A simple model for explaining muon-related anomalies and dark matter

We propose a model to explain several muon-related experimental anomalies and the abundance of dark matter. We introduce an vector-like exotic lepton that form an iso-doublet and three right-handed Majorana fermions as an iso-singlet. A real/complex scalar field is added as a dark matter candidate. We impose a global $U(1)_ \mu$ symmetry under which fields associated with the SM muon are charged. To stabilize the dark matter, we impose a $Z_2$ (or $Z_3$) symmetry under which the exotic lepton doublet and the real (or complex) scalar field are charged. We find that the model can simultaneously explain the muon anomalous magnetic dipole moment and the dark matter relic density in no conflict with any lepton flavor-violating/conserving observables, with some details depending upon whether the scalar field is real or complex. Besides, we extend the framework to the quark sector in a way similar to the lepton sector, and find that the recent anomalies associated with the $b \to s \mu^+ \mu^-$ transition can also be accommodated while satisfying constraints such as the $B_{s(d)} \to \mu^+ \mu^-$ decays and neutral meson mixings.