Measuring CP violation in two-Higgs-doublet models in light of the LHC Higgs data

In Two-Higgs-Doublet models, the conditions for CP violation can be expressed in terms of invariants under U(2) rotations among the two SU(2) Higgs doublet fields. In order to design a strategy for measuring the invariants we express them in terms of observables, i.e., masses and couplings of scalar bosons. We find amplitudes directly sensitive to the invariants. Observation of the Standard-Model-like Higgs boson at the LHC severely constrains the models. In particular, in the model with ℤ 2 $$ {\mathbb{Z}}_2 $$ symmetry imposed on dimension-4 terms (in order to eliminate tree-level flavour-changing neutral currents), CP violation is strongly suppressed. On the other hand, the most general Two-Higgs-Doublet model (without ℤ 2 $$ {\mathbb{Z}}_2 $$ symmetry) is compatible with the LHC data, and would still allow for CP violation to be present in the model. Consequently, also flavour-changing neutral currents would in general be expected. We briefly sketch a strategy for measuring the remaining CP violation