Unified Models of Neutrinos, Flavour and CP Violation

Abstract

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 $\delta = -100^{\circ}\pm 50 ^\circ$, and (more significantly) non-maximal atmospheric mixing. Global fits for the NO case yield lepton mixing angle one sigma ranges: $\theta_{23}\approx 41.4^\circ \pm 1.6^\circ$, $\theta_{12}\approx 33.2^\circ \pm 1.2^\circ$, $\theta_{13}\approx 8.45^\circ \pm 0.15^\circ$. 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, focussing on approaches based on the four pillars of: {\em predictivity}, {\em minimality}, {\em robustness} and {\em unification}. {\em Predictivity} can result from various mixing sum rules whose status is reviewed. {\em Minimality} can follow from the type I seesaw mechanism, including constrained sequential dominance of right-handed (RH) neutrinos, and the littlest seesaw model. {\em Robustness} requires enforcing a discrete CP and non-Abelian family symmetry, spontaneously broken by flavons with the symmetry preserved in a semi-direct way. {\em 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.