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

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 for small mass splittings and also discuss the hierarchical limit. The comparison, performed in a simple scalar toy model, helps to understand several issues that have been discussed in the literature.