[Paper Review] Universal Quadratic Hierarchy Rule in Lepton Flavor Physics and Large Neutrino Mixing

É. M. Lipmanov|ArXiv.org|Jul 9, 2007

Particle physics theoretical and experimental studies2 references3 citations

TL;DR

This paper proposes a universal quadratic hierarchy rule that explains large neutrino mixing angles in lepton flavor physics by unifying the mass-ratio patterns of charged leptons and quasi-degenerate neutrinos. It demonstrates that three distinct deviation-from-extreme-hierarchy scenarios—charged leptons, quasi-degenerate neutrinos, and their interplay—arise from a single underlying quadratic mass-ratio relationship, providing a unified framework for large lepton mixing without fine-tuning.

ABSTRACT

Large mixing parameters of neutrino mass eigenstates in the neutrino flavor eigenstates are determined, and interpreted as closely related to the neutrino and charged lepton mass-ratio patterns. The three known seemingly different charged lepton and quasi-degenerate neutrino deviation-from-extreme hierarchies are shown to be three particular manifestations of one unifying quadratic hierarchy-rule in lepton flavor physics.

Motivation & Objective

• To identify a unifying principle underlying large neutrino mixing angles observed in neutrino oscillation experiments.
• To explain the seemingly disparate mass-ratio patterns in charged leptons and quasi-degenerate neutrinos as manifestations of a single universal rule.
• To derive a consistent mathematical framework that connects lepton flavor mixing with mass hierarchy patterns across the lepton sector.
• To show that large mixing angles are not accidental but systematically related to quadratic mass ratios in the charged lepton and neutrino sectors.
• To eliminate the need for fine-tuning in models of large lepton mixing by introducing a universal hierarchy rule.

Proposed method

• Derives a universal quadratic hierarchy rule based on the square of mass ratios in the charged lepton and neutrino sectors.
• Analyzes the three known cases of deviation from extreme mass hierarchies: charged lepton mass ratios, quasi-degenerate neutrino masses, and their interplay.
• Uses the quadratic relationship to relate neutrino mixing angles to the square of the charged lepton mass ratios.
• Demonstrates that the observed large mixing angles (e.g., θ₂₃ ≈ 45°) emerge naturally from this rule without arbitrary parameters.
• Applies the rule to unify three distinct phenomenological scenarios into a single theoretical framework.
• Validates the consistency of the rule across known neutrino oscillation data and charged lepton mass hierarchies.

Experimental results

Research questions

• RQ1 Can large neutrino mixing angles be explained by a single underlying mass hierarchy rule?
• RQ2 How are the mass-ratio patterns of charged leptons and quasi-degenerate neutrinos related to large lepton mixing?
• RQ3 Is there a universal mathematical structure that unifies different deviation-from-extreme-hierarchy scenarios in lepton flavor physics?
• RQ4 Does the quadratic hierarchy rule naturally reproduce observed large mixing angles without fine-tuning?
• RQ5 Can the observed neutrino mixing parameters be derived from a consistent relation between charged lepton and neutrino mass ratios?

Key findings

• The paper identifies a universal quadratic hierarchy rule that unifies three distinct deviation-from-extreme-hierarchy scenarios in lepton flavor physics.
• Large neutrino mixing angles are shown to be directly related to the square of charged lepton mass ratios, providing a systematic explanation.
• The rule explains the observed near-maximal mixing in the atmospheric neutrino sector (θ₂₃ ≈ 45°) as a consequence of the quadratic mass-ratio pattern.
• The framework unifies the mass patterns of charged leptons and quasi-degenerate neutrinos under a single mathematical structure, eliminating ad hoc assumptions.
• The model reproduces large mixing without requiring fine-tuning, offering a natural explanation for the observed lepton mixing parameters.
• The results suggest that large lepton mixing is not accidental but a consequence of a deeper, universal mass hierarchy rule.