Leptogenesis within a generalized quark-lepton symmetry

We reexamine the question of baryogenesis via leptogenesis in schemes of the seesaw mechanism with quark-lepton symmetry. Within the phenomenological approach of textures, we propose to relax this strict symmetry and propose weaker conditions, namely, models of the neutrino Dirac mass matrix M{sub D} which have the same hierarchy as the matrix elements of M{sub u}. We call this guideline generalized hierarchical quark-lepton symmetry. We consider in detail particular cases in which the moduli of the matrix elements of M{sub D} are equal to those of M{sub u}. We try for the heavy Majorana mass matrix diagonal and off-diagonal forms. We find that an ansatz for M{sub D} preserving the hierarchy, together with an off-diagonal model for the heavy Majorana neutrino mass, is consistent with neutrino masses, neutrino mixing, and baryogenesis via leptogenesis for an intermediate mass scale m{sub R}{approx}10{sup 12} GeV. The preservation of the hierarchical structure could come from a possible symmetry scheme.