Possible Alternatives to Tri-bimaximal Mixing (1004.2798v1)

Abstract: Possible alternatives to tri-bimaximal mixing are presented based on other symmetry principles, and their predictions for |U_{e3}|, sin^2 theta_{12} and sin^2 theta_{23} are compared to the present neutrino mixing data. In some cases perturbations are required to give better agreement with the data, and the use of a minimal approach is illustrated. Precise experimental determinations of the mixing parameters will be required to decipher the correct mixing pattern and to pin down the appropriate flavor symmetry.

• The paper challenges the dominant tri-bimaximal mixing paradigm by investigating models that incorporate perturbative corrections and alternative symmetry principles.
• Researchers compare diverse frameworks such as trimaximal, symmetric, and geometrically motivated schemes to better align theoretical predictions with experimental neutrino data.
• The study highlights that precise measurements of key parameters like |Uₑ3| and sin²θ₁₂ are crucial in validating these alternatives and guiding future neutrino physics models.

Possible Alternatives to Tri-bimaximal Mixing

The paper "Possible Alternatives to Tri-bimaximal Mixing" explores various frameworks for neutrino mixing, challenging the dominant paradigm of tri-bimaximal mixing (TBM) by considering alternative mixing schemes based on different symmetry principles. This investigation is of particular relevance given the experimental advancements that necessitate closer examination and increased precision in determining mixing parameters, notably $|U_{e3}|$, $\sin^2 \theta_{12}$, and $\sin^2 \theta_{23}$.

Initially, it contextualizes the emergence of TBM as an attractive and simple formulation that aligns adequately with experimental data. TBM results from the assumption of maximal atmospheric neutrino mixing ($\theta_{23} = 45^\circ$), zero reactor angle ($\theta_{13} = 0$), and solar neutrino mixing angle of approximately $35.3^\circ$. It draws considerable support from models grounded on discrete symmetry groups like $A_4$, $S_4$, and similar structures.

Despite TBM's prominence, discrepancies between its predictions and best-fit experimental values highlight the necessity for perturbations and alternative approaches. The paper scrutinizes a variety of possible mixing scenarios, each with its theoretical motivations and implications for the neutrino mixing matrix:

1. Trimaximal Mixing and its Variants (TM$_i$, TM$^i$): This category maintains one row or column of the TBM matrix, introducing deviations in other parts. These variants allow flexible configurations that could align closer with empirical data under specific assumptions about perturbative corrections and phases.
2. Symmetric Mixing Matrices: Such matrices propose a symmetric form of the PMNS matrix. This symmetry can emerge from a unified description of quark and lepton sectors, rooted in so-called Quark-Lepton Universality models.
3. Geometrically-Motivated Angles: Including concepts like hexagonal and golden ratio mixing angles, this class seeks alignments with geometric symmetries or elegant mathematical alignments, although they may demand adjustments from an exact theoretical proposition to fit observations.
4. Bimaximal Mixing (BM): Bimaximal mixing suggests maximal solar and atmospheric angles while assuming a vanishing reactor angle. Although largely discrepant from current data, it frames an excellent starting point for certain classes of correction schemes, such as quark-lepton complementarity.
5. Triminimal Perturbations: A generalized strategy to perturb initial mixing schemes (including hexagonal and bimaximal schemes) to adjust for experimental constraints by introducing small deviations systematically from a starting configuration.

The discussion raises crucial theoretical inquiries, questioning if specific symmetries dictate the observed neutrino mass and mixing patterns or if the alignment seen is a product of other underlying physics yet to be fully elucidated. The consideration goes beyond TBM's nearly ubiquitous presence in model-building, underscoring speculative yet scientifically grounded examinations into various alternatives, some enabled by symmetry violations or the presence of unseen symmetries.

The paper implies profound implications for future theoretical and experimental developments in neutrino physics. Identifying the correct or most viable mixing pattern necessitates refined experimental determinations with greater precision. The accuracy in measurements for parameters like $|U_{e3}|$ could dramatically influence model selections and the perceived viability of alternate symmetries.

In conclusion, "Possible Alternatives to Tri-bimaximal Mixing" presents a detailed analysis of alternatives to TBM, emphasizing that focusing narrowly on TBM may obscure other viable models. The exploration underlines the intricacies and interrelations between experimental data, theoretical structures, and potential symmetry principles, requiring continued examination and model validation to better grasp neutrino mixing's underlying physics.