Long-range axion forces and hadronic CP violation

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 nonderivative coupling to nucleons, g¯aNN, thus mediating 'mass-mass' and 'mass-spin' forces in matter that can be probed experimentally. We revisit the nonperturbative generation of these CP-odd axion forces, and refine estimates of g¯aNN generated by the electric dipole moments and color electric dipole moments 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.