Spontaneous CP violation in the 2HDM: physical conditions and the alignment limit

Understand

For the general Two-Higgs-Doublet model, we present conditions for having spontaneous CP violation, in terms of physical masses and couplings.

• These relations involve the charged-Higgs mass, its cubic couplings with neutral scalars and quartic coupling, and become particularly simple in the alignment limit.
• In the simplified model with softly broken $Z_2$ symmetry, some deviation from alignment is required for spontaneous CP violation to be present.