The contributions of a second Higgs doublet to the electron electric dipole moment near the heavy Higgs decoupling limit are determined within an effective field theory framework. In models that satisfy the Glashow-Weinberg condition, the leading contributions in this limit at effective dimension six are shown to come from two-loop Barr-Zee diagrams that include the Standard Model-like Higgs boson. Additional diagrams that include heavy Higgs bosons are sub-leading and contribute only at effective dimension eight near the decoupling limit. This simplification implies that to leading order in this limit, contributions of a second Higgs doublet to the electron electric dipole moment can be couched entirely in terms of the ratio of Higgs doublet expectation values and a single universal phase appearing in the effective couplings of the Standard Model-like Higgs boson to fermions, without direct reference to the heavy Higgs boson masses or couplings. The recent bound from the ACME II experiment constrains the phases of the couplings of the Standard Model-like Higgs boson to up-type quarks and leptons at the part per mil level in Type I and IV two Higgs doublet models. In Type II and III models these phases are constrained at the two parts per mil or better level except in a tiny sliver of parameter space with nearly equal Higgs doublet expectation values where destructive interference among contributing diagrams happens to occur. In a more general phenomenological parameterization with individual effective phases in the couplings of the Standard Model-like Higgs boson to third generation fermions and the electron, the top quark and electron coupling phases are constrained at the part per mil level except in tiny slivers of parameter space, while the bottom quark and tau-lepton coupling phases are constrained only at the thirty percent level.
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