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

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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.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Philosophenweg 16, 69120, Heidelberg, Germany

    M. Maniatis, A. von Manteuffel & O. Nachtmann

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  1. M. Maniatis
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  2. A. von Manteuffel
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  3. O. Nachtmann
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Correspondence to M. Maniatis.

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

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  • DOI: https://doi.org/10.1140/epjc/s10052-006-0186-2

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