Models with several doublets of scalar bosons are a popular framework to go beyond the Standard model in electroweak symmetry breaking. Usually, only simple scalar sectors in such models are considered, and no systematic exploration of all the possibilities with N doublets exists so far. The main reason is that a general scalar potential with more than one doublet just cannot be minimized explicitly. I will present a geometric approach to the analysis of the most general scalar sector in multi-doublet model, which allows one to study many properties of the model without explicitl minimization of the potential. In the case of two doublets, the full phase diagram of the scalar sector can be reconstructed in the tree-level approximation, and many (astro)particle issues can be addressed. For more than two doublets, only partial success has been achieved so far.

Université de Liège