Simplest and Most Predictive Model of Muon g -2 and Thermal Dark Matter

The long-standing 4.2 σ muon g -2 anomaly may be the result of a new particle species which could also couple to dark matter and mediate its annihilations in the early Universe. In models where both muons and dark matter carry equal charges under a U (1 )L_μ-Lτ gauge symmetry, the corresponding Z^' can both resolve the observed g -2 anomaly and yield an acceptable dark matter relic abundance, relying on annihilations which take place through the Z^' resonance. Once the value of (g -2 )_μ and the dark matter abundance are each fixed, there is very little remaining freedom in this model, making it highly predictive. We provide a comprehensive analysis of this scenario, identifying a viable range of dark matter masses between approximately 10 and 100 MeV, which falls entirely within the projected sensitivity of several accelerator-based experiments, including NA62, NA 64 μ , M³, and DUNE. Furthermore, portions of this mass range predict contributions to Δ N_eff which could ameliorate the tension between early and late time measurements of the Hubble constant, and which could be tested by stage 4 CMB experiments.