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, v(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: epsilon < 3m(v3),M-vR/(8pi(H-u)(2)). This implies that epsilon and the mass M-vR of the lightest right-handed neutrino are not independent parameters, as is commonly assumed. If m(v3) = rootDeltam(atm)(2) and the v(R) are produced thermally, then leptogenesis requires a reheat temperature of the Universe T-reh > M-vR > 10(8) GeV. Reasonable estimates of v(R) production and the subsequent washout of the asymmetry, as made by Buchmuller and Plumacher, imply M-vR > 109 GeV, and T-reh > 10(10) GeV. Implications for the gravitino problem are also discussed. (C) 2002 Elsevier Science B.V. All rights reserved.