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arXiv · 1103.0252

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

C. C. Nishi
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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.

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C. C. Nishi. 2011-05-17. Custodial SO(4) symmetry and CP violation in N-Higgs-doublet potentials. https://doi.org/10.1103/physrevd.83.095005

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