Muon g-2 and a Geocentric New Field

Abstract: Light scalars can in principle couple to both bulk matter and fermion spin, with hierarchically disparate strengths. Storage ring measurements of fermion electromagnetic moments via spin precession can be sensitive to such a force, sourced by the Earth. We discuss how this force could lead to a deviation of the measured muon anomalous magnetic moment, $g-2$, from the Standard Model prediction. Due to its different parameters, the proposed JPARC muon $g-2$ experiment can provide a direct test of our hypothesis. A future search for the proton electric dipole moment can have good sensitivity for the coupling of the assumed scalar to nucleon spin. We also argue that supernova constraints on axion-muon coupling may not be applicable in our framework.