An explanation for the muon and electron $g-2$ anomalies and dark matter

We propose simple models with a flavor-dependent global $U(1)_\ell$ and a discrete $\mathbb{Z}_2$ symmetries to explain the anomalies in the measured anomalous magnetic dipole moments of muon and electron, $(g-2)_{\mu,e}$, while simultaneously accommodating a dark matter candidate. These new symmetries are introduced not only to avoid the dangerous lepton flavor-violating decays of charged leptons, but also to ensure the stability of the dark matter. Our models can realize the opposite-sign contributions to the muon and electron $g-2$ via one-loop diagrams involving new vector-like leptons. Under the vacuum stability and perturbative unitarity bounds as well as the constraints from the dark matter direct searches and related LHC data, we find suitable parameter space to simultaneously explain $(g-2)_{\mu,e}$ and the relic density. In this parameter space, the coupling of the Higgs boson with muons can be enhanced by up to $\sim 38\%$ from its Standard Model value, which can be tested in future collider experiments.