Spontaneous symmetry breaking in the $S_3$-symmetric scalar sector

Abstract

We present a detailed study of the vacua of the $S_3$-symmetric three-Higgs-doublet potential, specifying the region of parameters where these minimisation solutions occur. We work with a CP conserving scalar potential and analyse the possible real and complex vacua with emphasis on the cases in which the CP symmetry can be spontaneously broken. Results are presented both in the reducible-representation framework of Derman, and in the irreducible-representation framework. Mappings between these are given. Some of these implementations can in principle accommodate dark matter and for that purpose it is important to identify the residual symmetries of the potential after spontaneous symmetry breakdown. We are also concerned with constraints from vacuum stability.

37 pages. v2: Minor changes in the references, matches published version. v3: Table 6 corrected: two additional cases conserve CP. Related discussion adapted. Version consistent with JHEP Erratum

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• The $S3$ Symmetric Model with a Dark Scalar
• Quark mixing in an $S_3$ symmetric model with two Higgs doublets
• When the C in CP does not matter: anatomy of order-4 CP eigenstates and their Yukawa interactions
• Spontaneous CP violation in multi-Higgs potentials with triplets of $\Delta (3n^2)$ and $\Delta (6n^2)$
• A Simple Method to detect spontaneous CP Violation in multi-Higgs models
• An $S_3$ flavored left-right symmetric model of quarks
• Scalar triplet leptogenesis in the presence of right-handed neutrinos with S3 symmetry
• Systematic analysis of 3HDM symmetries
• Prospects of Indirect Detection for the Heavy S3 Dark Doublet
• Dark matter in a CP-violating three-Higgs-doublet model with $S_3$ symmetry
• Spontaneous symmetry breaking in three-Higgs-doublet $S_3$-symmetric models
• Implications of symmetries in the scalar sector
• Dark matter in three-Higgs-doublet models with $S_3$ symmetry
• CP-odd invariants for multi-Higgs models and applications with discrete symmetry
• A lepton model with nearly Cobimaximal mixing
• Generalised P and CP transformations in the 3-Higgs-doublet model
• CP Violation in the scalar sector
• Scalar and gauge sectors in the 3-Higgs Doublet Model under the S3-symmetry