Electron EDM in the complex two-Higgs doublet model

We present the first complete two loop calculation of the electron EDM in the complex two-Higgs doublet model. We confirm gauge-independence by demonstrating analytic cancellation of the gauge parameter $ξ$ in the background field gauge and the 't Hooft $R_ξ$ gauge. We also investigate the behavior of the electron EDM near the decoupling limit, and determine the short- and long-distance contributions by matching onto an effective field theory. Compared with earlier studies of the electron EDM in the complex two-Higgs doublet model, we note disagreements in several places and provide diagnoses where possible. We also provide expressions for EDMs of light quarks.