Leptogenesis with heavy neutrino flavours: from density matrix to Boltzmann equations

Leptogenesis with heavy neutrino flavours is discussed within a density matrix formalism. We write the density matrix equation that describes 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, the density matrix equation reduces to multiple-stage Boltzmann equa-tions. In this case we recover and extend results previously derived within a quan-tum state collapse description. We confirm the generic existence of phantom terms, which are not washed out at production and contribute to the flavoured asymmetries proportionally to the initial RH neutrino abundances. Even in the N1-dominated scenario they can give rise to lepton flavour asymmetries much larger than the baryon asymmetry with potential applications. 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 a 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 in this case as well. ar