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CP violation in the Higgs couplings to fermions is an intriguing, but not yetextensively explored possibility. We use inclusive and differential LHC Higgsboson measurements to fit the CP structure of the Higgs Yukawa couplings.Starting with simple effective models featuring CP violation in a singleHiggs-fermion coupling, we probe well-motivated models with up to nine freeparameters. We also investigate the complementarity of LHC constraints with theelectron electric dipole moment bound, taking into account the possibility of amodified electron Yukawa coupling, and assess to which extent CP violation inthe Higgs-fermion couplings can contribute to the observed baryon asymmetry ofthe universe. Even after including the recent analysis of angular correlationsin $H\to\tau^+\tau^-$ decays, we find that a complex tau Yukawa coupling alonemay be able to account for the observed baryon asymmetry, but with largeuncertainties in the baryogenesis calculation. A combination of complex top andbottom quark Yukawa couplings yields a result four times larger than the sum oftheir separate contributions, but remains insufficient to account for theobserved baryon asymmetry.

Constraining the CP structure of Higgs-fermion couplings with a global LHC fit, the electron EDM and baryogenesis