Vanishing or non-vanishing rainbow? Reduction formulas of electric dipole moment

TL;DR

This paper derives simplified formulas for fermion electric dipole moments, revealing that non-zero contributions mainly come from rainbow diagrams with chirality flips, and extends the formulas to broader models.

Contribution

It introduces generalized EDM formulas incorporating form factors, enabling application to a wider range of theoretical models beyond the Standard Model.

Findings

Exact cancellation of EDM due to Ward-Takahashi identity in the Standard Model.

Non-zero EDM contributions arise from rainbow diagrams with chirality flips.

Formulas are generalized for broader model applicability.

Abstract

In this paper, we derive a simplified formula of electric dipole moments (EDMs) of a fermion. In the Standard Model, it is well-known that non-trivial cancellations between some rainbow-type diagrams induced by $W$ boson exchanges occur in the calculation of the neutron EDM at the two-loop level due to the gauge symmetry. The fermion self-energy and the vertex correction are related through the Ward-Takahashi identity, and this relation causes the exact cancellation of the EDM. We derive EDM formulas for a more general setup by introducing the form factors for the fermion self-energy and the vertex correction so that the derived formulas can be applicable to a larger class of models. We conclude that the non-zero EDM contributions are induced from rainbow-type diagrams with the chirality flipping effects for internal fermions. We also discuss the other possible generalization of the EDM calculation which is applicable to the other classes of models.