Exploring Models of Electroweak Symmetry Breaking at the LHC and Beyond

We explore different scenarios of electroweak symmetry breaking by studying the phenomenology of several models that extend the scalar sector of the Standard Model (SM). We investigate resonant multiscalar production in a singlet extension of the SM. The resulting benchmark scenarios illustrate many previously unstudied signatures of Higgs-to-Higgs decays that could serve as discovery channels for additional scalars. While many properties of 125 GeV Higgs bosons ($h_{125}$) are precisely measured, it could nevertheless be a CP-mixed state with a sizeable CP-odd admixture. We investigate this possibility in the CP-violating two Higgs doublet model (2HDM) and discuss the impact of bounds from fermionic electric dipole moments. We find that maximally CP-violating Yukawa couplings of $h_{125}$ are compatible with current measurements. The Higgs sector could also contain CP violation that is confined to a dark sector. In the minimal model that allows this possibility, we find that the CP violation is in principle observable through loop-induced anomalous triple gauge couplings. However, the CP-violating form factor and the resulting asymmetries are strongly suppressed, making them challenging to observe even for maximally CP-violating scenarios. In many beyond the SM (BSM) models with extended scalar sectors — for example in this dark sector model — the scalar potential is so complicated that its vacuum structure can only be studied numerically. We present a novel approach to vacuum stability constraints that aims at an efficient and reliable evaluation for use in large parameter scans of BSM models. We study the vacuum structure of the next-to 2HDM (N2HDM) — an extension of the 2HDM by a real scalar singlet. We show analytically that — in contrast to the 2HDM — the electroweak vacuum of the N2HDM is not necessarily stable against charge- or CP-breaking vacua. Using our numerical approach, we study the phenomenological consequences of the intricate N2HDM vacuum structure and find a direct constraint from vacuum stability on the predictions for the decay of $h_{125}$ into two photons. We finally derive vacuum stability constraints on benchmark scenarios in the minimal supersymmetric extension of the SM. We validate our approach against results in the literature and find good agreement. In particular, we show that the better numerical stability of our approach can lead to more reliable results in a fraction of the runtime of alternative methods. The phenomenological studies carried out in this thesis aim to contribute to a better understanding of electroweak symmetry breaking and facilitate the exploration of models with extended scalar sectors using future experimental results