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arxiv: 2401.12829 · v4 · submitted 2024-01-23 · ✦ hep-ph

A non-unitary solar constraint for long-baseline neutrino experiments

Andres Lopez Moreno This is my paper

Pith reviewed 2026-05-24 04:24 UTC · model grok-4.3

classification ✦ hep-ph
keywords neutrino oscillationsnon-unitary mixingsolar neutrinosheavy neutral leptonsMSW effectlong-baseline experimentsBorexinoKamLAND
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The pith

Solar neutrino data limits the non-unitary mixing parameter for electron neutrinos to below 0.046 at 99 percent credible interval.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper extends the standard MSW large mixing angle approximation for solar neutrinos by adding one new parameter, alpha11, to account for possible mixing between the electron neutrino and heavy neutral leptons. It then reinterprets data from Borexino, SNO, and KamLAND to produce a constraint on this parameter that long-baseline oscillation experiments can use as an external input. A reader would care because those experiments need tight solar constraints on sin squared theta12 and the solar mass splitting to extract precise values for the rest of the leptonic mixing matrix, and unaccounted non-unitary effects could shift those results. The analysis yields the bound on one minus alpha11 together with a strong correlation between the solar mass splitting and the size of the non-unitary mixing.

Core claim

By constructing an MSW large mixing angle approximation that incorporates heavy neutral leptons through the single additional parameter alpha11, which represents the magnitude of nu_e mixing with the heavy sector, the existing solar neutrino measurements from Borexino, SNO, and KamLAND can be reinterpreted to constrain non-unitary effects. Solar data thereby limits one minus alpha11 to less than 0.046 at the 99 percent credible interval and produces a correlated bound linking the solar mass splitting to the magnitude of nu_e non-unitary mixing.

What carries the argument

The extended MSW large mixing angle approximation that adds the single parameter alpha11 to describe nu_e mixing with heavy neutral leptons.

If this is right

  • Long-baseline experiments can adopt this bound as an external constraint when measuring the leptonic mixing matrix in the presence of possible heavy neutral leptons.
  • The solar mass splitting and the non-unitary mixing magnitude must be treated as correlated when using the solar constraint in oscillation analyses.
  • Heavy neutral lepton searches in long-baseline data can now incorporate a solar-derived limit on the size of nu_e mixing with the heavy sector.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the bound holds, terrestrial long-baseline measurements of oscillation probabilities would be restricted from exhibiting large non-unitary deviations driven by electron-neutrino mixing with heavy states.
  • One could test the correlation by extracting the solar mass splitting from reactor antineutrino data and checking consistency with the solar constraint under the same non-unitary model.
  • Future solar neutrino detectors with higher statistics could tighten the limit on alpha11 or reveal whether the current correlation persists.

Load-bearing premise

The large mixing angle MSW description of solar neutrinos stays valid and complete when extended by one extra parameter for heavy-sector mixing, so that existing solar data can be used directly without further heavy-sector corrections.

What would settle it

A new global fit to solar neutrino data that returns an upper limit on one minus alpha11 substantially above 0.046 or that shows no correlation between the solar mass splitting and the non-unitary parameter would falsify the reported constraint.

Figures

Figures reproduced from arXiv: 2401.12829 by Andres Lopez Moreno.

Figure 1
Figure 1. Figure 1: FIG. 1. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Solar survival probabilities from Borexino and SNO. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Comparison of the usual (black) and non-unitary [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. 1 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Solar survival probabilities from Borexino and SNO. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
read the original abstract

Long-baseline neutrino oscillation experiments require external constraints on $\sin^2\theta_{12}$ and $\Delta m_{21}^2$ to make precision measurements of the leptonic mixing matrix. These constraints come from measurements of the Mikheyev-Smirnov-Wolfenstein (MSW) mixing in solar neutrinos. Here we develop an MSW large mixing angle approximation in the presence of heavy neutral leptons which adds a single new parameter ($\alpha_{11}$) representing the magnitude of the mixing between the $\nu_e$ state and the heavy sector. We use data from the Borexino, SNO and KamLAND collaborations to find a solar constraint appropriate for heavy neutral lepton searches in long-baseline oscillation experiments. Solar data limits the magnitude of the non-unitary parameter to $(1-\alpha_{11}) < 0.046$ at the $99\%$ credible interval and yields a strongly correlated constraint on the solar mass splitting and the magnitude of $\nu_e$ non-unitary mixing.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper develops an MSW large mixing angle approximation for solar neutrinos in the presence of heavy neutral leptons, introducing a single new parameter α11 for the magnitude of νe mixing with the heavy sector. It reinterprets data from Borexino, SNO, and KamLAND to derive the constraint (1-α11) < 0.046 at 99% credible interval, together with a strongly correlated bound on Δm21², for use as an external constraint in long-baseline neutrino oscillation experiments.

Significance. If the single-parameter extension of the MSW LMA approximation is valid, the result supplies a practical solar-derived limit on non-unitary mixing that can be directly applied to long-baseline analyses, addressing a genuine need for external constraints on sin²θ12 and Δm21². The approach of fitting existing solar data to bound a new parameter is a useful contribution when the underlying assumptions hold.

major comments (2)
  1. [MSW LMA approximation with α11 (abstract and derivation)] The central approximation assumes that non-unitary mixing with heavy neutral leptons introduces no extra terms in the effective Hamiltonian, no change to the adiabaticity condition, and no additional production/detection systematics beyond the rescaled mixing when the MSW LMA formula is extended by α11 alone. This assumption is load-bearing for the quoted (1-α11)<0.046 bound and its correlation with Δm21²; explicit verification that residual O(α) or phase-dependent contributions to P(νe→νe) remain negligible at solar energies and densities is required.
  2. [Data analysis and fit to Borexino/SNO/KamLAND] The reported 99% credible interval and the strong correlation between α11 and Δm21² are obtained by fitting the extended model to solar data. The treatment of systematic uncertainties, the precise likelihood construction, and any post-hoc choices in the fit must be shown to be robust before the bound can be adopted as an external constraint for long-baseline experiments.
minor comments (2)
  1. Provide the explicit functional form of the extended survival probability used in the fit, including the precise definition of α11 in terms of the non-unitary mixing matrix.
  2. Add a brief comparison of the new solar constraint with existing limits on non-unitary parameters from other sectors or experiments.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful review of our manuscript. We address each of the major comments below and will make revisions to incorporate additional verifications and details as appropriate.

read point-by-point responses

  1. Referee: The central approximation assumes that non-unitary mixing with heavy neutral leptons introduces no extra terms in the effective Hamiltonian, no change to the adiabaticity condition, and no additional production/detection systematics beyond the rescaled mixing when the MSW LMA formula is extended by α11 alone. This assumption is load-bearing for the quoted (1-α11)<0.046 bound and its correlation with Δm21²; explicit verification that residual O(α) or phase-dependent contributions to P(νe→νe) remain negligible at solar energies and densities is required.

    Authors: In the manuscript, we derive the approximation by integrating out the heavy neutral leptons, showing that their contribution to the effective Hamiltonian is suppressed by their large masses, resulting in no additional terms at the order relevant for solar neutrinos. The adiabaticity is preserved because the level crossing remains between the light states. However, to explicitly address the referee's request for verification of negligible residuals, we will add numerical comparisons in the revised manuscript demonstrating that O(α) and phase-dependent effects are below the percent level for solar parameters. revision: yes

  2. Referee: The reported 99% credible interval and the strong correlation between α11 and Δm21² are obtained by fitting the extended model to solar data. The treatment of systematic uncertainties, the precise likelihood construction, and any post-hoc choices in the fit must be shown to be robust before the bound can be adopted as an external constraint for long-baseline experiments.

    Authors: The fit details are provided in the methods section, using the standard χ² or likelihood from the experimental papers with their systematics included. We did not make post-hoc choices. To further demonstrate robustness, we will include additional tests in the revision, such as varying the treatment of correlated systematics between experiments. revision: partial

Circularity Check

0 steps flagged

No circularity: constraint obtained via direct fit of new parameter α11 to solar data in extended MSW model

full rationale

The paper introduces a single new parameter α11 into an MSW LMA approximation for non-unitary mixing with heavy neutral leptons, then constrains it (and its correlation with Δm21²) by reinterpreting existing Borexino/SNO/KamLAND data. This is standard parameter estimation from external measurements rather than any self-definitional loop, fitted input renamed as prediction, or self-citation chain. The central result (1-α11)<0.046 at 99% CI) is the output of the fit, not equivalent to the inputs by construction. No load-bearing steps reduce to tautology.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on the validity of the extended MSW approximation and on the new parameter α11 being the only addition needed; heavy neutral leptons are drawn from prior literature without new independent evidence supplied here.

free parameters (1)
  • α11
    Single new parameter quantifying νe mixing with the heavy sector; its magnitude is constrained by the solar data fit.
axioms (1)
  • domain assumption MSW large mixing angle approximation remains valid when heavy neutral leptons are included via one extra mixing parameter
    Invoked to derive the non-unitary solar constraint from existing data.
invented entities (1)
  • heavy neutral leptons no independent evidence
    purpose: Source of non-unitary mixing in the neutrino sector
    Postulated extension allowing the single-parameter α11 description; no new falsifiable prediction for their masses or couplings is given.

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