  We explore the parameter space of a U(1) extension of the standard model --
also called the super-weak model -- from the point of view of explaining the
observed dark matter energy density in the Universe. The new particle spectrum
contains a complex scalar singlet and three right-handed neutrinos, among which
the lightest one is the dark matter candidate. We explore both freeze-in and
freeze-out mechanisms of dark matter production. In both cases, we find regions
in the plane of the super-weak coupling vs. the mass of the new gauge boson
that are not excluded by current experimental constraints. These regions are
distinct and the one for freeze-out will be explored in searches for neutral
gauge boson in the near future.
