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 ${}^{1}S_0\text{−}{}^{3}P_0$ transitions due to the attractive and singular nature of the strong tensor force in the ${}^{3}P_0$ channel. The short-distance operator leads to $O\left(1\right)$ 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 $\overline{\theta }$ term by the connection to charge-symmetry violation in nuclear systems.

• Received 4 September 2020
• Accepted 14 January 2021

DOI:https://doi.org/10.1103/PhysRevC.103.L012501

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Published by the American Physical Society