Muon Spin Force

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 O(10-13 ( 10 - 13 eV) ) spin energy splitting between muon state polarized in the vertical direction. We suggest that an extension of the muon spin resonance (mu SR) 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.