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.