Probing the freeze-in mechanism in dark matter models with $U(1)^\prime$
  gauge extensions
  New gauge bosons at the MeV scale with tiny gauge couplings (so-called dark
photons) can be responsible for the freeze-in production of dark matter and
provide a clear target for present and future experiments. We study the effects
of thermal mixing between dark photons and Standard Model gauge bosons and of
the resulting plasmon decays on dark matter production before and after the
electroweak phase transition. In the parameter regions preferred by the
observed dark matter relic abundance, the dark photon is sufficiently
long-lived to be probed with fixed-target experiments and light enough to
induce direct detection signals. Indeed, current limits from XENON1T already
constrain Dirac fermion dark matter in the GeV to TeV range produced via the
freeze-in mechanism. We illustrate our findings for the case of a $U(1)_{B-L}$
gauge extension and discuss possible generalisations.
