Scalars that carry lepton number can help mediate would-be lepton-number-violating processes, such as neutrinoless double $beta$ decay or lepton-scattering-mediated nucleon-antinucleon conversion. Here we show that such new scalars can also solve the anomaly in precision determinations of the fine-structure constant $alpha$ from atom interferometry and from the electrons anomalous magnetic moment, $a_e equiv (g-2)_e/2$, by reducing $|a_e|$. Study of the phenomenological constraints on these solutions favor a doubly-charged scalar with mass below the GeV scale. Significant constraints arise from the measurement of the parity-violating asymmetry in M{o}ller scattering, and we consider the implications of the next-generation MOLLER experiment at Jefferson Laboratory and of an improved $a_e$ measurement.
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