Gravitational Effects on Measurements of the Muon Dipole Moments

TL;DR

This paper discusses how Earth's gravity can influence muon spin precession measurements, potentially mimicking signals of a muon electric dipole moment and offering a novel way to test gravity theories using muons.

Contribution

It highlights the significance of gravitational effects on muon spin precession and proposes using muon experiments to distinguish classical gravity from general relativity.

Findings

Earth's gravity can mimic a muon EDM signal of ~10^{-29} e cm.

Gravitational effects could dominate at sensitivities of 10^{-8} Hz precession.

Muon-based experiments could test fundamental gravity theories.

Abstract

If the technology for muon storage rings one day permits sensitivity to precession at the order of $10^{-8}$ 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 $d_\mu \sim 10^{-29}$ e cm in a storage ring with vertical magnetic field of $\sim$ 1 T, which is significantly larger than the expected upper limit in the Standard Model, $d_\mu \lesssim 10^{-36}$ e cm. 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.