Models of Neutrino Mass, Mixing and CP Violation (1510.02091v2)

Abstract: In this topical review we argue that neutrino mass and mixing data motivates extending the Standard Model 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 Standard Model 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 flavour 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 Pati-Salam and a fairly complete $A_4\times SU(5)$ SUSY GUT of flavour, where both models have interesting implications for leptogenesis.

Models of Neutrino Mass, Mixing and CP Violation

The paper by Stephen F. King provides a comprehensive review of models explaining neutrino mass, mixing, and CP violation, underscoring the necessity to extend the Standard Model (SM) with a discrete non-Abelian flavor symmetry. This approach aims to predict large leptonic mixing angles and CP violation, which are inadequately accounted for by the SM.

Overview and Puzzles of the Standard Model

The paper begins with an exploration of longstanding puzzles presented by the SM, including the origin of mass, the quest for unification, and the problem of flavor. Despite its successes, the SM fails to address the intricate hierarchies and mixing patterns observed in quark and lepton masses. The discovery of neutrino oscillations, which imply non-zero neutrino masses, necessitates physics beyond the SM. This review focuses on developments following 2012, notably in the field of neutrino physics—the measurement of the neutrino reactor angle being a pivotal advancement.

Deviation from Mixing Patterns

King discusses several classic patterns of lepton mixing—Bimaximal, Tri-bimaximal, and Golden Ratio mixing—all predicting zero reactor angles, which have been refuted by recent experimental data. The paper explores deviations from Tri-bimaximal mixing, employing deviation parameters to adjust the lepton mixing angles, specifically leveraging solar and atmospheric sum rules.

Seesaw Mechanism and Sequential Dominance

The seesaw mechanism, particularly with two or three right-handed neutrinos, features prominently in King's survey. The mode of sequential dominance (SD) elucidates how these models can lead to large lepton mixing angles and CP violation. In these frameworks, the hierarchy of neutrino masses emerges naturally, with constrained sequential dominance (CSD) offering predictions consistent with observed phenomena, such as the reactor angle and the normal ordering of neutrino mass hierarchies.

Symmetry-Based Approaches

The paper advocates that the adoption of discrete family symmetries like $A_4$, combined with Grand Unified Theories (GUTs), provides an elegant pathway to resolving the flavor problem. King proposes models incorporating direct and semi-direct approaches to family symmetry, highlighting the significance of spontaneous CP violation, which is essential in understanding discrepancies between theoretical models and empirical observations.

Indirect Models and Realistic Speculations

Moving from a theoretical framework to practical models, King presents the indirect approach, where the family symmetry is completely disconnected after flavor symmetry is applied. He outlines notable indirect models, such as the $A_4 \times SU(5)$ SUSY GUT, and the "A to Z" flavor model with Pati-Salam gauge group. Furthermore, King speculates on the origin of these models from F-theory, suggesting that non-Abelian discrete symmetries can evolve from high-dimensional string-theoretic contexts.

Implications and Future Prospects

The paper elucidates the implications of these models on key questions in neutrino physics, such as the nature of CP violation and the prospects for leptogenesis—a mechanism potentially underpinning the observed matter-antimatter asymmetry in the universe. This work paves the way for profound investigations into discrete family symmetries and their realization in unified frameworks, inviting speculation on future developments in artificial intelligence for model optimization and analysis.

In summary, King's review bridges gaps between theoretical predictions and experimental data, encouraging future research to explore discrete symmetries in the broader context of unified theories and contribute to advancing our understanding of fundamental particle interactions.