Probing the seesaw mechanism with neutrino data and leptogenesis

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∝m_Di²; the lightest mass is M₁ ≈ 10³−10⁶ GeV and the generated baryon-to-photon ratio η_B≲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 ≈ 0 (1-2 crossing) and d₁₂ ≈ 0 (2-3 crossing), where m_ee and d₁₂ 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 M₁ ≈ M₂ ≈ 10⁸ GeV,M₃ ≈ 10¹⁴ GeV and (M₂−M₁)/M₂≲10⁻⁵.