Discovery Prospects for Electron and Neutron Electric Dipole Moments in the General Two Higgs Doublet Model

Baryon asymmetry of the Universe offers one of the strongest hints for physics Beyond the Standard Model (BSM). Remarkably, in the general two Higgs Doublet Model (g2HDM) that possesses a second set of Yukawa matrices, one can have electroweak baryogenesis (EWBG) while the electron electric dipole moment (eEDM) is evaded by a natural flavor tuning that echoes SM. We show that eEDM may first emerge around ${10}^{-30}e$ cm or so, followed by neutron EDM (nEDM) down to ${10}^{-27}e$ cm. We illustrate a cancellation mechanism for nEDM itself, which in turn can be probed when a facility capable of pushing down to ${10}^{-28}e$ cm becomes available.