Constructing the large mixing angle MNS matrix in see-saw models with right-handed neutrino dominance

Recent SNO results strongly favour the large mixing angle (LMA) MSW solar solution. We argue that there are only two technically natural low energy neutrino mass matrix structures consistent with the LMA MSW solution, corresponding to either a hierarchy or an inverted hierarchy with pseudo-Dirac neutrinos. We first present a model-independent analysis in which we diagonalise each of these two mass matrix structures to leading order in $\theta_{13}$ and extract the neutrino masses, mixing angles and phases. In this analysis we express the MNS matrix to leading order in the small angle $\theta_{13}$ including the neutrino {\em and} charged lepton mixing angles and phases, the latter playing a crucial r\^{o}le for allowing the inverted hierarchy case to be consistent with the LMA MSW solution. We then consider the see-saw mechanism with right-handed neutrino dominance and show how the successful neutrino mass matrix structures may be constructed with no tuning and with small radiative corrections, leading to a full, partial or inverted neutrino mass hierarchy. In each case we derive approximate analytic relations between the input see-saw parameters and the resulting neutrino masses, mixing angles and phases, which will provide a useful guide for unified model building. For the hierarchical cases the LMA MSW solution gives a soft lower bound $|U_{e3}|\simgt 0.1$, just below the current CHOOZ limit. Both hierarchical and inverted hierarchical cases predict small $\beta \beta_{0\nu}$ with $|m_{ee}|\sim 0.01$ eV within the sensitivity of future proposals such as GENIUS. Successful leptogenesis is possible if the dominant right-handed neutrino is the heaviest one, but the leptogenesis phase is unrelated to the MNS phases.