Structure of potentials with $N$ Higgs doublets

Abstract

Extensions of the Standard Model with $N$ Higgs doublets are simple extensions presenting a rich mathematical structure. An underlying Minkowski structure emerges from the study of both variable space and parameter space. The former can be completely parametrized in terms of two future lightlike Minkowski vectors with spatial parts forming an angle whose cosine is $-(N-1{)}^{-1}$. For the parameter space, the Minkowski parametrization enables one to impose sufficient conditions for bounded below potentials, characterize certain classes of local minima and distinguish charge breaking vacua from neutral vacua. A particular class of neutral minima presents a degenerate mass spectrum for the physical charged Higgs bosons.

11 pages. Revtex4. Typos corrected. Few comments added

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• Abelian symmetries in multi-Higgs-doublet models
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• Scalar and gauge sectors in the 3-Higgs Doublet Model under the S3-symmetry
• The Hilbert Series and the Flavor Invariants of the 3HDM
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