[Paper Review] Overview of Neutrino Mixing Models and Ways to Differentiate among Them

Carl H. Albright|ArXiv.org|May 1, 2009

Neutrino Physics Research3 references22 citations

TL;DR

This paper reviews neutrino mixing models, focusing on horizontal flavor and vertical family symmetries to classify models based on their predictions for mixing angles, mass hierarchy, and CP phases. It identifies that precise measurements of sin²θ₁₃, neutrinoless double beta decay, and charged lepton flavor violation can significantly reduce the viable model space, with upcoming reactor experiments expected to eliminate roughly two-thirds of models if sin²θ₁₃ ≲ 0.001 is confirmed.

ABSTRACT

An overview of neutrino-mixing models is presented with emphasis on the types of horizontal flavor and vertical family symmetries that have been invoked. Distributions for the mixing angles of many models are displayed. Ways to differentiate among the models and to narrow the list of viable models are discussed.

Motivation & Objective

• To survey and categorize neutrino mixing models based on horizontal flavor symmetries and vertical family symmetries.
• To identify how future experimental data can reduce the number of viable models by distinguishing predictions for mixing angles, mass hierarchy, and CP phases.
• To evaluate the role of neutrinoless double beta decay and charged lepton flavor violation in differentiating between models.
• To assess the impact of upcoming reactor experiments (Double CHOOZ, Daya Bay) in constraining the parameter space of neutrino mixing models.
• To determine whether tri-bimaximal mixing is an accidental or softly-broken symmetry by analyzing deviations in mixing angles.

Proposed method

• Classifies models based on their underlying horizontal flavor and vertical family symmetries, including GUT-based models with family symmetry.
• Applies the seesaw mechanism (type I and II) to derive the effective light neutrino mass matrix from Dirac and Majorana mass matrices.
• Uses the PMNS mixing matrix to relate charged lepton and neutrino mass matrices via bi-unitary transformations, incorporating Majorana phases.
• Performs perturbative analysis of tri-bimaximal mixing by rotating the charged lepton mass matrix from diagonal form to study deviations in sin²θ₁₃.
• Computes effective mass for neutrinoless double beta decay using the formula ⟨mββ⟩ = |∑mᵢU²ₑᵢΦ²ᵢᵢ|, with Majorana phases included.
• Evaluates constraints from charged lepton flavor violation, particularly μ→e+γ and μ-e conversion, using current and projected experimental limits.

Experimental results

Research questions

• RQ1 Which neutrino mixing models predict sin²θ₁₃ values within the range of 0.001–0.05, and how many remain viable after future reactor data?
• RQ2 How do perturbations to tri-bimaximal mixing affect predictions for sin²θ₁₃ and sin²θ₂₃, and what do they imply about the nature of flavor symmetry?
• RQ3 Can accurate measurements of neutrinoless double beta decay effective mass distinguish between normal and inverted neutrino mass hierarchies?
• RQ4 To what extent can charged lepton flavor violation processes like μ→e+γ help rule out specific neutrino mixing models?
• RQ5 What role do Majorana phases play in determining the effective mass in neutrinoless double beta decay, and how can they be probed experimentally?

Key findings

• Upcoming reactor experiments (Double CHOOZ, Daya Bay) are expected to eliminate approximately two-thirds of surveyed models if sin²θ₁₃ ≲ 0.001 is confirmed and no flux depletion is observed.
• Models with lepton flavor symmetries predict extremely small values of sin²θ₁₃ ≲ 10⁻⁴, while most other models prefer sin²θ₁₃ in the 0.001–0.05 range.
• Most models predict sin²θ₁₂ ≲ 0.31, slightly below the tri-bimaximal value of 1/3 ≈ 0.333, consistent with the current best-fit value of 0.312.
• A significant fraction of models predict sin²θ₂₃ ≥ 0.50, in contrast to the current best-fit value of 0.466, suggesting a potential tension with data.
• Effective mass plots for neutrinoless double beta decay show a clear separation between normal and inverted mass hierarchies when tri-bimaximal mixing is perturbed, indicating that future experiments could decisively distinguish the two.
• Accurate determination of all three mixing angles and the three CP-violating phases will be essential to identify the most viable models.