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

TL;DR

This paper develops a comprehensive density matrix formalism for leptogenesis with heavy neutrino flavours, extending previous models to include gauge interactions and phantom terms, and applies it to a two RH neutrino scenario.

Contribution

It introduces a generalized density matrix approach for leptogenesis, incorporating gauge interactions and phantom terms, and connects it to Boltzmann equations for hierarchical neutrino masses.

Findings

Phantom terms are confirmed to exist and can influence the asymmetry.

Gauge interactions wash out phantom terms at production, halving their effect.

In a two RH neutrino model, phantom terms can significantly contribute to the final asymmetry.

Abstract

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.