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Register a new userLIght scalars with lepton number to solve the $(g-2)_e$ anomaly
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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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The present work introduces two possible extensions of the Standard Model Higgs sector. In the first case, the Zee-Babu type model for the generation of neutrino mass is augmented with a scalar triplet and additional singly charged scalar singlets. The second scenario, on the other hand, generalizes the Type-II seesaw model by replicating the number of the scalar triplets. A $mathbb{Z}_3$ symmetry is imposed in case of both the scenarios, but, allowed to be violated by terms of mass dimension two and three for generating neutrino masses and mixings. We examine how the models so introduced can explain the experimental observation on the muon anomalous magnetic moment. We estimate the two-loop contribution to neutrino mass induced by the scalar triplet, in addition to what comes from the doubly charged singlet in the usual Zee-Babu framework, in the first model. On the other hand, the neutrino mass arises in the usual Type-II fashion in the second model. In addition, the role of the $mathbb{Z}_3$ symmetry in suppressing lepton flavor violation is also elucidated.
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