Probing MeV Dark Matter at Low--Energy $e^+e^-$ Colliders

It has been suggested that the annihilation of Dark Matter particles \chi with mass between 0.5 and 20 MeV into e^+e^- pairs could be responsible for the excess flux of 511 keV photons coming from the central region of our galaxy that has been detected by the IINTEGRAL satellite. The simplest way to achieve the required cross section for \chi pair annihilation while respecting existing constraints is to introduce a new vector boson U with mass M_U below a few hundred MeV. In this Letter we point out that over most of the allowed parameter space, the process e^+e^- to U \gamma, followed by the decay of U into either an e^+e^- pair or into an invisible (\nu \bar \nu or \chi \bar \chi) channel, should lead to signals that can be detected by the B-factory experiments BaBar and Belle. A smaller, but still substantial, region of parameter space can also be probed at the \Phi factory DAFNE.