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

Abstract

Leptogenesis with heavy neutrino flavours is discussed within a density matrixformalism. We write the density matrix equation, describing the generation ofthe 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 casewe recover and extend results previously derived within a quantum state collapse description.We confirm the generic existence of phantom terms. However, taking into account theeffect of gauge interactions, we show that they arewashed out at the production with a wash-out rate that is halved compared to that one actingon the total asymmetry. In the N1-dominated scenario they cancel withoutcontributing to the final baryon asymmetry. In other scenarios they do not in generaland they have to be taken into account.We also confirm that there is a (orthogonal) component in the asymmetry produced bythe heavier RH neutrinos which completely escapes the washout from the lighter RH neutrinos and showthat phantom terms additionally contribute to it. The other (parallel) component is washedout with the usual exponential factor, even for weak washout.Finally, as an illustration, we study the two RH neutrino model in the light ofthe above findings, showing that phantom terms can contributeto the final asymmetry also in this case.