Custodial SO(4) symmetry and CP violation in N-Higgs-doublet potentials

Abstract

We study the implementation of global $SO(4)\sim SU(2{)}_L\otimes SU(2{)}_R$ symmetry in general potentials with N-Higgs-doublets in order to obtain models with custodial $SO(3{)}_C$ symmetry. We conclude that any implementation of the custodial SO(4) symmetry is equivalent, by a basis transformation, to a canonical one if $SU(2{)}_L$ is the gauge factor, $U(1{)}_Y$ is embedded in $SU(2{)}_R$ and we require $N$ copies of the doublet representation of $SU(2{)}_R$. The invariance by SO(4) automatically leads to a CP invariant potential and the basis of the canonical implementation of SO(4) is aligned to a basis where CP-symmetry acts in the standard fashion. We show different but equivalent implementations for the 2HDM, including an implementation not previously considered.

22pp, REVTeX4. Published version

References in corpus (14)

• Improved Naturalness with a Heavy Higgs: An Alternative Road to LHC Physics
• Basis-independent methods for the two-Higgs-doublet model III: The CP-conserving limit, custodial symmetry, and the oblique parameters S, T, U
• Minkowski space structure of the Higgs potential in 2HDM: II. Minima, symmetries, and topology
• A Twisted Custodial Symmetry in the Two-Higgs-Doublet Model
• Basis-independent methods for the two-Higgs-doublet model II. The significance of tan(beta)
• Natural Multi-Higgs Model with Dark Matter and CP Violation
• Structure of potentials with $N$ Higgs doublets
• Properties of the general NHDM. I. The orbit space
• A new type of CP symmetry, family replication and fermion mass hierarchies
• Physical parameters and basis transformations in the Two-Higgs-Doublet model
• Generalized CP Invariance and the Yukawa sector of Two-Higgs Models
• Properties of the general NHDM. II. Higgs potential and its symmetries
• Symmetry and Mass Degeneration in Multi-Higgs-Doublet Models
• The flavor puzzle in multi-Higgs models

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