Contribution from neutrino Yukawa couplings to lepton electric dipole moments

To explain the observed neutrino masses through the seesaw mechanism, a supersymmetric generalization of the standard model should include heavy right-handed neutrino supermultiplets. Then the neutrino Yukawa couplings can induce $CP$ violation in the lepton sector. In this paper, we compute the contribution of these $CP$ violating terms to lepton electric dipole moments. We introduce a new formalism that makes use of supersymmetry to expose the Glashow-Iliopoulos-Maiani cancellations. In the region of small $\tan \beta$, we find a different result from that given previously by Ellis, Hisano, Raidal, and Shimizu. We confirm the structure found by this group, but with a much smaller overall coefficient. In the region of large $\tan \beta$, we recompute the leading term that has been identified by Masina and confirm her result up to minor factors. We discuss the implications of these results for constraints on the $Y_{\nu }$.