  In the framework of the baryogenesis via leptogenesis mechanism we study the
link between the amount of baryon asymmetry and neutrino mass matrices. In
particular, neglecting phases, we find that if the Dirac neutrino mass matrix
is related to the up quark mass matrix, the baryon asymmetry is about three
orders smaller than the required value. If the Dirac neutrino mass matrix is
related to the down quark or the charged lepton mass matrix, the baryon
asymmetry is about two orders smaller than the required value. In order to get
a sufficient amount of baryon asymmetry we need a more moderate hierarchy in
the Dirac neutrino mass matrix.
