Neutrino Mass and Mixing with Discrete Symmetry (1301.1340v3)

Abstract: This is a review article about neutrino mass and mixing and flavour model building strategies based on discrete family symmetry. After a pedagogical introduction and overview of the whole of neutrino physics, we focus on the PMNS mixing matrix and the latest global fits following the Daya Bay and RENO experiments which measure the reactor angle. We then describe the simple bimaximal, tri-bimaximal and golden ratio patterns of lepton mixing and the deviations required for a non-zero reactor angle, with solar or atmospheric mixing sum rules resulting from charged lepton corrections or residual trimaximal mixing. The different types of see-saw mechanism are then reviewed as well as the sequential dominance mechanism. We then give a mini-review of finite group theory, which may be used as a discrete family symmetry broken by flavons either completely, or with different subgroups preserved in the neutrino and charged lepton sectors. These two approaches are then reviewed in detail in separate chapters including mechanisms for flavon vacuum alignment and different model building strategies that have been proposed to generate the reactor angle. We then briefly review grand unified theories (GUTs) and how they may be combined with discrete family symmetry to describe all quark and lepton masses and mixing. Finally we discuss three model examples which combine an SU(5) GUT with the discrete family symmetries A4, S4 and Delta(96).

• The paper presents a novel framework integrating discrete symmetries with neutrino oscillation data to refine mass and mixing models.
• It details modifications to the PMNS matrix, highlighting key deviations such as the non-zero reactor angle from tri-bimaximal predictions.
• The review emphasizes the role of family symmetries like A4 and S4 in developing viable theoretical models and guiding future neutrino research.

An Overview of "Neutrino Mass and Mixing with Discrete Symmetry"

The paper presented, authored by Stephen F. King and Christoph Luhn, provides an in-depth review of the interplay between neutrino masses, mixing, and discrete symmetry in particle physics. The framework presented stands on the experimental foundations of neutrino mass and mixing phenomena, particularly focusing on results from oscillation experiments like Daya Bay and RENO. The paper does not merely report on these results; it seeks to integrate them with advanced model-building theories that employ discrete symmetries to account for observed data.

A primary focus of the paper is the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix, which is pivotal to understanding neutrino oscillations. The latest experimental data necessitate revisions and enhancements in theoretical models. Here, discrete symmetries, such as those from groups like $A_4$, $S_4$, and $\Delta(96)$, are shown to play a significant role. These symmetries provide a structural basis for flavor mixing patterns, such as tri-bimaximal and bi-trimaximal mixing, which align closely with experimental observations.

Key Components and Theoretical Implications

1. Experimental Basis:

The paper emphasizes the compelling evidence for neutrino oscillations obtained from experiments like KamLAND, SNO, and Super-Kamiokande, which suggest non-zero neutrino masses. These results pose questions that challenge the Standard Model, which did not predict neutrino masses originally.

2. The PMNS Matrix and Mixing Angles:

King and Luhn delve into the specific mixing patterns and angles described by the PMNS matrix, elucidating how deviations from tri-bimaximal mixing are necessary due to the recently observed non-zero reactor angle $\theta_{13}$. The paper explores how various discrete symmetry models attempt to reconcile these deviations with theoretical predictions.

3. Discrete Family Symmetries:

The discussion on discrete family symmetries, such as $A_4$ and $S_4$, forms the theoretical foundation of the paper. These symmetries provide a convenient mechanism for explaining the hierarchical nature of neutrino masses and large mixing angles. This theoretical framework encourages models like the SU(5) grand unified theory (GUT) to incorporate family symmetries, further enhancing their explanatory power.

4. Theoretical Models and Mechanisms:

Several models and mechanisms are reviewed, including the see-saw mechanism in its various forms, and the role of sequential dominance. These mechanisms offer insight into how small neutrino masses might stem from interactions at very high energy scales, integrating them into the broader context of GUTs.

5. Flavon Alignment and Model Predictions:

One highlight is the detailed discussion on the vacuum alignment of flavons and how this affects neutrino mass terms. The paper outlines methods of achieving desired alignments, crucial for realizing specific mixing patterns. This theoretical elaboration is directly tied to predicting and understanding experimental outcomes for neutrino masses and mixing.

Practical and Theoretical Implications

Practically, this review provides essential insights for constructing viable theoretical models that could offer predictions for future experimental tests. The discrete symmetry approach holds promise for making predictions regarding unresolved aspects such as CP violation in the lepton sector, the mass hierarchy, and the absolute neutrino mass scale.

Theoretically, the integration of discrete symmetries within the framework of GUTs signifies a mature and comprehensive approach to addressing the flavor problem in particle physics. The confluence of GUT ideas and neutrino physics bridges gaps in our understanding of fundamental particles, potentially offering paths toward new physics beyond the Standard Model.

Future Prospects

The exploration of discrete symmetries in particle physics, particularly in the context of neutrino mass and mixing, is an ongoing endeavor in the theoretical community. Continued advancements in experimental precision will further challenge and refine these models, facilitating a deeper understanding of the neutrino sector and possibly leading to breakthroughs in particle physics.

As future experimental advancements refine measurements of parameters like $\theta_{23}$ and $\delta_{CP}$, the theorized patterns and symmetries will either be validated or necessitate further refinement. The marriage of discrete symmetry and neutrino physics forms a dynamic and promising frontier in high-energy physics, as articulated meticulously in this review.