Invariant see-saw models and sequential dominance

We propose an invariant see-saw (ISS) approach to model building, based on the observation that see-saw models of neutrino mass and mixing fall into basis invariant classes labelled by the Casas-Ibarra R-matrix, which we prove to be invariant not only under basis transformations but also non-unitary right-handed neutrino transformations S. According to the ISS approach, given any see-saw model in some particular basis one may determine the invariant R-matrix and hence the invariant class to which that model belongs. The formulation of see-saw models in terms of invariant classes puts them on a firmer theoretical footing, and allows different see-saw models in the same class to be related more easily, while their relation to the R-matrix makes them more easily identifiable in phenomenological studies. To illustrate the ISS approach we show that sequential dominance (SD) models form basis invariant classes in which the R-matrix is approximately related to a permutation of the unit matrix, and quite accurately so in the case of constrained sequential dominance (CSD) and tri-bimaximal mixing. Using the ISS approach we discuss examples of models in which the mixing naturally arises (at least in part) from the charged lepton or right-handed neutrino sectors and show that they are in the same invariant class as SD models. We also discuss the application of our results to flavour-dependent leptogenesis where we show that the case of a real R-matrix is approximately realized in SD, and accurately realized in CSD.