Eur. Phys. J. C (2007) 49: 1067-1076
https://doi.org/10.1140/epjc/s10052-006-0186-2

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

^* e-mail: m.maniatis@thphys.uni-heidelberg.de

Received: 12 October 2006
Published online: 20 January 2007

Abstract

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.