$(g-2{)}_{\mu ,e}$ and the ANITA anomalous events in a three-loop neutrino mass model

The most recent measurement of the fine structure constant leads to a 2.4 $\sigma$ deviation in the electron anomalous magnetic moment $g_e$-2, while the muon anomalous magnetic moment $g_{\mu }$-2 has a long standing 3.7 $\sigma$ deviation in the opposite direction. We show that these deviations can be explained in a three-loop neutrino mass model based on an $E_6$ Grand Unified Theory. We also study the impact such a model can have on the anomalous events observed by the ANITA experiment and find an insufficient enhancement of the event rate.