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

TL;DR

This paper derives physical conditions under which spontaneous CP violation occurs in the general Two-Higgs-Doublet Model, highlighting the role of masses and couplings, especially in the alignment limit.

Contribution

It provides explicit conditions for spontaneous CP violation in the 2HDM using physical parameters, including simplified relations in the alignment limit.

Findings

Conditions for spontaneous CP violation involve charged-Higgs mass and scalar couplings.

Alignment limit simplifies the relations for CP violation.

Deviations from alignment are necessary for CP violation in the softly broken Z2 symmetric model.

Abstract

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.