  Electric dipole moments of nuclei, diamagnetic atoms, and certain molecules
are induced by CP-violating nuclear forces. Naive dimensional analysis predicts
these forces to be dominated by long-range one-pion-exchange processes, with
short-range forces entering only at next-to-next-to-leading order in the chiral
expansion. Based on renormalization arguments we argue that a consistent
picture of CP-violating nuclear forces requires a leading-order short-distance
operator contributing to ${}^1S_0$-${}^3P_0$ transitions, due to the attractive
and singular nature of the strong tensor force in the ${}^3P_0$ channel. The
short-distance operator leads to $\mathcal O(1)$ corrections to static and
oscillating, relevant for axion searches, electric dipole moments. We discuss
strategies how the finite part of the associated low-energy constant can be
determined in the case of CP violation from the QCD theta term by the
connection to charge-symmetry violation in nuclear systems.
