Composite Higgs as a Viable Scenario for Electro-Weak Symmetry Breaking : Some Prospects in next-to-minimal Model Building and Model Specific Experimental Signatures

This thesis presents a general discussion of the Composite Higgs scenario of Electro-Weak Symmetry Breaking (EWSB). We start by reviewing the Standard Model of Electro-Weak interaction, discussing its experimental tests and conceptual pitfalls. Emphasis is given to the effective field theory point of view. In particular, the inherent tension related to the stability of the Electro-Weak scale motivates us to explore the possibility of having the Higgs field emerging as a Nambu-Goldstone boson from a new strongly coupled sector. Our construction is to a large extent inspired by the picture of the long range dynamics of QCD. The main ingredients are the symmetry of the UV theory, the pattern of its spontaneous breakdown and the sources of explicit breaking. In QCD, the latter are provided by the light quark masses and by the electromagnetic interaction. In Composite Higgs models, the most relevant symmetry breaking couplings are those related to the generation of the third family quark Yukawas through partial compositeness. They generate a potential for the Higgs and thus trigger EWSB. The constraints on the scenario are exposed, with a particular emphasis on the composite Two Higgs Doublet Model (THDM). While a residual SO(4) symmetry is sufficient to ensure a realistic phenomenology in presence of a single composite Higgs doublet, an extended Higgs sector needs more symmetries. For two doublets we show how either CP or a ℤ2 symmetry can play this role and construct a model for each realisation relying on the SO(6)/SO(4) × SO(2) coset. Finally, we discuss the phenomenology of this scenario. In particular, we present de differences between an elementary and a composite THDM. We also conclude that composite fermions associated to the third family quarks seem to be the most promising experimental handles for these models. We discuss their discovery range at the LHC, and the possibility of measuring the structure of their couplings. This knowledge would allow important insight into the strong dynamics.