Leptogenesis with heavy neutrino flavours is discussed within a density matrix formalism. We write the density matrix equation, describing the generation of the matter-antimatter asymmetry, for an arbitrary choice of the right-handed (RH) neutrino masses. For hierarchical RH neutrino masses lying in the fully flavoured regimes, this reduces to multiple-stage Boltzmann equations. In this case we recover and extend results previously derived within a quantum state collapse description. We confirm the generic existence of phantom terms. However, taking into account the effect of gauge interactions, we show that they are washed out at the production with a wash-out rate that is halved compared to that one acting on the total asymmetry. In the N 1 -dominated scenario they cancel without contributing to the final baryon asymmetry. In other scenarios they do not in general and they have to be taken into account. We also confirm that there is a (orthogonal) component in the asymmetry produced by the heavier RH neutrinos which completely escapes the washout from the lighter RH neutrinos and show that phantom terms additionally contribute to it. The other (parallel) component is washed out with the usual exponential factor, even for weak washout. Finally, as an illustration, we study the two RH neutrino model in the light of the above findings, showing that phantom terms can contribute to the final asymmetry also in this case.

We revisit leptogenesis in the minimal non-supersymmetric type I see-saw mechanism with two right-handed (RH) neutrinos, including flavour effects and allowing both RH neutrinos N 1 and N 2 to contribute, rather than just the lightest RH neutrino N 1 that has hitherto been considered. By performing scans over parameter space in terms of the single complex angle z of the orthogonal matrix R, for a range of PMNS parameters, we find that in regions around z ∼ ±π/2, for the case of a normal mass hierarchy, the N 2 contribution can dominate the contribution to leptogenesis, allowing the lightest RH neutrino mass to be decreased by about an order of magnitude in these regions, down to M 1 ∼ 1.3 × 10 11 GeV for vanishing initial N 2 -abundance, with the numerical results supported by analytic estimates. We show that the regions around z ∼ ±π/2 correspond to light sequential dominance, so the new results in this paper may be relevant to unified model building.

We discuss N 2 -dominated leptogenesis in the presence of flavour dependent effects that have hitherto been neglected, in particular the off-diagonal entries of the flavour coupling matrix that connects the total flavour asymmetries, distributed in different particle species, to the lepton and Higgs doublet asymmetries. We derive analytical formulae for the final asymmetry including the flavour coupling at the N 2 -decay stage as well as at the stage of washout by the lightest right-handed neutrino N 1 . Moreover, we point out that in general part of the electron and muon asymmetries (phantom terms), can completely escape the wash-out at the production and a total B − L asymmetry can be generated by the lightest RH neutrino wash-out yielding so called phantom leptogenesis. However, the phantom terms are proportional to the initial N 2 abundance and in particular they vanish for initial zero N 2 -abundance. Taking any of these new effects into account can significantly modify the final asymmetry produced by the decays of the next-to-lightest RH neutrinos, opening up new interesting possibilities for N 2 -dominated thermal leptogenesis.