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

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In the seesaw model, the baryon asymmetry of the Universe can be generated by the decay of the lightest right-handed neutrino, nuᵣ. 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: epsilon < 3 mnu₃ Mnuᵣ/(8 pi <Hᵤ>²). This implies that epsilon and the mass Mnuᵣ of the lightest right-handed neutrino are not independent parameters, as is commonly assumed. If mnu₃ = sqrtDelta m²atm and the nuᵣ are produced thermally, then leptogenesis requires a reheat temperature of the Universe Treh > Mnuᵣ > 10⁸ GeV. Reasonable estimates of nuᵣ production and the subsequent washout of the asymmetry, as made by Buchmuller and Plumacher, imply Mnuᵣ > 10⁹ GeV, and Treh > 10¹⁰ GeV. Implications for the gravitino problem are also discussed.