Properties of the general NHDM. II. Higgs potential and its symmetries

Abstract

We continue our analysis of the general N-Higgs-doublet model and focus of the Higgs potential description in the space of gauge orbits. We develop a geometric technique that allows us to study the global minimum of the potential without explicitly finding its position. We discuss symmetry patterns of the NHDM potential, and illustrate the general discussion with various specific variants of the three-Higgs-doublet model.

arXiv comment28 pages, 9 figures; v2: introduction rewritten, matches the published version

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• $S_3$-inspired three-Higgs-doublet models: A class with a complex vacuum
• Minima of multi-Higgs potentials with triplets of $\Delta (3n^2)$ and $\Delta (6n^2)$
• Tree-level vacuum stability of two-Higgs-doublet models and new constraints on the scalar potential
• Custodial SO(4) symmetry and CP violation in N-Higgs-doublet potentials
• Basis-invariant conditions for CP symmetry of order 4
• Yet another lesson on the stability conditions in multi-Higgs potentials
• Light charged Higgs boson with dominant decay to a charm quark and a bottom quark and its search at LEP2 and future $e^{+}{e}^{-}$ colliders
• Spontaneous CP violation in multi-Higgs potentials with triplets of $\Delta (3n^2)$ and $\Delta (6n^2)$
• Further study of the global minimum constraint on the two-Higgs-doublet models: LHC searches for heavy Higgs bosons
• Slight excess at 130 GeV in search for a charged Higgs boson decaying to a charm quark and a bottom quark at the Large Hadron Collider
• Frustrated symmetries in multi-Higgs-doublet models
• Higgs-portal dark matter from non-supersymmetric strings
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• Symmetries from outer automorphisms and unorthodox group extensions
• CP-odd invariants for multi-Higgs models and applications with discrete symmetry
• Vacuum Stability Conditions for New $SU(2)$ Multiplets