Searching for axion forces with precision precession in storage rings

We consider different types of storage rings as precision probes of axion-mediated monopole-dipole forces. We show that current and planned experiments aiming to measure magnetic and electric dipole moments of protons, muons and electrons very precisely may explore new parts of the parameter space beyond existing laboratory bounds and, in some cases, beyond astrophysical constraints. Remarkably, a light axion coupled to muons may explain the FNAL/BNL $(g-2)_\mu$ anomaly as an environmental effect -- the coherent axion field generated by the earth nucleons induces an extra contribution to the anomalous precession frequency of the muon explaining the discrepancy with respect to the SM prediction.