Exploring Leptophilic Dark Matter with NA64-$\mu$

We investigate the prospects for detecting light leptophilic dark sectors with a missing-momentum experiment at NA64 running in muon mode. In particular, we consider models in which dark matter connects to the visible sector through a lepton- or muon-specific scalar mediator. These scalars can also account for the $\sim 3.5\sigma$ discrepancy between the measured and predicted values of $(g-2{)}_{\mu }$ . We emphasize the complementarity between NA64-$\mu$ and other terrestrial and astrophysical probes.