Classification of finite reparametrization symmetry groups in the three-Higgs-doublet model

Regular Article - Theoretical Physics

Abstract

Symmetries play a crucial role in electroweak symmetry breaking models with non-minimal Higgs content. Within each class of these models, it is desirable to know which symmetry groups can be implemented via the scalar sector. In N-Higgs-doublet models, this classification problem was solved only for N=2 doublets. Very recently, we suggested a method to classify all realizable finite symmetry groups of Higgs-family transformations in the three-Higgs-doublet model (3HDM). Here, we present this classification in all detail together with an introduction to the theory of solvable groups, which play the key role in our derivation. We also consider generalized-CP symmetries, and discuss the interplay between Higgs-family symmetries and CP-conservation. In particular, we prove that presence of the ℤ4 symmetry guarantees the explicit CP-conservation of the potential. This work completes classification of finite reparametrization symmetry groups in 3HDM.

Keywords

Symmetry Group Nilpotent Group Abelian Subgroup Continuous Symmetry Normal Abelian Subgroup 

Notes

Acknowledgements

This work was supported by the Belgian Fund F.R.S.-FNRS, and in part by grants RFBR 11-02-00242-a, RFBR 12-01-33102, RF President grant for scientific schools NSc-3802.2012.2, and the Program of Department of Physics SC RAS and SB RAS “Studies of Higgs boson and exotic particles at LHC.”

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Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  1. 1.IFPAUniversité de LiègeLiègeBelgium
  2. 2.Sobolev Institute of MathematicsNovosibirskRussia

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