Muon and Electron $g-2$ and the Origin of Fermion Mass Hierarchy

Understand

We present a model that gives a natural explanation to the charged lepton mass hierarchy and study the contributions to the electron and the muon $g-2$.

• In the model, we introduce lepton-flavor-dependent $U(1)_F$ symmetry and three additional Higgs doublets with $U(1)_F$ charges, to realize that each generation of charged leptons couples to one of the three additional Higgs doublets.
• The $U(1)_F$ symmetry is softly broken by $+1$ charges, and the smallness of the soft breaking naturally gives rise to the hierarchy of the Higgs VEVs, which then accounts for the charged lepton mass hierarchy.
• Since electron and muon couple to different scalar particles, each scalar contributes to the electron and the muon $g-2$ differently.