| Summary: | The discovery of neutrino masses and large lepton mixing may be an indication for an underlying non-Abelian family symmetry in nature, although the measurement of a relatively large reactor angle effectively ruled out the simplest models of flavour, such as those predicting tri-bimaximal mixing. However, more sophisticated realisations are still viable, such as those based on constrained sequential dominance (CSD) with a type-I seesaw mechanism. We study the CSD(n) class of models, showing how special vacuum alignments of Standard Model singlet flavons may give rise to highly constrained lepton mass matrices. A dedicated numerical t based on X2 minimisation gives predictions for lepton mixing parameters, and excellent agreement with experimental data is found for n = 3. The CSD(3) alignments are implemented in several supersymmetric grand unied theories (GUTs) of flavour with discrete family symmetries. We propose fairly complete models based on A4 SU(5), (27) SO(10), and S4 SO(10), which are spontaneouslybroken to the minimal supersymmetric Standard Model. Each model leads to predictive mass matrix structures for both quarks and leptons; in particular, those based on SO(10) lead naturally to near-universal matrices as sums over low-rank matrices, so calleduniversal sequential dominance, giving a natural explanation for fermion mass hierarchies. Theoretical predictions are underpinned by dedicated X2 ts, and in the S4 SO(10) model, estimates of the errors using Monte Carlo methods. We show that thermal leptogenesis from decays of the lightest right-handed neutrino can produce the observed baryon asymmetry of the Universe in CSD(n), and in the A4 SU(5) and (27) SO(10) models. GUT breaking, proton decay, doublet-triplet splitting and the problem are also addressed.
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