Unified Models of Neutrinos, Flavour and CP Violation (1701.04413v1)

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.

• The paper presents a unified framework combining experimental data with theoretical models of neutrino mass, lepton flavor, and CP violation.
• It rigorously evaluates seesaw mechanisms and discrete non-Abelian symmetries to explain neutrino mass hierarchies and mixing patterns.
• The study integrates grand unified theories with string theory prospects, outlining a roadmap toward a comprehensive theory of flavor.

Unified Models of Neutrinos, Flavour, and CP Violation

The paper under consideration offers a comprehensive review of the theoretical frameworks addressing neutrino masses and mixing, flavored by the discussion on potential flavor models, symmetry principles, and the unification of these into a grand unified theory of flavor. This paper, authored by S. F. King, aims to synthesize the developments in neutrino physics and chart a course through the multi-faceted terrain of lepton flavor and CP violation, presenting a structured approach based on four pillars: predictivity, minimality, robustness, and unification.

Neutrino Mass and Mixing: Empirical and Theoretical Inputs

The empirical landscape detailed is rooted in the advancing precision of neutrino oscillation experiments which, as recent data hint, reveal preferences for a normal mass ordering and non-maximal atmospheric mixing. The paper consolidates the latest fits, indicating lepton mixing angles in a one-sigma range. Cosmology provides an upper limit on the sum of neutrino masses, predicating a preference for hierarchical rather than quasi-degenerate mass states.

The paper critiques and reviews the status of neutrino parameters, employing the convention of the PMNS mixing matrix to bridge neutrino flavor and mass states. Comparisons with the CKM matrix elucidate the differences and analogies in quark and lepton sector mixings, bringing attention to significant disparities in optical mechanisms such as CP phases.

Theoretical Framework: Seesaw Mechanism and Flavor Models

The paper establishes the theoretical underpinnings by centering on the type I seesaw mechanism, analyzing configurations ranging from one to three right-handed neutrinos (RHNs). Particularly, the Minimal Type I seesaw with two RHNs is reviewed, leading to predictions such as a zero lightest neutrino mass and the hierarchy integral to the sequential dominance conditions.

These skeletal models are scaffolded within a framework of discrete non-Abelian family symmetries, like $S_4$ and $A_4$, which embody the so-called "direct" and "semi-direct" model approaches. The formalism discussed explores how lepton mixing patterns, such as tri-bimaximal or trimaximal mixing, and their deviations yield empirical predictions aligning more closely with recent data.

The robust base in this discourse involves discrete symmetry preservation in mass matrices—considering constraints like the Klein symmetry related to the Majorana nature of neutrinos. These symmetries form a foundation upon which precise mixing angles and potential sum rules suggest pathways for empirical engagement.

Unification and Beyond: GUTs and String Theoretic Prospects

A key aspect of the paper is its exploration of embedding neutrino mass models within grand unified theories (GUTs), particularly SU(5), Pati-Salam SU(4) × SU(2) × SU(2), and SO(10). These constructions not only pitch an interconnected paradigm linking all lepton and quark sectors but also demand the incorporation of high-energy scales and additional dimensions typical in gauge unification scenarios.

Furthermore, the prospect of integrating these GUT models with family symmetries to formulate "Flavored GUTs" is emphasized as a unifying avenue—allowing for a cohesive understanding of fermion mass hierarchies and mixing patterns in a stringent theoretical construct.

The speculative extension into string theory, including avenues like F-theory and M-theory, serves to couch the discussion within the most fundamental theoretical foundations. Conceptual structures like orbifold compactifications hint at a reconciliation of gravity with flavor symmetries, offering a profound incentive to examine higher-dimensional approaches to neutrinoless physics.

Conclusion and Speculation on the Future

S. F. King presents a meticulous critique of the current state of neutrino model building, emphasizing the necessity for stringent, easily falsifiable models grounded in strong theoretical principles. By advocating for a cross-disciplinary pedagogy involving predictivity, simplicity, theoretical robustness, and potential unification, the paper envisions a structured advancement in particle physics' understanding of the flavor puzzle.

In conclusion, this paper situates itself as a reference for those aiming to integrate experimental data with theoretical advancements, encouraging a future where neutrino physics provides the inroads into unraveling the intricate tapestry of particle physics and potentially realizing a comprehensive theory of flavor. The Littlest Seesaw model stands as a prototype embodying the paper's proposed alignment with these foundational pillars, serving as an interlocutor amidst ongoing experimental and theoretical endeavors.