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, ν _R. 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 < 3m _ν3 M _νR/(8π H _u ²). This implies that ε and the mass M _νR of the lightest right-handed neutrino are not independent parameters, as is commonly assumed. If m _ν3 = √Δm _atm ² and the ν _R are produced thermally, then leptogenesis requires a reheat temperature of the Universe T _reh > M _νR > 10 ⁸ GeV. Reasonable estimates of ν _R production and the subsequent washout of the asymmetry, as made by Buchmüller and Plümacher, imply M _νR > 10 ⁹ GeV, and T _reh > 10 ¹⁰ GeV. Implications for the gravitino problem are also discussed.