Unified models of neutrinos, flavour and CP Violation

Recent data from neutrino experiments gives intriguing hints about the mass ordering, the CP violating phase and non-maximal atmospheric mixing. There seems to be a (one sigma) preference for a normal ordered (NO) neutrino mass pattern, with a CP phase δ=−100°±50°, and (more significantly) non-maximal atmospheric mixing. Global fits for the NO case yield lepton mixing angle one sigma ranges: θ23≈41.4°±1.6°, θ12≈33.2°±1.2°, θ13≈8.45°±0.15°. Cosmology gives a limit on the total of the three masses to be below about 0.23 eV, favouring hierarchical neutrino masses over quasi-degenerate masses. Given such experimental advances, it seems an opportune moment to review the theoretical status of attempts to explain such a pattern of neutrino masses and lepton mixing, focusing on approaches based on the four pillars of: predictivity, minimality, robustness and unification. Predictivity can result from various mixing sum rules whose status is reviewed. Minimality can follow from the type I seesaw mechanism, including constrained sequential dominance of right-handed (RH) neutrinos, and the littlest seesaw model. Robustness requires enforcing a discrete CP and non-Abelian family symmetry, spontaneously broken by flavons with the symmetry preserved in a semi-direct way. Unification can account for all lepton and quark masses, mixing angles and CP phases, as in Supersymmetric Grand Unified Theories of Flavour, with possible string theory origin.