On the Vanishing of the CP Asymmetry in Leptogenesis due to Form Dominance

We emphasize that the vanishing of the CP asymmetry in leptogenesis, previously observed for models with tri-bimaximal mixing and family symmetry, may be traced to a property of the type I see-saw mechanism satisfied by such models known as Form Dominance, corresponding to the case of a diagonal Casas-Ibarra R-matrix. Form Dominance leads to vanishing flavour-dependent CP asymmetries irrespective of whether one has tri-bimaximal mixing or a family symmetry. Successful leptogenesis requires violation of Form Dominance, but not necessarily violation of tri bimaximal mixing. This may be achieved in models where the family symmetry responsible for tri-bimaximal mixing is implemented indirectly and a strong neutrino mass hierarchy is present with the Form Dominance broken only softly by the right-handed neutrino responsible for the lightest neutrino mass, as in constrained sequential dominance.