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 ex- pressed 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 sen- sitive to the invariants. Observation of the Standard-Model-like Higgs boson at the LHC severely constrains the models. In particular, in the model with Z₂ 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 Z₂ 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