A lower bound on the right-handed neutrino mass from leptogenesis

In the see-saw model, the baryon asymmetry of the Universe can be generated by the decay of the lightest right-handed neutrino, νR. For a hierarchical spectrum of right-handed neutrinos, we show that there is a model independent upper bound on the CP asymmetry produced in these decays: ϵ<3mν3MνR/(8π〈Hu〉2). This implies that ϵ and the mass MνR of the lightest right-handed neutrino are not independent parameters, as is commonly assumed. If mν3=Δm2atm and the νR are produced thermally, then leptogenesis requires a reheat temperature of the Universe Treh>MνR>108 GeV. Reasonable estimates of νR production and the subsequent washout of the asymmetry, as made by Buchmüller and Plümacher, imply MνR>109 GeV, and Treh>1010 GeV. Implications for the gravitino problem are also discussed.