Limits on Treh for thermal leptogenesis with hierarchical neutrino masses

We make a simple observation that if one of the right-chiral neutrinos is very heavy or its Yukawa couplings to the standard lepton doublets are negligible, so that it effectively decouples from the see-saw mechanism, the prediction for the baryon asymmetry of the universe resulting from leptogenesis depends only on the masses M1 and M2 of the remaining two right-chiral neutrinos and the element Y-tildeν22 of the neutrino Yukawa coupling. For M2∼>5M1 the lower bound on M1 and also on Treh, resulting from the requirement of 'successful leptogenesis' is then significantly increased compared to the one computed recently by Buchmueller et al. in the most general case. Within the framework of thermal leptogenesis, the only way to lower this limit is then to allow for sufficiently small mass difference M2-M1