highlighting the role of the mono-jet results in the context of dark matter searches.Lastly, a set of possible analysis improvements are proposed to reduce the main uncertainties that affect the signal region and to increase the discovery potential by further exploiting the information on the final state.

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.

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.