Gravitational effects on measurements of the muon dipole moments

Andrew Kobach

doi:10.1016/j.nuclphysb.2016.08.011

Andrew Kobach

Open Access

https://doi.org/10.1016/j.nuclphysb.2016.08.011

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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 dμ∼10−29 ecm in a storage ring with vertical magnetic field of ∼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.

Highlights

While colliders are suitable for producing heavy particles, uncovering precise detail of the underlying theory is left to precision measurements performed by dedicated experiments
The muon anomalous magnetic dipole moment aμ was best measured to ∼ 0.5 ppm by the (g − 2)μ experiment at BNL [6], but resulted in about a 2.7σ - 3.6σ discrepancy with the value expected in the Standard Model (SM), depending on the details of the contributions of the strong interactions [7,8,9,10,11,12]
Comes at the price of understanding in minute detail the expected behavior of the experiment on a whole. One such effect is the role of gravity in these experiments

Summary

INTRODUCTION

While colliders are suitable for producing heavy particles, uncovering precise detail of the underlying theory is left to precision measurements performed by dedicated experiments. The muon anomalous magnetic dipole moment aμ was best measured to ∼ 0.5 ppm by the (g − 2)μ experiment at BNL [6], but resulted in about a 2.7σ - 3.6σ discrepancy with the value expected in the SM, depending on the details of the contributions of the strong interactions [7,8,9,10,11,12] Whether or not this is a sign of new physics may be settled as improved experimental [13, 14] and theoretical techniques [15,16,17,18,19,20,21,22,23] are employed. For a typical cyclotron with a vertical magnetic field of ∼ 1 T, Earth’s gravity will induce the same dynamics as a nonzero muon EDM of magnitude dμ ∼ 10−29 e cm, which is about 5 orders of magnitude greater than the upper limit on the SM expectation

GRAVITATIONAL EFFECTS ON A STORED MUON

Findings

SUMMARY AND CONCLUSIONS