Determining the global minimum of Higgs potentials via Groebner bases - applied to the NMSSM

Maniatis M, von Manteuffel A, Nachtmann O (2007)
European Physical Journal C 49(4): 1067-1076.

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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.
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Maniatis M, von Manteuffel A, Nachtmann O. Determining the global minimum of Higgs potentials via Groebner bases - applied to the NMSSM. European Physical Journal C. 2007;49(4):1067-1076.
Maniatis, M., von Manteuffel, A., & Nachtmann, O. (2007). Determining the global minimum of Higgs potentials via Groebner bases - applied to the NMSSM. European Physical Journal C, 49(4), 1067-1076.
Maniatis, M., von Manteuffel, A., and Nachtmann, O. (2007). Determining the global minimum of Higgs potentials via Groebner bases - applied to the NMSSM. European Physical Journal C 49, 1067-1076.
Maniatis, M., von Manteuffel, A., & Nachtmann, O., 2007. Determining the global minimum of Higgs potentials via Groebner bases - applied to the NMSSM. European Physical Journal C, 49(4), p 1067-1076.
M. Maniatis, A. von Manteuffel, and O. Nachtmann, “Determining the global minimum of Higgs potentials via Groebner bases - applied to the NMSSM”, European Physical Journal C, vol. 49, 2007, pp. 1067-1076.
Maniatis, M., von Manteuffel, A., Nachtmann, O.: Determining the global minimum of Higgs potentials via Groebner bases - applied to the NMSSM. European Physical Journal C. 49, 1067-1076 (2007).
Maniatis, Markos, von Manteuffel, A., and Nachtmann, O. “Determining the global minimum of Higgs potentials via Groebner bases - applied to the NMSSM”. European Physical Journal C 49.4 (2007): 1067-1076.
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