  We compute in the density-matrix formalism the baryon asymmetry generated by
the decay of the Higgs doublet into a right-handed (RH) neutrino and a Standard
Model lepton. The emphasis is put on the baryon asymmetry produced by the total
lepton-number violating decay. From the derivation of the corresponding
evolution equations, and from their integration, we find that this contribution
is fully relevant for large parts of the parameter space. This confirms the
results found recently in the CP-violating decay formalism with thermal
corrections and shows in particular that the lepton-number violating processes
are important not only for high-scale leptogenesis but also when the
RH-neutrino masses are in the GeV range. For large values of the Yukawa
couplings, we also find that the strong washout is generically much milder for
this total lepton-number violating part than for the usual RH-neutrino
oscillation flavour part.
