Tale of two anomalies

A recent improved determination of the fine structure constant, alpha = 1/137.035999046(27), leads to a similar to 2.4 sigma negative discrepancy between the measured electron anomalous magnetic moment and the standard model prediction. That situation is to be compared with the muon anomalous magnetic moment where a positive similar to 3.7 sigma discrepancy has existed for some time. A single scalar solution to both anomalies is shown to be possible if the two-loop electron Barr-Zee diagrams dominate the scalar one-loop electron anomaly effect and the scalar couplings to the electron and two photons are relatively large. We also briefly discuss the implications of that scenario.