Importance of the Heavier Singlet Neutrinos in Leptogenesis

We argue that fast interactions of the lightest singlet neutrino $N_1$ would project part of a preexisting lepton asymmetry $L_p$ onto a direction that is protected from $N_1$ washout effects, thus preventing it from being erased. In particular, we consider an asymmetry generated in $N_2$ decays, assuming that $N_1$ interactions are fast enough to bring $N_1$ into full thermal equilibrium. If $N_1$ decays occur at $T\gtrsim {10}^9\mathrm{GeV}$, that is, before the muon Yukawa interactions enter into thermal equilibrium, then generically part of $L_p$ survives. In this case some of the constraints implied by the standard $N_1$ leptogenesis scenario hold only if $L_p\approx 0$. For $T\lesssim {10}^9\mathrm{GeV}$, $L_p$ is generally erased, unless special alignment or orthogonality conditions in flavor space are realized.