Muon ${g-2}$ Anomaly and Neutrino Magnetic Moments

We show that a unified framework based on an $SU(2)_H$ horizontal symmetry which generates a naturally large neutrino transition magnetic moment and explains the XENON1T electron recoil excess also predicts a positive shift in the muon anomalous magnetic moment. This shift is of the right magnitude to be consistent with the Brookhaven measurement as well as the recent Fermilab measurement of the muon $g-2$. A relatively light neutral scalar from a Higgs doublet with mass near 100 GeV contributes to muon $g-2$, while its charged partner induces the neutrino magnetic moment. In contrast to other multi-scalar theories, in the model presented here there is no freedom to control the sign and strength of the muon $g-2$ contribution. We analyze the collider tests of this framework and find that the HL-LHC can probe the entire parameter space of these models.