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

## TL;DR

This paper introduces a minimal $Z_4$-symmetric scalar doublet model that explains the muon g-2 anomaly while naturally avoiding lepton flavor violation and satisfying experimental constraints.

## Contribution

It presents a novel minimal scalar doublet model with $Z_4$ symmetry that accounts for muon g-2 and remains consistent with various experimental bounds.

## Key findings

- The model explains the muon g-2 anomaly without conflicting with flavor constraints.
- Parameter space is compatible with electroweak precision tests and LHC bounds.
- Potential signals include muon EDM and Higgs decay modifications.

## Abstract

We propose a minimal model which accommodates the long-standing anomaly of muon magnetic moment based on abelian discrete flavor symmetries. The standard model is extended by scalar doublets charged under a $Z_n$ lepton flavor symmetry. In these models, a large contribution to the muon magnetic moment can be obtained by the chirality enhancement from new scalar mediated diagrams without conflicting with the flavor symmetry. Thanks to the lepton flavor symmetry, these models automatically forbid lepton flavor violation. The minimal model is based on $Z_4$ symmetry with only one extra scalar doublet. In this model, we show that the parameter space favored by the muon $g-2$ can easily be consistent with experimental constraints and theoretical bounds such as the electroweak precision tests, lepton universality, potential stability condition and triviality bound as well as the LHC direct search mass bound. The new contributions to the muon electric dipole moment and the Higgs decay into $\gamma\gamma$ can be indirect signals of the model.