Confronting Higgcision with Electric Dipole Moments
  Current data on the signal strengths and angular spectrum of the 125.5 GeV Higgs boson still allow a CP-mixed state, namely, the pseudoscalar coupling to the top quark can be as sizable as the scalar coupling: $C_u^S \approx C_u^P =1/2$. CP violation can then arise and manifest in sizable electric dipole moments (EDMs). In the framework of two-Higgs-doublet models, we not only update the Higgs precision (Higgcision) study on the couplings with the most updated Higgs signal strength data, but also compute all the Higgs-mediated contributions from the 125.5 GeV Higgs boson to the EDMs, and confront the allowed parameter space against the existing constraints from the EDM measurements of Thallium, neutron, Mercury, and Thorium monoxide. We found that the combined EDM constraints restrict the pseudoscalar coupling to be less than about $10^{-2}$, unless there are contributions from other Higgs bosons, supersymmetric particles, or other exotic particles that delicately cancel the current Higgs-mediated contributions. 
Kingman Cheung, Jae Sik Lee, Eibun Senaha, and Po-Yan Tseng
hep-ph hep-ex