Résumé
JHEP0309:021,2003 In the framework of the seesaw mechanism with three heavy right-handed Majorana neutrinos and no Higgs triplets we carry out a systematic study of the structure of the right-handed neutrino sector. Using the current low-energy neutrino data as an input and assuming hierarchical Dirac-type neutrino masses$m_{Di}$ , we calculate the masses$M_i$and the mixing of the heavy neutrinos. We confront the inferred properties of these neutrinos with the constraints coming from the requirement of a successful baryogenesis via leptogenesis. In the generic case the masses of the right-handed neutrinos are highly hierarchical:$M_i \propto m_{Di}^2$ ; the lightest mass is$M_1 \approx 10^3 - 10^6$GeV and the generated baryon-to-photon ratio$\eta_B\lesssim 10^{-14}$is much smaller than the observed value. We find the special cases which correspond to the level crossing points, with maximal mixing between two quasi-degenerate right-handed neutrinos. Two level crossing conditions are obtained:${m}_{ee}\approx 0$(1-2 crossing) and$d_{12}\approx 0$(2-3 crossing), where${m}_{ee}$and$d_{12}$are respectively the 11-entry and the 12-subdeterminant of the light neutrino mass matrix in the basis where the neutrino Yukawa couplings are diagonal. We show that sufficient lepton asymmetry can be produced only in the 1-2 crossing where$M_1 \approx M_2 \approx 10^{8}$GeV,$M_3 \approx 10^{14}$GeV and$(M_2 - M_1)/ M_2 \lesssim 10^{-5}$ .