Constraints on CP violation in the Higgs sector from the $ρ$ parameter

We discuss the relation between the CP symmetry and the custodial $SU(2)$ symmetry in the Higgs sector. In particular, we show that CP violation in the Higgs-gauge sector is allowed only if the custodial $SU(2)$ symmetry is broken. We exploit these facts to constrain CP violation using the experimental bounds on $ρ-1$. CP nonconservation in the Higgs-fermion interactions can also be constrained in a similar way although a possible exception is pointed out.

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