Long-range axion forces and hadronic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math> violation
Shohei Okawa, Maxim Pospelov, Adam Ritz
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 nonderivative coupling to nucleons, ${\overline{g}}_{aNN}$, 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 ${\overline{g}}_{aNN}$ 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.