Properties of S3-Symmetric Three-Higgs-Doublet Models

Abstract

Some aspects of the S3-symmetric three-Higgs-doublet models are analysed. A CP conserving potential with both real and complex vacuum configurations is considered. The S3-symmetric potential is presented in the irreducible representation, which the main part of the thesis is based on, and in the Higgs basis. Hidden symmetries of the S3-symmetric 3HDM potential are analysed: behaviour of the scalar potential under the subgroups of the U(3) group, which result in Goldstone bosons, and the discrete Z2 symmetry required for a stable dark matter candidate. Possible models capable of accommodating the dark matter candidate are presented. Two vacuum configurations, one real and one complex, which can possibly accommodate the dark matter candidate, are further analysed. One of the vacuum configurations results in massless scalars and therefore the concept of soft symmetry breaking is applied. A numerical check of two vacuum configurations is performed based on the theoretical and experimental constraints.