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 $Y_{\nu }$.

Figure 1

The general form of the diagrams contributing to the EDM of a charged lepton $\ell$. The photon line should be attached at all possible positions in the diagram.

Figure 2

Diagrams giving the dominant contribution to EDM of charged lepton $\ell$ (a) for small $\tan \beta$, (b) for large $\tan \beta$.

Figure 3

Diagram giving the field strength renormalization of the supermultiplet $L_i$. In this and the next few figures, we treat $F$ components as independent fields; the $F$ terms of $N_k$ multiplets have the propagators (4).

Figure 4

Diagram giving the one-loop radiative correction to the vertex $A_{\ell }$. The heavy dot is an $A_{\nu }$ vertex.

Figure 5

Diagrams giving the one-loop corrections to the supersymmetry breaking $\tilde{L}$ mass term. The heavy dot is an $A_{\nu }$ vertex; the marked insertion is a soft mass term $m_0^2$.

Figure 6

Diagrams giving the terms proportional to $Y_{\nu }^2$ in the RGE evolution of the neutrino Yukawa coupling.

Figure 7

The structure of the two-loop contributions to $\Delta m_{\tilde{E}}^2$ that involve the neutrino Yukawa couplings. All possible particles from each supermultiplet should be put on each line of each diagram: (a) proper two-loop contributions; (b) one-loop diagrams containing one-loop counterterms for $\Delta m_{\tilde{L}}^2$.

Figure 8

Subdominant diagram contributing to EDMs. The vertices marked by heavy dots are $A_{\ell }$ vertices, and the marked insertion is a one-loop correction to $m_{\tilde{L}}^2$. All of the momenta flowing through the indicated loops are of order $M_{\mathrm{S}\mathrm{U}\mathrm{S}\mathrm{Y}}$.

Figure 9

A contribution to the renormalization of $A_{\ell }$ in two-loop order from two one-loop diagrams.

Figure 10

Irreducible two-loop diagrams contributing to $A_{\ell }$. The shaded boxes represent the full one-loop propagator corrections from the $N$, $H_2$ supermultiplets.