Models of neutrino mass, mixing and CP violation

Abstract

motivates extending the Standard Model (SM) to include a non-Abelian discrete flavour symmetry in order to accurately predict the large leptonic mixing angles and CP violation. We begin with an overview of the SM puzzles, followed by a description of some classic lepton mixing patterns. Lepton mixing may be regarded as a deviation from tri-bimaximal mixing, with charged lepton corrections leading to solar mixing sum rules, or tri-maximal lepton mixing leading to atmospheric mixing rules. We survey neutrino mass models, using a roadmap based on the open questions in neutrino physics. We then focus on the seesaw mechanism with right-handed neutrinos, where sequential dominance (SD) can account for large lepton mixing angles and CP violation, with precise predictions emerging from constrained SD (CSD). We define the flavour problem and discuss progress towards a theory of favour using GUTs and discrete family symmetry. We classify models as direct, semidirect or indirect, according to the relation between the Klein symmetry of the mass matrices and the discrete family symmetry, in all cases focussing on spontaneous CP violation. Finally we give two examples of realistic and highly predictive indirect models with CSD, namely an A to Z of flavour with PatiSalam and a fairly complete A4 × SU(5) SUSY GUT of flavour, where both models have interesting implications for leptogenesis.