Probing Dark Sector CP Violation with Electric Dipole Moments and Colliders

We study the experimental constraints on dark sector CP violation that enters the visible sector through a Higgs portal coupling $H^{\dagger} H Z^{\prime}_{\mu\nu} \widetilde Z^{\prime \mu\nu}$, where the $Z^{\prime}$ is from a new U(1) gauge symmetry which is assumed to couple to lepton number. We compute explicitly the leading two-loop contribution of this effective operator to the electron electric dipole moment (EDM) and show that the resulting constraints are comparable to those from direct $Z^{\prime}$ searches at electron-positron colliders when the effective operator is generated at tree level. We also examine an explicit UV completion for this effective operator that was first introduced to achieve electroweak baryogenesis and show that collider constraints from $B$-factories already exclude viable baryogenesis for $Z^{\prime}$ masses below 10 GeV, and that future electron-positron Higgs factories will exclude viable baryogenesis for $Z^{\prime}$ masses up to the $e^+e^-$ center-of-mass energy if anticipated luminosities are achieved. For higher $Z^{\prime}$ masses, the full viable baryogenesis parameter space lies within six orders of magnitude of the current upper bound on the electron EDM.