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.
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Fujiwara, M., Hisano, J. & Toma, T. Vanishing or non-vanishing rainbow? Reduction formulas of electric dipole moment. J. High Energ. Phys. 2021, 237 (2021). https://doi.org/10.1007/JHEP10(2021)237
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DOI: https://doi.org/10.1007/JHEP10(2021)237