Composite Higgs at high transverse momentum

The Standard Model (SM) of particle physics provides no explanation of the lightness of the Higgs particle found at the Large Hardron Collider (LHC) in 2012 compared to the natural scale of its mass, the Planck scale. This problem leads to the study of the class of physics models known as composite Higgs models, where the Higgs boson is considered to be a bound state of a new strongly interacting gauge theory. In this type of models, elementary particles have to couple with this composite state in order to gain masses. The dependence on the composite partners of the top quark, known as the top-partners, of Higgs production through gluon fusion has been studied. There it was found that, due to a subtle cancellation between the contribution of the top and that of the top partners, it is not possible to infer the top-partner mass from that process. However, there has been a study on the Higgs plus jet production from gluon fusion in a model with a top and an additional top partner. In that case, the transverse momentum distribution of the Higgs boson showed a depenence on the top-partner mass and coupling. In this thesis we extend that study by considering Higgs production with a jet in explicit composite Higgs models, which has never been considered before in the literature. In particular, we consider composite Higgs models where the right handed top quark tR was considered to be a composite state of a strong interacting sector containing either one or two top-partner multiplets. We then study Higgs production in association with a jet in these models, and in particular we examine thoroughly the impact of increasing number of the top partner multiplets. The models studied in our work were categorised according to the representation of the top partners and the way the standard model left-handed doublet is embedded in the representations of the symmetry of the strong sector. In the case where there is only one top partner multiplet in the models, we derived the explicit forms of the Yukawa couplings of the top quark and the top partners, and the CP-odd couplings that are present as a result of having a bound state tR. In the case where there are two top partners multiplets, we discussed the behaviour of the Yukawas and the masses of the top partners as a function of the input parameters of the models. Numerical values of the masses, Yukawa couplings, and CP-odd couplings were calculated for both cases, and these values were input in a numerical programme to calculate the transverse momentum distribution of the Higgs. Various deviations from the Standard Model behaviour appear. They are typically model dependent, and have been studied on a case-by-case basis. In particular, we have discussed the di?erence between models with one and two top-partners.