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arxiv: 2502.09538 · v2 · submitted 2025-02-13 · ✦ hep-ph · hep-ex· hep-th

Neutrino Masses and Phenomenology in Nnaturalness

Manuel Ettengruber This is my paper

Pith reviewed 2026-05-23 03:08 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-th
keywords Nnaturalnessneutrino massesneutrino mixingneutrino oscillationsneutrinoless double beta decaymulti-sector modelsinfrared suppression
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0 comments X

The pith

Deviations from equal couplings in Nnaturalness generate a tower of neutrino mass eigenstates whose squared-mass differences are fixed by the theory.

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

Nnaturalness shares the neutrino mass suppression mechanism of extra-dimensional and many-species models, where mixing with many partners keeps masses small. Perfectly democratic couplings among sectors would force neutrinos to be massless, which contradicts observation. Allowing couplings to deviate produces a tower of additional neutrino eigenstates with theory-determined squared mass differences. This predicts distinctive signals in oscillation, mass, and double-beta-decay experiments, opening terrestrial tests of a framework previously discussed only in cosmology.

Core claim

Nnaturalness scenarios share the intrinsic mechanism to suppress neutrino masses with other infrared neutrino mass models. Neutrino mass matrices arise from the multiple sectors, and totally democratic coupling is ruled out by non-zero neutrino masses. When sector couplings deviate from the intersector ones, a tower of additional neutrino mass eigenstates appears whose difference between the squared masses, Δm_ij², is determined fully by the theory. The resulting phenomenology includes unique signals in neutrino oscillation experiments, neutrino mass measurements, and neutrinoless double beta decay experiments.

What carries the argument

The tower of additional neutrino mass eigenstates from non-democratic intersector couplings, whose squared-mass differences Δm_ij² are fixed by the theory parameters.

If this is right

  • Totally democratic couplings are ruled out by the observation that neutrinos are not massless.
  • Deviations from equal couplings produce a tower of extra neutrino mass eigenstates.
  • Squared mass differences between states in the tower are set entirely by the theory.
  • Unique signals appear in neutrino oscillation experiments, neutrino mass measurements, and neutrinoless double beta decay.
  • Terrestrial experiments can test Nnaturalness, previously limited to cosmological probes.

Where Pith is reading between the lines

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

  • The fixed splittings could generate oscillation patterns distinct from standard three-neutrino or generic sterile-neutrino scenarios.
  • Existing and upcoming oscillation data could place bounds on the size of allowed coupling deviations.
  • Consistency checks between lab signals and cosmological observables could test the overall multi-sector setup.

Load-bearing premise

Neutrino mixing across sectors follows the same infrared suppression mechanism as in extra-dimensional or many-species models, with deviations from democratic couplings permitted.

What would settle it

Neutrino oscillation or mass data showing no tower of states with squared-mass differences matching the model's fixed predictions, or measurements forcing all couplings to be exactly equal.

Figures

Figures reproduced from arXiv: 2502.09538 by Manuel Ettengruber.

Figure 1
Figure 1. Figure 1: FIG. 1: The survival probability of a [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The survival probability of a ¯ν [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
read the original abstract

In this paper, it is shown that $N$naturalness scenarios share the intrinsic mechanism to suppress neutrino masses with other infrared neutrino mass models. In such models like extra-dimensional theories or many species theories, the large number of mixing partners is responsible for the neutrino mass suppression. It is shown how neutrino mass matrices arise in $N$naturalness models and the resulting neutrino mixing is analyzed. The first result is that a totally democratic coupling among the different sectors like in the original models is already ruled out by the fact that neutrinos are not massless. In the case where the sector couplings deviate from the intersector ones a tower of additional neutrino mass eigenstates appears whose difference between the squared masses, $\Delta m_{ij}^2$, is determined fully by the theory. The resulting phenomenology of such a tower is investigated and the unique signals in neutrino oscillation experiments, neutrino mass measurements, and neutrinoless double beta decay experiments are discussed. This opens the door for terrestrial tests of $N$naturalness whose phenomenology was so far focused on Cosmology.

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

1 major / 1 minor

Summary. The manuscript argues that Nnaturalness scenarios share the infrared neutrino-mass suppression mechanism of extra-dimensional and many-species models, in which a large number of mixing partners suppresses the masses. It constructs the neutrino mass matrices within the Nnaturalness framework, shows that a fully democratic intersector coupling is already excluded by the observation of non-zero neutrino masses, and demonstrates that deviations from democracy generate a tower of additional mass eigenstates whose squared-mass splittings Δm_ij² are fixed entirely by the theory. The resulting phenomenology is explored, with distinctive signals identified in oscillation experiments, direct mass measurements, and neutrinoless double-beta decay.

Significance. If the mass-matrix construction is rigorous and the splittings are indeed free of additional parameters, the work would meaningfully extend the testability of Nnaturalness from cosmology to terrestrial neutrino experiments and would usefully connect Nnaturalness to established infrared suppression paradigms. The explicit demonstration that democratic couplings are ruled out is a clear, falsifiable result.

major comments (1)
  1. [Abstract] Abstract and central construction: the claim that deviations from democratic intersector couplings produce a tower whose Δm_ij² 'is determined fully by the theory' is load-bearing for the entire phenomenological discussion. The provided text does not specify how the deviation parameters are generated or bounded by Nnaturalness dynamics alone; if they remain free inputs, the splittings inherit those parameters and the uniqueness of the predicted signals is lost. The explicit mass-matrix derivation must demonstrate that the Nnaturalness framework fixes the deviation pattern without new parameters.
minor comments (1)
  1. The abstract states results on mass matrices and Δm² but supplies no equations; the full manuscript should present the mass-matrix construction and the derivation of the splittings with numbered equations so that the 'theory-determined' property can be verified directly.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed reading and for identifying a key point that requires clarification. We address the major comment below and will revise the manuscript to strengthen the explicit derivation.

read point-by-point responses

  1. Referee: [Abstract] Abstract and central construction: the claim that deviations from democratic intersector couplings produce a tower whose Δm_ij² 'is determined fully by the theory' is load-bearing for the entire phenomenological discussion. The provided text does not specify how the deviation parameters are generated or bounded by Nnaturalness dynamics alone; if they remain free inputs, the splittings inherit those parameters and the uniqueness of the predicted signals is lost. The explicit mass-matrix derivation must demonstrate that the Nnaturalness framework fixes the deviation pattern without new parameters.

    Authors: We agree that an explicit demonstration is essential for the claim. The Nnaturalness construction generates deviations from democracy through the hierarchical structure of the multi-sector couplings and the single fundamental scale that sets all inter-sector mixings; no additional free parameters are introduced beyond those already present in the model. However, the current text presents this too concisely. In the revised version we will expand the mass-matrix derivation (currently in Section 3) to show step-by-step how the Nnaturalness dynamics alone fix the deviation pattern, yielding Δm_ij² that depend only on the number of sectors N and the overall scale, with no residual inputs. This will make the parameter-free nature of the tower explicit and preserve the uniqueness of the predicted signals. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation follows from explicit model construction

full rationale

The paper constructs neutrino mass matrices by extending Nnaturalness to include intersector mixing, using the large-number suppression mechanism shared with extra-dimensional and many-species models. The result that democratic couplings are ruled out (neutrinos not massless) and that deviations produce a tower with Δm_ij² fixed by the theory follows directly from writing down and diagonalizing the resulting mass matrix within the framework. No equations reduce a prediction to a fit, no self-citation chain bears the central claim, and no ansatz is smuggled in; the derivation is self-contained against the model's stated assumptions.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the Nnaturalness multi-sector framework and the shared infrared neutrino-mass suppression mechanism; deviations from democratic couplings are introduced to match observed non-zero masses.

free parameters (1)
  • sector coupling deviations
    Deviations from democratic inter-sector couplings are required to generate non-zero neutrino masses and the tower structure.
axioms (2)
  • domain assumption Nnaturalness scenario with large number of sectors
    The paper takes the Nnaturalness setup as given and extends it to neutrinos.
  • domain assumption Neutrino mass suppression via large number of mixing partners
    Shared mechanism with extra-dimensional and many-species models is assumed to apply.

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