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.
Highlights
W dα ui dβ uj dα by quantum corrections
As shown in our reduction formulas, eq (2.28) and eq (2.33), it is essential to pick up the chirality flipping effects from the internal loop in order to obtain the non-zero electric dipole moments (EDMs) contributions
We have derived the reduced formulas for the EDM calculation at two-loop level or higher introducing the form factors of the self-energy and vertex correction that are related through the Ward-Takahashi identity
Summary
We derive reduction formulas for EDM that are induced from the diagrams with sub-diagram structures. We briefly review the SM calculation of the neutron EDM diagrams at the two-loop level as discussed in ref. We summarize the essential points in the SM calculation and derive the EDM reduction formulas with a more general setup
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