Analysis of the Higgs potentials for two doublets and a singlet

We consider the most general CP-conserving renormalizable effective scalar potential involving two doublets plus one singlet Higgs and satisfying the electroweak gauge symmetry. After deriving the electroweak-symmetry breaking conditions, we focus on special cases, characterized by specific symmetry properties and/or relations to supersymmetry-inspired extensions of the Standard Model (e.g. n/NMSSM, UMSSM). We then investigate the question of the reconstruction of the potential parameters from the Higgs masses and mixing angles and show that in some specific cases, such as the one of an underlying NMSSM, an accuracy at the order of leading-logarithms is achievable with minimal effort. We finally study a few phenomenological consequences for this latter model. More specifically, we consider how our parameter reconstruction modifies the outcome of two publicly available codes : micrOMEGAs and NMSSMTools. We observed noteworthy effects in regions of parameter space where Higgs-to-Higgs decays are relevant, impacting the collider searches for light Higgs states and the prediction of the Dark-Matter relic density.