Kadanoff-Baym Approach to Flavour Mixing and Oscillations in Resonant Leptogenesis

TL;DR

This paper develops a loopwise perturbative scheme within the Kadanoff-Baym formalism to accurately describe flavour mixing and oscillations in resonant leptogenesis, highlighting the limitations of common approximations.

Contribution

It introduces a new truncation scheme that avoids quasi-particle ansaetze and distinguishes between flavour mixing and oscillations in heavy-neutrino propagators.

Findings

Identifies two key flavour effects: mixing and oscillations.

Shows that common approximations only capture oscillations, not mixing.

Provides a more accurate framework for quantum transport in leptogenesis.

Abstract

We describe a loopwise perturbative truncation scheme for quantum transport equations in the Kadanoff-Baym formalism, which does not necessitate the use of the so-called Kadanoff-Baym or quasi-particle ansaetze for dressed propagators. This truncation scheme is used to study flavour effects in the context of Resonant Leptogenesis (RL), showing explicitly that, in the weakly-resonant regime, there exist two distinct and pertinent flavour effects in the heavy-neutrino sector: (i) the resonant mixing and (ii) the oscillations between different heavy-neutrino flavours. Moreover, we illustrate that Kadanoff-Baym and quasi-particle ansaetze, whilst appropriate for the flavour-singlet dressed charged-lepton and Higgs propagators of the RL scenario, should not be applied to the dressed heavy-neutrino propagators. The use of these approximations for the latter is shown to capture only flavour oscillations, whilst discarding the separate phenomenon of flavour mixing.