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### arXiv:2104.03297 [hep-ph]AbstractReferencesReviewsResources

#### Distinguishing $U(1)_{L_μ-L_τ}$ from $U(1)_{L_μ}$ as a solution for $(g-2)_μ$ with neutrinos

Published 2021-04-07Version 1

The recent measurement of the muon anomalous magnetic moment by the Fermilab E989 experiment, when combined with the previous result at BNL, has confirmed the tension with the SM prediction at $4.2\,\sigma$~CL, strengthening the motivation for new physics in the leptonic sector. Among the different particle physics models that could account for such an excess, a gauged $U(1)_{L_\mu-L_{\tau}}$ stands out for its simplicity, but it is yet indistinguishable from other constructions with a muon-philic vector boson, such as e.g.~a simplified $U(1)_{L_\mu}$ model. In this article we explore how the combination of data from different future probes can help identify the nature of the new physics behind the muon anomalous magnetic moment. We first show that muon fixed target experiments such as NA64$\mu$ will be able to measure the coupling of the hidden photon to the muon sector in the region compatible with $(g-2)_\mu$, having also some sensitivity to the hidden photon's mass. We then study how experiments looking for coherent elastic neutrino-nucleus scattering (CE$\nu$NS) at spallation sources will provide crucial additional information on the kinetic mixing of the hidden photon. When combined with NA64$\mu$ results, the exclusion limits (or reconstructed regions) of future CE$\nu$NS detectors also allow a better measurement of the mediator mass. Finally, the observation of nuclear recoils from solar neutrinos in direct detection experiments will provide unique information about the coupling of the hidden photon to the tau sector. The signal expected for $U(1)_{L_\mu-L_{\tau}}$ is larger than for $U(1)_{L_\mu}$ with the same kinetic mixing and future multi-ton liquid xenon proposals (such as DARWIN) have the potential to separate both models.

Comments: 30 pages, 14 figures, 2 tables
Categories: hep-ph
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