Electric dipole moments with and beyond flavor invariants

In this paper, the flavor structure of quark and lepton electric dipole moments in the SM and beyond is investigated using tools inspired from Minimal Flavor Violation. While Jarlskog-like flavor invariants are adequate for estimating $\mathrm{CP}$-violation from closed fermion loops, non-invariant structures arise from rainbow-like processes. Our goal is to systematically construct these latter flavor structures in the quark and lepton sectors, assuming different mechanisms for generating neutrino masses. Numerically, they are found typically much larger, and not necessarily correlated with, Jarlskog-like invariants. Finally, the formalism is adapted to deal with a third class of flavor structures, sensitive to the flavored $U\left(1\right)$ phases, and used to study the impact of the strong $\mathrm{CP}$-violating interaction and the interplay between the neutrino Majorana phases and possible baryon and/or lepton number violating interactions.