Explaining Dark Matter and $B$ Decay Anomalies with an $L_\mu - L_\tau$ Model

We present a dark sector model based on gauging the $L_\mu - L_\tau$ symmetry that addresses anomalies in $b \rightarrow s \mu^+ \mu^-$ decays and that features a particle dark matter candidate. The dark matter particle candidate is a vector-like Dirac fermion coupled to the $Z^\prime$ gauge boson of the $L_{\mu}-L_{\tau}$ symmetry. We compute the dark matter thermal relic density, its pair-annihilation cross section, and the loop-suppressed dark matter-nucleon scattering cross section, and compare our predictions with current and future experimental results. We demonstrate that after taking into account bounds from $B_s$ meson oscillations, dark matter direct detection, and the CMB, the model is highly predictive: $B$ physics anomalies and a viable particle dark matter candidate, with a mass of $\sim (5-23)$~GeV, can be accommodated only in a tightly-constrained region of parameter space, with sharp predictions for future experimental tests. The viable region of parameter space expands if the dark matter is allowed to have $L_\mu-L_\tau$ charges that are smaller than those of the SM leptons.