Strong CP violation in nuclear physics

Electric dipole moments of nuclei, diamagnetic atoms, and certain molecules are induced by $C\!P$-violating nuclear forces. The 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 $C\!P$-violating nuclear forces requires a short-distance operator acting in the unique $j=0$ ${}^1S_0$-${}^3P_0$ transition due to the attractive and singular nature of the strong tensor force in the ${}^3P_0$ channel. We discuss strategies on how the finite part of the associated low-energy constant can be determined in the case of strong $C\!P$ violation from the QCD $\bar \theta$ term, and speculate on the impact on observables of experimental interest such as nuclear EDMs and axion searches.