[Paper Review] Neutrino Mass Models: Impact of non-zero reactor angle

Stephen F. King|arXiv (Cornell University)|Jun 21, 2011

Neutrino Physics Research32 references3 citations

TL;DR

This paper reviews neutrino mass models, focusing on the implications of a non-zero reactor angle θ₁₃, which deviates from the tri-bimaximal mixing (TBM) pattern. It proposes benchmark models—TBM⊗GUT, TBR, QLC, and Abelian symmetry models—where high-precision neutrino oscillation experiments are required to distinguish them, with key predictions for θ₁₃, θ₂₃, θ₁₂, and the Dirac phase δ, especially in light of T2K's evidence for a large θ₁₃.

ABSTRACT

In this talk neutrino mass models are reviewed and the impact of a non-zero reactor angle and other deviations from tri-bimaximal mixing are discussed. We propose some benchmark models, where the only way to discriminate between them is by high precision neutrino oscillation experiments.

Motivation & Objective

• To analyze the impact of a non-zero reactor angle θ₁₃ on neutrino mass models beyond the Standard Model.
• To identify and classify benchmark models that predict deviations from tri-bimaximal mixing (TBM), including TBM⊗GUT, TBR, QLC, and Abelian symmetry models.
• To determine the conditions under which high-precision neutrino oscillation experiments can discriminate between these models.
• To assess the implications of T2K's evidence for a large θ₁₃ on existing theoretical frameworks.
• To clarify the role of flavor symmetries (e.g., A₄, S₄, U(1)) in generating realistic mixing patterns and mass hierarchies.

Proposed method

• Uses the tri-bimaximal mixing matrix U_TB as a reference point, parameterizing deviations via three parameters r, s, a for θ₁₃, θ₁₂, and θ₂₃.
• Applies family symmetry groups (A₄, S₄, U(1)) to construct neutrino mass matrices invariant under specific transformations, leading to predictive mixing patterns.
• Employs sequential dominance and partially constrained sequential dominance (PCSD) to generate hierarchical mass spectra and small θ₁₃.
• Introduces the TBR (tri-bimaximal-reactor) mixing pattern via a complex phase δ and small parameter r, linking it to vacuum alignment in flavor models.
• Considers quark-lepton complementarity (QLC) as a sum rule: θ₁₂ + θ_C ≈ 45°, with θ_C ≈ 13°, under δ ≈ 180°, to explain large deviations from TBM.
• Compares theoretical predictions of sin²2θ₁₃ against future experimental sensitivities, particularly in Abelian U(1) models with undetermined Yukawa ratios.

Experimental results

Research questions

• RQ1 How do non-zero reactor angle measurements affect the viability of tri-bimaximal mixing models?
• RQ2 What are the distinguishing predictions of benchmark models (TBM⊗GUT, TBR, QLC, Abelian) for θ₁₃, θ₂₃, θ₁₂, and the Dirac phase δ?
• RQ3 Can quark-lepton complementarity (QLC) be realized in a GUT-compatible framework with large θ₁₃ and δ ≈ 180°?
• RQ4 What role do non-Abelian (A₄, S₄) and Abelian U(1) family symmetries play in generating the observed mixing pattern and small θ₁₃?
• RQ5 What experimental precision is required to distinguish between competing neutrino mass models, especially in light of T2K's evidence for a large θ₁₃?

Key findings

• The reactor angle θ₁₃ is predicted to be small in TBM and TBR models, with sinθ₁₃ ≈ r/√2, and r ∈ (0.07, 0.21) at 1σ, consistent with current constraints.
• TBM⊗GUT models predict θ₁₃ ≈ 3°, with |θ₂₃ − 45°| ≤ 1° and |θ₁₂ − 35°| ≤ 1°, and δ = 90° or 270°, making them distinguishable via precision measurements.
• TBR models allow any θ₁₃ but maintain small deviations from TBM in θ₂₃ and θ₁₂, with δ unconstrained, making them testable through phase measurements.
• QLC models predict θ₁₃ ≈ 13° (θ_C), θ₁₂ ≈ 32°, and δ ≈ 180°, with a sum rule θ₁₂ + θ_C ≈ 45°, requiring large deviations from TBM.
• Abelian U(1) models predict θ₁₃ ∼ O(m₂/m₃), but the exact value depends on an undetermined Yukawa ratio r, making predictions sensitive to model details.
• T2K's evidence for a large non-zero θ₁₃ (≈ 13°) strongly disfavors small-θ₁₃ models like TBM and TBR, favoring QLC or large-deviation models, and necessitates high-precision experiments to resolve model differences.