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The anomalous magnetic moments of the electron and the muon are interestingobservables, since they can be measured with great precision and their valuescan be computed with excellent accuracy within the Standard Model (SM). Thecurrent experimental measurement of this quantities show a deviation of a fewstandard deviations with respect to the SM prediction, which may be a hint ofnew physics. The fact that the electron and the muon masses differ by twoorders of magnitude and the deviations have opposite signs makes it difficultto find a common origin of these anomalies. In this work we introduce a complexsinglet scalar charged under a Peccei-Quinn-like (PQ) global symmetry togetherwith the electron transforming chirally under the same symmetry. In thisrealization, the CP-odd scalar couples to electron only, while the CP-even partcan couple to muons and electrons simultaneously. In addition, the CP-oddscalar can naturally be much lighter than the CP-even scalar, as apseudo-Goldstone boson of the PQ-like symmetry, leading to an explanation ofthe suppression of the electron anomalous magnetic moment with respect to theSM prediction due to the CP-odd Higgs effect dominance, as well as anenhancement of the muon one induced by the CP-even component.

A light complex scalar for the electron and muon anomalous magnetic moments