Constraints on CP-violating Higgs couplings to the third generation

Discovering CP-violating effects in the Higgs sector would constitute an indisputable sign of physics beyond the Standard Model. We derive constraints on the CP-violating Higgs-boson couplings to top and bottom quarks as well as to tau leptons from low-energy bounds on electric dipole moments, resumming large logarithms when necessary. The present and future projections of the sensitivities and comparisons with the LHC constraints are provided. Non-trivial constraints are possible in the future, even if the Higgs boson only couples to the third-generation fermions.