  We propose a new ``disappearing positron track'' channel at Belle II to
search for dark matter, in which a positron that is produced at the primary
interaction vertex scatters with the electromagnetic calorimeter to produce
dark matter particles. Such scatterings can occur via either annihilation with
atomic electrons, or the bremsstrahlung process with target nuclei. The main
backgrounds are due to photons and neutrons that are produced in the same
scatterings and then escape detection. We require a large missing energy and
further veto certain activities in the KLM detector to suppress such
backgrounds. To illustrate the sensitivity of the new channel, we consider a
new physics model where dark matter interacts with the standard model via a
dark photon, which decays predominantly to dark matter; we find that our
proposed channel can probe some currently unexplored parameter space,
surpassing both the mono-photon channel at Belle II and the NA64 constraints.
