Long-range axion forces and hadronic CP violation

Abstract: Axions and other pseudoscalar fields comprise an interesting class of ultralight dark matter candidates, that may independently play a role in solving the strong $CP$ problem. In the presence of $CP$-violating sources, these pseudoscalar fields can develop a coherent non-derivative coupling to nucleons, $\bar g_{aNN}$, thus mediating mass-mass' andmass-spin' forces in matter that can be probed experimentally. We revisit the non-perturbative generation of these $CP$-odd axion forces, and refine estimates of $\bar g_{aNN}$ generated by the EDMs and color EDMs of quarks. We also revisit the Standard Model contribution to $CP$-odd axion couplings generated by the phase of the Cabibbo-Kobayashi-Maskawa quark mixing matrix.