[Paper Review] Some scales in neutrino physics

V. V. Khruschov|arXiv (Cornell University)|Jun 28, 2011

Neutrino Physics Research4 references3 citations

TL;DR

This paper proposes a phenomenological two-scale model for neutrino masses, assuming contributions from a Majorana mass scale (ξ) and a seesaw scale (M), using a simplified mass formula (m_i = ±ξ − m²_li/M). It estimates key neutrino observables—m_C, m_β, m_2β—and finds δ ≈ 90° in the inverted hierarchy case, with m_2β ≈ 0.0526 eV, consistent with experimental limits.

ABSTRACT

The problem of an active neutrinos mass origin is considered at the phenomenological level. At first an assumption is made that neutrino mass values depend on two contributions with their characteristic scales, a next assumption consists in their dependence on three dominant scales. The neutrino mass values as well as the values of neutrino mass observables $m_C$ and $m_β$ are estimated.

Motivation & Objective

• To address the unresolved problem of neutrino mass origin by proposing a phenomenological two-scale model.
• To estimate absolute neutrino mass observables (m_C, m_β, m_2β) using two dominant mass contributions.
• To determine the CP-violating phase δ using a quasi-Dirac neutrino approximation in the schizophrenic neutrino framework.
• To provide testable predictions for future neutrino experiments, especially in the context of neutrinoless double-beta decay.

Proposed method

• Assumes two dominant contributions to neutrino masses: a Majorana mass scale ξ and a seesaw scale M, with m_i = ±ξ − m²_li/M.
• Uses the PMNS mixing matrix in standard parametrization with measured mixing angles and mass-squared differences from global fits.
• Applies the 'schizophrenic neutrino' model where one neutrino is Majorana and two are quasi-Dirac, enabling CP-phase determination via symmetry condition on matrix elements.
• Derives δ ≈ 90° from the condition |U_μ₃| = |U_τ₃|, leading to a trigonometric equation involving θ₁₂, θ₂₃, and θ₁₃.
• Calculates m_C, m_β, and m_2β using the derived masses and mixing parameters, with m_2β interpreted as the effective mass in neutrinoless double-beta decay.
• Compares results with experimental limits: m_C < 0.2 eV, m_β < 2.2 eV, m_2β < 0.34 eV (up to 1 eV with nuclear matrix element uncertainty).

Experimental results

Research questions

• RQ1 What are the values of the two dominant mass scales (ξ and M) that reproduce the observed neutrino mass splittings and mixing angles?
• RQ2 How can the CP-violating phase δ be estimated phenomenologically when it is not yet measured experimentally?
• RQ3 What are the predicted values of the absolute neutrino mass observables m_C, m_β, and m_2β under the two-scale model?
• RQ4 Does the model’s prediction for m_2β remain consistent with current experimental limits, especially from neutrinoless double-beta decay?
• RQ5 Can the assumption of quasi-Dirac neutrinos in the schizophrenic neutrino model yield a consistent and predictive value for δ?

Key findings

• In the normal hierarchy (NH), the model predicts m_C ≈ 0.07473 eV, m_β ≈ 0.0696 eV, and m_2β ≈ 0.04717 eV.
• In the inverted hierarchy (IH), the model predicts m_C ≈ 0.07202 eV, m_β ≈ 0.07747 eV, and m_2β ≈ 0.05263 eV, which is consistent with the upper limit of 0.34 eV from experiments.
• The CP-violating phase δ is estimated to be approximately 90°, differing from the commonly assumed δ = 0°, based on the quasi-Dirac neutrino symmetry condition.
• The characteristic scales are found to be ξ ≈ 0.069259 eV and M ≈ 2.0454 × 10¹⁹ eV in the NH case, and ξ ≈ 0.07751 eV and M ≈ 2.2872 × 10¹⁹ eV in the IH case.
• The absolute neutrino masses are estimated as μ₁ ≈ 0.06926 eV, μ₂ ≈ 0.06981 eV, μ₃ ≈ 0.08513 eV in NH, and μ₁ ≈ 0.07751 eV, μ₂ ≈ 0.078 eV, μ₃ ≈ 0.06056 eV in IH.
• The model provides a phenomenological framework that links two mass scales to observable neutrino parameters, enabling predictions for future experiments.