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.

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 thesis presents innovative contributions to the CMS experiment in the new trigger system for the restart of the LHC collisions in Run II, as well as original analysis methods and important results that led to official publications of the Collaboration. The author's novel reconstruction algorithms, deployed on the Field-Programmable Gate Arrays of the new CMS trigger architecture, have brought a gain of over a factor 2 in efficiency for the identification of tau leptons, with a very significant impact on important H boson measurements, such as its decays to tau lepton pairs and the search for H boson pair production. He also describes a novel analysis of HH → bb tautau, a high priority physics topic in a difficult channel. The original strategy, optimisation of event categories, and the control of the background have made the result one of the most sensitive concerning the self-coupling of the Higgs boson among all possible channels at the LHC.

The theoretical foundations of the Standard Model of elementary particles relies on the existence of the Higgs boson, a particle which has been revealed for the first time by the experiments run at the Large Hadron Collider (LHC) in 2012. As the Higgs boson is an unstable particle, its search strategies were based on its decay products. In this thesis, Francesco Pandolfi conducted a search for the Higgs boson in the H → ZZ → l + l - qq Decay Channel with 4.6 fb -1 of 7 TeV proton-proton collision data collected by the Compact Muon Solenoid (CMS) experiment. The presence of jets in the final state poses a series of challenges to the experimenter: both from a technical point of view, as jets are complex objects and necessitate of ad-hoc reconstruction techniques, and from an analytical one, as backgrounds with jets are copious at hadron colliders, therefore analyses must obtain high degrees of background rejection in order to achieve competitive sensitivity. This is accomplished by following two directives: the use of an angular likelihood discriminant, capable of discriminating events likely to originate from the decay of a scalar boson from non-resonant backgrounds, and by using jet parton flavor tagging, selecting jets compatible with quark hadronization and discarding jets more likely to be initiated by gluons. The events passing the selection requirements in 4.6 fb -1 of data collected by the CMS detector are examined, in the search of a possible signal compatible with the decay of a heavy Higgs boson. The thesis describes the statistical tools and the results of this analysis. This work is a paradigm for studies of the Higgs boson with final states with jets. The non-expert physicists will enjoy a complete and eminently readable description of a proton-proton collider analysis. At the same time, the expert reader will learn the details of the searches done with jets at CMS.

The Higgs boson is an undiscovered elementary particle, thought to be a vital piece of the closely fitting jigsaw of particle physics. Like all particles, it has wave properties akin to those ripples on the surface of a pond which has been disturbed; indeed, only when the ripples travel as a well defined group is it sensible to speak of a particle at all. In quantum language the analogue of the water surface which carries the waves is called a field. Each type of particle has its own corresponding field. The Higgs field is a particularly simple one -- it has the same properties viewed from every direction, and in important respects in indistinguishable from empty space. Thus physicists conceive of the Higgs field being "switched on", pervading all of space and endowing it with "grain" like that of a plank of wood. The direction of the grain in undetectable, and only becomes important once the Higgs' interactions with other particles are taken into account. for instance, particles call vector bosons can travel with the grain, in which case they move easily for large distances and may be observed as photons - that is, particles of light that we can see or record using a camera; or against, in which case their effective range is much shorter, and we call them W or Z particles. These play a central role in the physics of nuclear reactions, such as those occurring in the core of the sun. The Higgs field enables us to view these apparently unrelated phenomenon as two sides of the same coin; both may be described in terms of the properties of the same vector bosons. When particles of matter such as electrons or quarks (elementary constituents of protons and neutrons, which in turn constitute the atomic nucleus) travel through the grain, they are constantly flipped "head-over-heels". this forces them to move more slowly than their natural speed, that of light, by making them heavy.

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.

The Standard Model of electroweak and strong interactions contains a scalar field which permeates all of space and matter, and whose properties provide the explanation of the origin of the masses. Commonly referred to as the Higgs field, it assumes in the physical vacuum a non-vanishing classical expectation value to which the masses of not only the vector bosons, but all the other known fundamental particles (quarks and leptons) are proportional. This volume presents a concise summary of the phenomenological properties of the Higgs boson.