Neutrinoless double $\beta$ decay and low scale leptogenesis
  The extension of the Standard Model by right handed neutrinos with masses in
the GeV range can simultaneously explain the observed neutrino masses via the
seesaw mechanism and the baryon asymmetry of the universe via leptogenesis. It
has previously been claimed that the requirement for successful baryogenesis
implies that the rate of neutrinoless double $\beta$ decay in this scenario is
always smaller than the standard prediction from light neutrino exchange alone.
In contrast, we find that the rate for this process can also be enhanced due to
a dominant contribution from heavy neutrino exchange. In a small part of the
parameter space it even exceeds the current experimental limit, while the
properties of the heavy neutrinos are consistent with all other experimental
constraints and the observed baryon asymmetry is reproduced. This implies that
neutrinoless double $\beta$ decay experiments have already started to rule out
part of the leptogenesis parameter space that is not constrained by any other
experiment, and the lepton number violation that is responsible for the origin
of baryonic matter in the universe may be observed in the near future.
