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We propose a minimal model which accommodates the long-standing anomaly ofmuon magnetic moment based on abelian discrete flavor symmetries. The standardmodel is extended by scalar doublets charged under a $Z_n$ lepton flavorsymmetry. In these models, a large contribution to the muon magnetic moment canbe obtained by the chirality enhancement from new scalar mediated diagramswithout conflicting with the flavor symmetry. Thanks to the lepton flavorsymmetry, these models automatically forbid lepton flavor violation. Theminimal model is based on $Z_4$ symmetry with only one extra scalar doublet. Inthis model, we show that the parameter space favored by the muon $g-2$ caneasily be consistent with experimental constraints and theoretical bounds suchas the electroweak precision tests, lepton universality, potential stabilitycondition and triviality bound as well as the LHC direct search mass bound. Thenew contributions to the muon electric dipole moment and the Higgs decay into$\gamma\gamma$ can be indirect signals of the model.

A $\mu$-$\tau$-philic scalar doublet under $Z_n$ flavor symmetry