Gravitational effects on measurements of the muon dipole moments

If the technology for muon storage rings one day permits sensitivity to precession at the order of 10−8 Hz10−8 Hz, the local gravitational field of Earth can be a dominant contribution to the precession of the muon, which, if ignored, can fake the signal for a nonzero muon electric dipole moment (EDM). Specifically, the effects of Earth's gravity on the motion of a muon's spin is indistinguishable from it having a nonzero EDM of magnitude dμ∼10−29 ecm in a storage ring with vertical magnetic field of ∼1 T∼1 T, which is significantly larger than the expected upper limit in the Standard Model, dμ≲10−36 ecm. As a corollary, measurements of Earth's local gravitational field using stored muons would be a unique test to distinguish classical gravity from general relativity with a bonafide quantum mechanical entity, i.e., an elementary particle's spin.