CP-violating phenomenology of flavor conserving two Higgs doublet models

We analyze the constraints on CP-violating, flavor conserving two Higgs doublet models implied by measurements of Higgs boson properties at the Large Hadron Collider (LHC) and by the nonobservation of permanent electric dipole moments (EDMs) of molecules, atoms, and neutrons. We find that the LHC and EDM constraints are largely complementary, with the LHC studies constraining the mixing between the neutral CP-even states and the EDMs probing the effect of mixing between the CP-even and CP-odd scalars. Presently, the most stringent constraints are implied by the nonobservation of the ThO molecule EDM signal. Future improvements in the sensitivity of neutron and diamagnetic atom EDM searches could yield competitive or even more severe constraints. We analyze the quantitative impact of hadronic and nuclear theory uncertainties on the interpretation of the latter systems and conclude that these uncertainties cloud the impact of projected improvements in the corresponding experimental sensitivities.