The deviation of the measured value of the muon anomalous magnetic moment from the standard model prediction can be completely explained by mixing of the muon with extra vectorlike leptons, L and E, near the electroweak scale. This mixing simultaneously contributes to the muon mass. We show that the correlation between contributions to the muon mass and muon g-2 is controlled by the mass of the neutrino originating from the doublet L. Positive correlation, simultaneously explaining both measured values, requires this mass below 200 GeV. The decay rate of the Higgs boson to muon pairs is modified and, in the region of the parameter space that can explain the muon anomalous magnetic moment within one standard deviation, it ranges from 0.5 to 24 times the standard model prediction. In the same scenario, $h to gamma gamma$ can be enhanced or lowered by ~50% from the standard model prediction. The explanation of the muon g-2 anomaly and predictions for $h to gamma gamma$ are not correlated since these are controlled by independent parameters. This scenario can be embedded in a model with three complete vectorlike families featuring gauge coupling unification, sufficiently stable proton, and the Higgs quartic coupling remaining positive all the way to the grand unification scale.
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