On different approaches to freeze-in and freeze-out leptogenesis with quasi-degenerate neutrinos

TL;DR

This paper compares two theoretical approaches for leptogenesis involving quasi-degenerate neutrinos, demonstrating their near equivalence except at large mass splittings, thus clarifying their applicability in neutrino oscillation models.

Contribution

It provides a detailed comparison between the density matrix formalism and a propagator-based approach for leptogenesis, highlighting their similarities and differences.

Findings

The two approaches are nearly equivalent for small mass splittings.

They diverge significantly in the limit of very large mass splittings.

The comparison clarifies issues discussed in the neutrino oscillation literature.

Abstract

We compare two approaches for determining the generation of lepton asymmetry during production and decay of quasi-degenerate neutrinos, namely the density matrix formalism and a recent proposal which does not involve any counting of neutrino number densities and is based on plugging the resummed propagator in a quantum field theory model for neutrino oscillations. We show numerically and analytically that they are almost equivalent except in the limit of very large mass splittings. The comparison, performed in a simple scalar toy model, helps to understand several issues that have been discussed in the literature.