Muon spin force

TL;DR

This paper explores the hypothesis that a long-range muon spin force could explain the muon g-2 discrepancy, proposing experimental tests and analyzing indirect constraints with current nuclear spin precession data.

Contribution

It introduces a novel model of a muon spin force to address the muon g-2 anomaly and suggests experimental and indirect methods to test and constrain this hypothesis.

Findings

A tiny spin energy splitting could resolve the g-2 discrepancy.

Proposed muon spin resonance experiments as a definitive test.

Existing nuclear spin precession data provide constraints, but with significant uncertainties.

Abstract

Current discrepancy between the measurement and the prediction of the muon anomalous magnetic moment can be resolved in the presence of a long-range force created by ordinary atoms acting on the muon spin via axial-vector and/or pseudoscalar coupling, and requiring a tiny, $\mathcal{O}(10^{-13}\,{\rm eV})$ spin energy splitting between muon state polarized in the vertical direction. We suggest that an extension of the muon spin resonance ($\mu$SR) experiments can provide a definitive test of this class of models. We also derive indirect constraints on the strength of the muon spin force, by considering the muon-loop-induced interactions between nuclear spin and external directions. The limits on the muon spin force extracted from the comparison of $^{199}$Hg/$^{201}$Hg and $^{129}$Xe/$^{131}$Xe spin precession are strong for the pseudoscalar coupling, but are significantly relaxed for the axial-vector one. These limits suffer from significant model uncertainties, poorly known proton/neutron spin content of these nuclei, and therefore do not exclude the possibility of a muon spin force relevant for the muon $g-2$.