Light $Z^\prime$ and Dark Matter from U(1)$_X$ Gauge Symmetry
  We consider a U(1)$_X$ gauge symmetry extension of the Standard Model (SM)
with a $Z^\prime$-portal Majorana fermion dark matter that allows for a
relatively light gauge boson $Z^\prime$ with mass of 10 MeV$-$ a few GeV and a
much heavier dark matter through the freeze-in mechanism. In a second scenario
the roles are reversed, and the dark matter mass, in the keV range or so, lies
well below the $Z^\prime$ mass, say, $\sim 1$ GeV. We outline the parameter
space that can be explored for these two scenarios at the future Lifetime
Frontier experiments including Belle-II, FASER, LDMX and SHiP.
