| Summary: | On July 2012 the ATLAS and CMS collaborations announced the historic discovery of a Higgs boson at the CERN Large Hadron Collider. A remarkable century exploring Nature's sub- atomic constituents led to the Standard Model (SM) of particle physics with the Higgs as the last missing piece. In this thesis we review the construction of this theory and its experimental successes, focusing on the Higgs sector responsible for electroweak symmetry breaking and providing mass to matter and force particles. The de ning signature of a Higgs particle is that of a scalar coupling proportionally to mass. We show how early data suggests indirectly that the observed particle has spin zero, and propose a method for directly measuring the spin using an invariant mass distribution of the Higgs produced in association with a vector boson. We also perform a global analysis of its couplings before and after the discovery, testing the expected mass-proportionality and constraining models in which the Higgs may be composite or even another scalar entirely, such as a pseudo-dilaton. In the absence of any signi cant deviations from the properties of the SM Higgs boson, the SM is then treated as an e ective eld theory (EFT) assuming new physics beyond the SM (BSM) is decoupled at higher energies. The leading lepton-number-conserving operators arise at the dimension-6 level, parametrised by their Wilson coecients. These are constrained by their e ects in Higgs physics, triple-gauge coupling measurements, and electroweak precision tests. The coecients may also be calculated in a speci c BSM theory by integrating out heavy particles. We illustrate this in the case of stops and sbottoms in the minimally supersymmetric SM, using the covariant derivative expansion method and generalising the universal one-loop e ective Lagrangian in the process. Finally the potential for discovering BSM physics at future colliders is investigated. We conclude with a summary and outlook on prospects for the future.
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