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

TL;DR

This paper performs a comprehensive three-loop calculation of the electron EDM contribution from SU(2)$_L$ multiplets with CP-violating interactions, revealing a larger effect than previously estimated from the electroweak-Weinberg operator alone.

Contribution

It provides the first full three-loop computation of the electron EDM in this scenario, showing the total effect is three times larger than prior estimates based on the electroweak-Weinberg operator.

Findings

Full three-loop electron EDM contribution is three times larger than previous estimates.

The CP-violating Yukawa interactions significantly impact the electron EDM.

The calculation refines predictions for future experimental probes of new physics.

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.