PUB - Publikationen an der Universität Bielefeld

The study of models with extended Higgs sectors requires to minimize thecorresponding Higgs potentials, which is in general very difficult. Here, weapply a recently developed method, called numerical polynomial homotopycontinuation (NPHC), which guarantees to find all the stationary points of theHiggs potentials with polynomial-like nonlinearity. The detection of allstationary points reveals the structure of the potential with maxima,metastable minima, saddle points besides the global minimum. We apply the NPHCmethod to the most general Higgs potential having two complex Higgs-bosondoublets and up to five real Higgs-boson singlets. Moreover the method isapplicable to even more involved potentials. Hence the NPHC method allows to gofar beyond the limits of the Gr\"obner basis approach.