Minimizing Higgs potentials via numerical polynomial homotopy continuation
Faculty of Physics, Bielefeld University, 33615, Bielefeld, Germany
2 Physics Department, Syracuse University, 13244, Syracuse, NY, USA
* e-mail: email@example.com
Accepted: 27 July 2012
Published online: 28 August 2012
The study of models with extended Higgs sectors requires to minimize the corresponding Higgs potentials, which is in general very difficult. Here, we apply a recently developed method, called numerical polynomial homotopy continuation (NPHC), which guarantees to find all the stationary points of the Higgs potentials with polynomial-like non-linearity. The detection of all stationary points reveals the structure of the potential with maxima, metastable minima, saddle points besides the global minimum. We apply the NPHC method to the most general Higgs potential having two complex Higgs-boson doublets and up to five real Higgs-boson singlets. Moreover the method is applicable to even more involved potentials. Hence the NPHC method allows to go far beyond the limits of the Gröbner basis approach.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2012