Regular Article - Theoretical Physics
Determining the global minimum of Higgs potentials via Groebner bases – applied to the NMSSM
Institut für Theoretische Physik, Philosophenweg 16, 69120, Heidelberg, Germany
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Published online: 20 January 2007
Determining the global minimum of Higgs potentials with several Higgs fields like the next-to-minimal supersymmetric extension of the standard model (NMSSM) is a non-trivial task already at the tree level. The global minimum of a Higgs potential can be found from the set of all its stationary points defined by a multivariate polynomial system of equations. We introduce here the algebraic Groebner basis approach to solve this system of equations. We apply the method to the NMSSM with CP-conserving as well as CP-violating parameters. The results reveal an interesting stationary-point structure of the potential. Requiring the global minimum to give the electroweak symmetry breaking observed in Nature excludes large parts of the parameter space.
© Springer-Verlag Berlin Heidelberg, 2007