The longstanding $4.2 , sigma$ 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 $U(1)_{L_mu-L_tau}$ gauge symmetry, the
corresponding $Z^prime$ can both resolve the observed $g-2$ anomaly and yield
an acceptable dark matter relic abundance, relying on annihilations which take
place through the $Z^prime$ resonance. Once the value of $(g-2)_{mu}$ 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,
NA64$mu$, $M^3$, and DUNE. Furthermore, portions of this mass range predict
contributions to $Delta N_{rm eff}$ 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.
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