Mathematical and Computational Analysis of Vacuum Structures in Extended Higgs Sectors

Among other restrictions, vacuum stability is a theoretical constraint for vacuumconfigurations in BSM theories to be allowed or excluded. But due to multidimensionalfield spaces, computing the vacuum stability is a challenging task. This thesis investi-gates vacuum structures in the N2HDM and the cS2HDM and examines the possibilityto take multiple vacuum decay channels into account. It also introduces three differentalgorithms to compute vacuum stability and compares them. One of these algorithmsis the recently developed code NNBounce that has been refined with a hyperparameteroptimization algorithm and is made publicly available.