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.

Comments: 22pp, REVTeX4. Published version