From flavour and Higgs precision physics to LHC discoveries

While the Standard Model is a great experimental success, it is unsatisfactory as a theory. For instance, it does not explain the origin of the hierarchies between quark masses, nor resolve the hierarchy problem or unify couplings in the UV. In this thesis, we address these shortcomings by performing precision calculations, building BSM models and studying their collider phenomenology. We improve the precision for the QCD prediction of the kaon bag parameter, which enters a dominant short-distance contribution to indirect CP violation. This is achieved by performing the first conversion between the SMOM and the MS scheme at two-loop order. Furthermore, we consider scalar and fermionic top partners that carry exotic charges and can propagate through the detector independently as well as form a charmonium-like bound state. The first bounds on the masses of coloured particles up to charge |Q| = 8 are presented and the prospects of exclusion and discovery at higher luminosities are discussed. We also consider composite Higgs models as they promise a natural solution to the hierarchy problem and fermion masses. In particular, we investigate the pT spectra of the top partners for the Higgs+Jet process and obtain QCD limits for CP-odd contributions. Moreover, we discuss a specific CH realisation with partial compositeness and pNGB Higgs in an SO(11)/SO(10) GUT model. We identify many promising parameter points that are consistent with most of the EW and collider constraints.