  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.
