Limits on $T_{RH}$ 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, apart from the masses $M_1$ and $M_2$ of the remaining two right-chiral neutrinos, only on the element $\YY{22}$ of the neutrino Yukawa coupling. For $M_2\simgt10M_1$ the lower bound on $M_1$ and also on $T_{\rm reh}$, resulting from the requirement of 'successful leptogenesis' is then significantly increased compared to the one computed recently by Buchm\"uller {\it 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 $M_2-M_1$.