Long-range axion forces and hadronic C P 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 C P problem. In the presence of C P -violating sources, these pseudoscalar fields can develop a coherent nonderivative coupling to nucleons, g_{¯a N N}, thus mediating `mass-mass' and `mass-spin' forces in matter that can be probed experimentally. We revisit the nonperturbative generation of these C P -odd axion forces, and refine estimates of g_{¯a N N} generated by the electric dipole moments and color electric dipole moments of quarks. We also revisit the Standard Model contribution to C P -odd axion couplings generated by the phase of the Cabibbo-Kobayashi-Maskawa quark mixing matrix.