Probing the seesaw mechanism with neutrino data and leptogenesis

Abstract

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 $\hat{I}{\cdot }_B\lesssim 10^{-14}$ 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 $(M_2-M_1)/M_2\lesssim 10^{-5}$.

30 pages, 2 eps figures, JHEP3.cls, typos corrected, note (and references) added on non-thermal leptogenesis