Full Three-Loop Electroweak Multiplet Contributions to the Electron Electric Dipole Moment

TL;DR

This work computes the full three-loop electron EDM induced by CP-violating Yukawa couplings of additional SU(2)_L multiplets, including both the two-loop-generated electroweak-Weinberg operator and the three-loop leptonic dipole contributions captured in the full theory. The authors derive a compact full-theory expression d_e^{Full}/e ∝ Im(sa^*) m_A m_B B(m_A,m_B,m_S,m_W) and show that, in the degenerate-mass limit, the result scales with a Clausen-function structure and is approximately three times larger than the SMEFT EW-only prediction at leading order. This enhancement strengthens the potential to probe TeV-scale new physics (e.g., higher SU(2)_L representations like the fermionic quintuplet) with forthcoming EDM experiments, while also highlighting that current constraints already exclude portions of the parameter space for certain representations. The study is constrained to the (A,B,S)=(r,r,1) case; a more general treatment would require additional diagrams with gauge insertions on the multiplet lines.

Abstract

Experimental sensitivity to the electric dipole moment (EDM) of the electron has improved remarkably in recent years. Consequently, future prospects could probe new physics whose contribution to the electron EDM first arises at three-loop order. Additional SU(2)$_L$ multiplets with CP-violating Yukawa interactions, which contribute to the electron EDM at three-loop level, is one such testable new physics scenario. In this scenario, the electron EDM is radiatively induced from two contributions: the CP-odd trilinear $W$-boson coupling, called the electroweak-Weinberg operator, and the CP-odd dipole operator of electron. The former and the latter operators are generated at two-loop and three-loop levels, respectively, after integrating out the SU(2)$_L$ multiplets. Within the same models, according to an analysis based on the Standard Model Effective Field Theory (SMEFT), we previously found that the contribution to the electron EDM from the electroweak-Weinberg operator can be probed in future experiments. However, the one-loop matching condition between the electron EDM and the electroweak-Weinberg operator does not receive a large logarithmic enhancement because the associated anomalous dimension is zero. The CP-odd dipole operator of the electron would contribute to the electron EDM at the same three-loop order as the contribution through the electroweak-Weinberg operator. In this paper, we directly calculate the electron EDM induced by the CP-violating Yukawa interactions of the SU(2)$_L$ multiplets at full three-loop level. A central result is that the full three-loop calculation is a factor of three larger than that of the electroweak-Weinberg operator alone.

Figures (7)

• Figure 1: Two-loop diagrams generating the Wilson coefficient $C_W$ of the electroweak-Weinberg operator after integrating out the heavy fields.
• Figure 2: One-loop matching diagram that induces the electron EDM from the electroweak-Weinberg operator.
• Figure 3: Feynman diagrams contribute to the electron EDM at three-loop level.
• Figure 4: Electron EDM induced by the CP-violating Yukawa couplings of $(r,r,1)$ SU(2)$_L$ multiplets degenerated mass $m_A=m_B=m_S$ in full theory. Here, $\operatorname{Im} (s a^*) = 0.25$ is taken. The four color lines illustrate each SU(2)$_L$ representation, where $r=2,3,4,5$, respectively. The magenta region is excluded by current experimental bound, $|d_e^{\rm exp.}| < 4.1 \times 10^{-30} e \, {\rm cm}$Roussy:2022cmp, and the cyan region cannot be probed due to CKM contribution through $e$--$N$ four-Fermi interaction Ema:2022yra.
• Figure 5: Comparison of contributions for the electron EDM in the full theory and only through the electroweak-Weinberg operator when representations of two fermions are $r=2$. Here, $m_S$ is fixed to 1 TeV, and $\operatorname{Im} (s a^*) = 0.25$ is taken. Black (Red) solid line shows the contribution to the electron EDM in the full theory (effective field theory for the electroweak-Weinberg operator).