A natural Higgs boson: models and phenomenology

After a brief description of the Standard Model of Particle Physics, we introduce the Hierarchy Problem and its possible resolutions. Among several possibilities we choose two protection mechanisms that realize a Natural Fermi scale: Composite Higgs and Supersymmetry. Our aim is to consider realistic natural models for the Fermi scale and compare them with the experimental data coming (mainly) from precision measurements. In the case of Composite Higgs, we discuss the ne tuning needed to realize a successful electro-weak symmetry breaking and accommodate a 125 GeV Higgs. Composite Higgs can naturally explain such light mass if new coloured fermions with the same quantum numbers of the top are below or at 1000 GeV. Direct searches are starting to probe the natural region of this kind of models. However, there are strong constraints on this picture coming from electro-weak and avour tests. Although non trivially, it is possible to satisfy the bounds if appropriate representations of the composite fermions are chosen and an approximate U(2)3 flavour symmetry is at work. The Minimal Supersymmetric Standard Model (MSSM) experiences a significant finetuning because a 125 GeV Higgs boson is too heavy to be obtained naturally. After a brief review of the MSSM and a discussion of its Higgs sector, we consider the Next-to-Minimal Supersymmetric Standard Model (NMSSM). The NMSSM provides a 125 GeV Higgs boson with milder tuning and it also mitigates naturalness upper bounds on stops and gluinos, which start to be strongly constrained from below by direct searches. Another relevant aspect of the NMSSM is the suggestion that the lightest new particles could be the CP-even scalars of its extended Higgs sector. This possibility can be efficiently constrained from the measurements of the Higgs mass and branching ratios at LHC. In many cases the Higgs fit is an important constraint, competitive with direct searches. When these constraints are absent we outline possible strategies for future experimental searches. We conclude with a brief summary and comment on the relative importance of electroweak and Higgs precision measurements in the models discussed in the thesis.