We conduct an analysis of model-independent contributions to the Electric Dipole Moment (EDM) of the electron.
Our study focuses on contributions that originate from a linearly independent heavy scalar sector. Specifically, we discuss the decoupling limit of the aligned two-Higgs-doublet model (A2HDM).
In this framework, Barr-Zee diagrams involving a fermion loop induce logarithmically-enhanced terms proportional to potentially sizable new sources of CP violation. In the decoupling regime these contributions originate from effective dimension-6 operators through the renormalization-group mixing of four-fermion operators into electroweak dipole operators.
These logarithmic contributions are absent in more constrained $\mathcal Z_2$-symmetric realizations of the 2HDM, where this discrete symmetry dictates the structure of effective operators providing new-physics contributions to the electron EDM and thereby yields a suppression mechanism.
During our comparison of the results from the A2HDM with the leading logarithms from SMEFT, we have identified and corrected signs of expressions found in the literature.
Finally, we examine how the current experimental bounds on the electron EDM constrain the parameter space of the A2HDM.

