  We study the impact of effective thermal masses and widths on resonant
leptogenesis. We identify two distinct possibilities which we refer to as
crossing and runaway regimes. In the runaway regime the mass difference grows
monotonously with temperature, whereas it initially decreases in the crossing
regime, such that the effective masses become equal at some temperature.
Following the conventional logic the source of the asymmetry would vanish in
the latter case. Using non-equilibrium quantum field theory, we analytically
demonstrate that the vanishing of the difference of the effective masses does
however neither imply a suppression nor a strong enhancement of the source for
the lepton asymmetry. In the vicinity of the crossing point the asymmetry
calculated in an (improved) Boltzmann limit develops a spurious peak, which
signals the breakdown of the quasiparticle approximation. In the exact result
this spurious enhancement is compensated by coherent transitions between the
two mass shells. Despite the breakdown of the quasiparticle approximation
off-shell contributions remain negligibly small even at the crossing point.
