For Light Dark Matter, − 2, the 511 keV excess and the Hubble tension

In this paper we introduce a light Dirac particle ψ as thermal dark matter candidate in a U(1)Lμ−Lτ model. Together with the new gauge boson X, we find a possible parameter space with mX≃20 MeV, U(1)Lμ−Lτ coupling gX≃5⋅10−4 and mψ≳mX/2 where the (g−2)μ anomaly, dark matter, the Hubble tension, and (part of) the excess of 511 keV photons from the region near the galactic center can be explained simultaneously. This model is safe from current experimental and astrophysical constraints, but can be probed by the next generation of neutrino experiments as well as low–energy e+e− colliders.