Probing the Higgs potential at current and future colliders

The Higgs boson provides unique opportunities for searching for phenomena that go beyond the Standard Model (SM). Among the least known properties of the scalar sector of the SM is the shape of Higgs potential. In the SM, the cu- bic and quartic Higgs self-couplings are completely determined by the Fermi constant and the Higgs boson mass. Measuring the self-interactions is there- fore essential to first test the SM and then to interpret possible deviations. The overarching goal of this thesis is to present a detailed study of the feasibility of measuring Higgs boson self-couplings at current and future colliders. One of the main novelties of this work is the systematic exploration of the possibility of accessing information on the self-couplings through effects that appear the first time via loops. In particular, we establish a framework based on the effec- tive field theory approach that allows to consistently evaluate loop corrections in presence of deformations of the Higgs potential. This method allows to per- form consistent computations and then to combine indirect constraints coming from loops to direct measurements. This study encompasses not only the cur- rent LHC and planned HL-LHC, but also a future 100 TeV hadron collider, circular and linear e + e − colliders, and a futuristic muon collider.