Pith. sign in

REVIEW 3 major objections 4 minor 55 references

Terrestrial neutrino data exclude the no-fine-tuning Majorana N-naturalness benchmark with N=10^4 sectors.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-02 02:44 UTC pith:B44YYKCM

load-bearing objection First experimental search for the N-naturalness neutrino tower, with a plausible Majorana exclusion of the r=1 benchmark — but the reach hinges on a hand-set coupling ratio whose robustness is asserted rather than shown. the 3 major comments →

arxiv 2607.14243 v1 pith:B44YYKCM submitted 2026-07-15 hep-ph hep-ex

Searching for the N-naturalness tower of neutrinos

Sofia Lonardi , Manuel Ettengruber , Philipp Eller This is my paper
classification hep-ph hep-ex
keywords N-naturalnessneutrino towerhierarchy problemneutrinoless double beta decayreactor neutrino oscillationsMajorana neutrinoDirac neutrinofine-tuning
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper asks whether the N-naturalness solution to the hierarchy problem—which posits N copies of the Standard Model with different Higgs masses—leaves observable traces in neutrinos. It builds a two-parameter model (N sectors, fine-tuning r) and compares predictions for reactor oscillations and neutrinoless double-beta decay against public data from Daya Bay and GERDA, as well as projected JUNO+TAO and LEGEND sensitivities. The central result is that for Majorana neutrinos, all non-fine-tuned scenarios with r=1 up to N=10^4 are excluded by current data, including the benchmark N=10^4 that would unify gauge couplings at the GUT scale. This turns neutrino experiments into a direct test of an infrared solution to the hierarchy problem. The Dirac realization is far less constrained.

Core claim

The paper's central claim is that the N-naturalness tower of neutrinos, in its Majorana realization, produces observable enhancements in the effective Majorana mass m_ββ and distortions in reactor neutrino oscillations. Using a global fit, the authors find that with current GERDA data combined with Daya Bay, all non-fine-tuned scenarios with r=1 up to N=10^4 are excluded at 90% confidence level, in both normal and inverted mass ordering. This rules out the benchmark scenario in which N=10^4 sectors with a cutoff around 10 TeV solve the hierarchy problem without additional fine-tuning while preserving gauge coupling unification. For projected JUNO+TAO data, the exclusion extends to N<500 for

What carries the argument

The key object is the N-sector neutrino mass matrix, parametrised so that the intra-to-inter-sector coupling ratio is fixed at η=1+1/N (i.e., (a²−b²)=b²/N), leaving only N and r as free parameters. The authors numerically diagonalise the full 3N/2 × 3N/2 matrix to compute three-flavour oscillation probabilities and the generalised effective Majorana mass m_ββ, which includes contributions from the heavy tower states via the formalism of eq. (37) with benchmark nuclear matrix elements. The m_ββ prediction is the main driver of the bound: for large N and r near 1, the heavy states push m_ββ above the GERDA limit.

Load-bearing premise

The entire reach of the search rests on the choice η=1+1/N—that the inter-sector Yukawa coupling differs from the intra-sector one by exactly one part in N; if the inter-sector coupling is smaller by hand, the oscillation distortions and the m_ββ enhancement that produce the exclusions would largely disappear.

What would settle it

Recompute the predicted Majorana m_ββ for N=10^4, r=1 using the full allowed range of heavy-neutrino nuclear matrix elements (e.g., M_0ν_N=401 and M_0ν_ν=2.89 instead of the adopted benchmarks 194 and 5.28). If the resulting 0νββ half-life for 76Ge exceeds the GERDA limit of 1.8×10^26 yr, the ruling out of the N=10^4 benchmark would no longer follow.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If correct, the simplest Majorana N-naturalness benchmark—N=10^4, r=1, Λ_H~10 TeV—is experimentally excluded, so a no-fine-tuning solution to the hierarchy problem of this type must move to N>10^4 or to the Dirac realization.
  • The surviving Majorana parameter space requires either N>10^4 or r≤0.1 for 500≤N≤10^4, meaning the theory must reintroduce some degree of fine-tuning to remain viable in this region.
  • The Dirac realization remains viable for N up to about 50 (and for all N at larger r), so the neutrino tower solution is not dead overall, only the Majorana version at moderate N.
  • Projected JUNO+TAO data will exclude N<500 for any r in the Majorana case, and LEGEND-1000 will further tighten m_ββ bounds, potentially extending the excluded region beyond N=10^4.
  • The analysis demonstrates a new, purely terrestrial probe of N-naturalness, complementary to cosmological constraints.

Where Pith is reading between the lines

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

  • The exclusion strength relies on η=1+1/N; if a UV theory naturally suppressed the inter-sector coupling b, the predicted oscillations and m_ββ would shrink and the bounds would weaken. A derivation of b's size from a UV completion would clarify whether the N=10^4 benchmark is truly excluded.
  • The m_ββ bound passes through the heavy-neutrino regime where nuclear matrix elements are uncertain; the paper asserts insensitivity without showing it, so recomputing contours with M_0ν_N over its full [104, 401] range would provide a direct check.
  • The same global-fit machinery could be applied to other tower models (e.g., extra-dimensional KK neutrinos) to compare their exclusion reach on a common footing.
  • Including KATRIN's β-decay spectrum, as the authors suggest, could strengthen the Dirac bound and might also probe the tower through spectral kinks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The manuscript presents a global fit of public terrestrial neutrino data to constrain the N-naturalness model in its neutrino sector, with parameters N (number of sectors) and r (fine-tuning measure). The model generates a tower of neutrino mass eigenstates from the N/2 SM-like sectors mixing with the SM neutrino. The authors numerically diagonalize the mass matrix (Section III), use Daya Bay data and JUNO+TAO projections for oscillation constraints, and compare the predicted 0νββ effective mass with GERDA/LEGEND half-life limits (Section V.B). The headline result is that for Majorana neutrinos, N ≤ 10^4 with r ≥ 0.1 is excluded by current data, ruling out the no-fine-tuning GUT-scale benchmark scenario, and that projected JUNO+TAO data will exclude all N < 500 and 500 ≤ N ≤ 10^4 for r ≥ 0.1. The main results are the exclusion contours shown in Figs. 7–9 for Majorana and Dirac cases in both mass orderings.

Significance. If the result is robust, this is an important first experimental probe of N-naturalness from the neutrino sector, with the striking conclusion that the N=10^4, r=1 Majorana benchmark is excluded. The analysis has definite strengths: it uses numerical diagonalization where the perturbative treatment of [28] is invalid, it relies on public data and the reproducible Newtrinos.jl framework, and it profiles 22 systematic parameters in the JUNO+TAO projection. However, the central claim is contingent on (i) the hand-set inter-sector coupling ratio η=1+1/N and (ii) the treatment of heavy-neutrino contributions to 0νββ using benchmark nuclear matrix elements and an ad hoc interpolation. The paper asserts robustness to these choices but does not demonstrate it quantitatively. The significance is therefore high if the sensitivity to these assumptions is shown to be small, but that demonstration is currently missing.

major comments (3)
  1. [Section III, Eq. (24)] The choice η=1+1/N (i.e., \tilde a^2 − \tilde b^2 = \tilde b^2/N) is an input assumption, not a prediction of the N-naturalness framework. The paper's exclusion reach scales directly with this ratio: the heavy-sector masses and their mixing, which drive mββ above the GERDA limit via Eq. (35), are controlled by η, and the text itself warns that 'if we turn down the inter-sector coupling by hand, many effects would vanish.' The statement that 'small deviations of O(1) from this regime do not affect our conclusions' is not sufficient, because the naturalness prior is precisely what is being tested. The authors should quantify how far η can deviate before the N=10^4, r=1 exclusion disappears, e.g., by showing contours for several η values or a robustness scan. Without this, the headline bound remains conditional on an unverified maximal-mixing prior.
  2. [Section V.B, Eqs. (37)–(38)] The 0νββ constraint is implemented as a point-like comparison of the predicted mββ to a single half-life limit with a nominal 10% uncertainty, rather than a spectral fit. More importantly, the heavy-state contribution uses the [52] formalism with benchmark nuclear matrix elements Mν=5.28, MN=194 and the piecewise interpolation function F(m). The paper asserts that 'studies are made on the final contours... and the results vary only slightly,' but no scan or quantitative bound is shown. Since the heavy-state term is what pushes mββ above the GERDA limit for N≈10^4, the contours in Figs. 7–8 must be demonstrated to be stable within the published ranges Mν∈[2.89,6.04] and MN∈[104,401] and across reasonable choices of F(m). Without this demonstration, the central exclusion is not established.
  3. [Section III, Eqs. (25)–(30)] The overall scales s1–s3 are fixed using the analytic perturbative expressions for the sector-0 masses, Eqs. (25)–(30), even though the paper explicitly abandons the perturbative diagonalization because it breaks down in the tested parameter region. There is no check that the numerically diagonalized eigenvalues obtained with these s_i actually reproduce the input neutrino masses and measured squared-mass splittings across the scanned (N,r) plane. If the numerical eigenvalues deviate from the analytic expressions, then the oscillation probabilities and mββ predictions are systematically miscalibrated. The authors should validate the calibration (e.g., by showing the numerical sector-0 masses versus the inputs) or fix the scales directly from the numerical eigenvalues. In addition, Eq. (29) contains a factor 2 in the denominator that is inconsistent with Eq. (26); this needs clarification
minor comments (4)
  1. [Section V.A] Wilks' theorem is misspelled as 'Wilk's theorem' in the sentence introducing the profile likelihood test statistic.
  2. [Section VI] The description of the combined analysis, 'combining the likelihood functions of the individual experiments,' does not specify whether or how correlations between experiments (e.g., reactor flux uncertainties common to Daya Bay and JUNO) are handled. A brief statement of the combination prescription and its independence assumptions would improve reproducibility.
  3. [Section II, Eqs. (9)–(10)] The matrices in Eqs. (9)–(10) appear to be (N/2+1)-dimensional with indices running over the SM-like sectors, while the text refers to N total sectors. The notation should be clarified explicitly to avoid confusion between total N and the dimension of the sector-space mass matrix.
  4. [Section VII] The concluding sentence 'non-fine-tuned model realisations (r=1 up to r=0.1)' is ambiguous; since the exclusion is for r≥0.1, it would be clearer to say 'r values from 0.1 to 1' or 'r≥0.1'.

Circularity Check

0 steps flagged

No significant circularity; the N≤10^4 Majorana exclusion is an external-data test of a stated model realization.

full rationale

The derivation is not circular. The scale parameters s1–s3 are calibrated to the observed neutrino masses (Eqs. 25–30), but this is a standard overall normalization, not a fit to the predicted observables. The predictions compared with data are the oscillation survival probabilities and the effective Majorana mass mββ, computed from the numerically diagonalized mass matrices as functions of N and r (Eqs. 31, 33, 35). The mββ enhancement that drives the GERDA exclusion comes from the heavy tower eigenstates, whose masses and mixings are determined by N and r through the matrix structure, not merely from the fitted light masses. The choice η = 1 + 1/N is an explicitly stated model assumption in Section III, with the caveat that turning down the inter-sector coupling would erase the effects; this makes the headline result conditional on a stated realization but does not reduce the prediction to its input. The paper's robustness assertions about η and the [52] nuclear matrix element benchmarks are abbreviated, but that is a support/evidence weakness, not circularity. Self-citations, including [28] for the mass-matrix structure and η prescription, supply the model setup; the central exclusion claim is nevertheless tested against independent public data (Daya Bay and GERDA), so it has genuine external content.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 3 invented entities

The exclusion rests on the N-naturalness framework and neutrino mass matrices inherited from [12, 28], a hand-set mixing ratio η = 1 + 1/N, normalization of the overall scale to the measured neutrino masses, and the heavy-state 0νββ treatment of [52]. No new entities are introduced by this paper; the testable tower, the N dark sectors, and the reheaton are inherited model content. Dominant free parameters: fitted mass scales s1–s3, η, m0, F(m) interpolation, and NME benchmarks.

free parameters (5)
  • per-flavor overall scales s1, s2, s3 = s1 = m1/((η−1)r); s2 = m2/(2(η−1)r); s3 = m3/((η−1)r), eqs. (28)-(30)
    Fixed so sector-0 masses match measured oscillation parameters; absorbs the model's unpredicted absolute neutrino mass scale, leaving only the tower differential structure testable.
  • η ≡ ã²/b̃² (intra- vs inter-sector coupling ratio) = 1 + 1/N (chosen by hand)
    Controls the size of all tower effects; naturalness-motivated following [28]; robustness to O(1) deviations asserted in Section III, but if inter-sector coupling is weaker, 'many effects would vanish'.
  • m0 (lightest neutrino mass) = 0.01 eV for headline; scan set {0, 10^-4, 10^-2, 10^-1} eV
    Sets the absolute scale and density of the tower; fixed to a value consistent with KATRIN/cosmology; claimed robust via fig. 10.
  • F(m) heavy-state interpolation values = 0.7 (10^4–10^6 eV), 1.0 (≥10^6 eV)
    Hand-chosen piecewise suppression for heavy neutrino NME contributions, adopted from [52]; the m_ββ contours have visible kinks at these thresholds ('small discontinuities').
  • Nuclear matrix element benchmarks M_ν^0ν, M_N^0ν, ⟨p²⟩ = 5.28, 194, per eq. (38)
    Selected benchmarks from [52] within quoted ranges [2.89, 6.04] and [104, 401]; the m_ββ exclusion scale is inversely proportional to √M_ν, so order-one NME shifts change the reach.
axioms (6)
  • domain assumption N-naturalness: Higgs mass parameters uniformly distributed as mu_i^2 = -(Lambda_H^2/N)(2i + r)
    Underpins the per-sector VEV pattern sqrt(2i+r) used in the mass matrices; inherited from [12].
  • domain assumption Neutrino mass matrices M_D, M_M and Yukawa structure lambda_ij = a*diag + b*off-diag, with b <= 1/sqrt(N)
    The central predictions (tower masses, mixings) are computed from these matrices taken from [28].
  • domain assumption Reheaton cosmology: only the lightest sector is populated; m_S ~ 100 GeV; Majorana reheaton S induces the Weinberg operator (eq. 8)
    Sets the scenario and the heavy-state spectrum; from [12, 28]; cosmological constraints are not computed here.
  • ad hoc to paper Heavy-state 0νββ formalism with interpolation F(m) and benchmark NMEs (eqs. 37-38)
    Phenomenological treatment adopted from [52]; the piecewise F is an interpolation; the m_ββ exclusion at N = 10^4 passes through this regime.
  • standard math Wilks' theorem: -2 Delta ln L ~ chi^2(2 dof) for the two-dimensional scans
    Asymptotic approximation assumed for drawing 90% contours; validity with limited data and non-Gaussian systematics is not assessed.
  • domain assumption Species bound M_f = M_P/sqrt(N); gauge-unification identity N ~ 10^4 corresponds to Lambda_H ~ 10 TeV (eq. 4)
    Used to translate the (r, N) exclusion into the claim that the GUT benchmark is ruled out; from [32, 33].
invented entities (3)
  • Tower of extra neutrino mass eigenstates (one per sector) independent evidence
    purpose: Produces the oscillation distortions and m_beta-beta enhancement the paper searches for
    Inherited from [28], not new to this paper; the falsifiable handle is the tower contribution to oscillation survival probabilities and to 0νββ, confronted with external Daya Bay/GERDA data here.
  • N dark sectors (copies of the Standard Model) no independent evidence
    purpose: N-naturalness solution to the hierarchy problem; each sector hosts a Higgs and neutrinos
    Inherited from [12]; no handle outside the model's own neutrino predictions; only the neutrino tower is probed by the experiments analyzed.
  • Fermionic reheaton S (Majorana case only) no independent evidence
    purpose: Generates the Weinberg operator (eq. 8) and sets which sectors are populated after inflation
    Inherited from [12, 28]; the mass scale (~100 GeV) is fixed by cosmological consistency, not by a direct search channel.

pith-pipeline@v1.3.0-alltime-deepseek · 16325 in / 42532 out tokens · 433438 ms · 2026-08-02T02:44:33.200337+00:00 · methodology

0 comments
read the original abstract

We present the first experimental search for the $N$-naturalness tower of neutrinos using a global analysis of publicly available neutrino data. As a potential solution to the hierarchy problem, the $N$-naturalness model employs a varying Higgs mass parameter among $N$ dark sectors and encodes the required fine-tuning of the placement of the sectors in a parameter $r$. We report exclusion limits on the parameter space ($r$, $N$), for normal and inverted ordering and in case the neutrino is Majorana or Dirac. In the case of a Majorana neutrino, we can rule out $N\leq 10^4$ sectors with $r\geq 0.1$. This is particularly exciting as it shows that a gauge and gravitational unification around $M_{GUT}$, which is a benchmark scenario of the $N$-naturalness framework with $N=10^4$ without fine-tuning, is ruled out by neutrino experiments.

Figures

Figures reproduced from arXiv: 2607.14243 by Manuel Ettengruber, Philipp Eller, Sofia Lonardi.

Figure 1
Figure 1. Figure 1: FIG. 1. Survival probability of electron antineutrino for dif [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Survival probability of electron antineutrino for dif [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Counts of Daya Bay data and predictions for different [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Counts of Daya Bay data and predictions for different [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Effective mass [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: illustrates the dependence on the parameter r. For each value of N there exists a region where the [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Excluded regions at 90% C.L. in the ( [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Excluded regions at 90% C.L. in the ( [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Excluded regions at 90% C.L. in the ( [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Excluded regions at 90% C.L. in the ( [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

55 extracted references · 34 linked inside Pith

  1. [1]

    Baryon and Lepton Nonconserving Processes,

    S. Weinberg, “Baryon and Lepton Nonconserving Processes,”Phys. Rev. Lett.43(1979) 1566–1570

    1979

  2. [2]

    µ→eγat a Rate of One Out of 10 9 Muon Decays?,

    P. Minkowski, “µ→eγat a Rate of One Out of 10 9 Muon Decays?,”Phys. Lett. B67(1977) 421–428

    1977

  3. [3]

    Complex Spinors and Unified Theories,

    M. Gell-Mann, P. Ramond, and R. Slansky, “Complex Spinors and Unified Theories,”Conf. Proc. C790927 (1979) 315–321,arXiv:1306.4669 [hep-th]

    Pith/arXiv arXiv 1979

  4. [4]

    Horizontal Symmetry and Masses of Neutrinos,

    T. Yanagida, “Horizontal Symmetry and Masses of Neutrinos,”Prog. Theor. Phys.64(1980) 1103

    1980

  5. [5]

    Neutrino Mass and Spontaneous Parity Nonconservation,

    R. N. Mohapatra and G. Senjanovic, “Neutrino Mass and Spontaneous Parity Nonconservation,”Phys. Rev. Lett.44(1980) 912

    1980

  6. [6]

    Seesaw mechanism and its implications,

    R. N. Mohapatra, “Seesaw mechanism and its implications,” inSEESA W25: International Conference on the Seesaw Mechanism and the Neutrino Mass, pp. 29–44. 12, 2004.arXiv:hep-ph/0412379

    Pith/arXiv arXiv 2004

  7. [7]

    The Hierarchy problem and new dimensions at a millimeter,

    N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, “The Hierarchy problem and new dimensions at a millimeter,”Phys. Lett. B429(1998) 263–272, arXiv:hep-ph/9803315

    Pith/arXiv arXiv 1998

  8. [8]

    Neutrino masses from large extra dimensions,

    N. Arkani-Hamed, S. Dimopoulos, G. R. Dvali, and J. March-Russell, “Neutrino masses from large extra dimensions,”Phys. Rev. D65(2001) 024032, arXiv:hep-ph/9811448

    Pith/arXiv arXiv 2001

  9. [9]

    Probing large extra dimensions with neutrinos,

    G. R. Dvali and A. Y. Smirnov, “Probing large extra dimensions with neutrinos,”Nucl. Phys. B563(1999) 63–81,arXiv:hep-ph/9904211

    Pith/arXiv arXiv 1999

  10. [10]

    Phenomenology of 10 32 Dark Sectors,

    G. Dvali and M. Redi, “Phenomenology of 10 32 Dark Sectors,”Phys. Rev. D80(2009) 055001, arXiv:0905.1709 [hep-ph]

    Pith/arXiv arXiv 2009

  11. [11]

    Neutrino physics in TeV scale gravity theories,

    M. Ettengruber, “Neutrino physics in TeV scale gravity theories,”Phys. Rev. D106no. 5, (2022) 055028, arXiv:2206.00034 [hep-ph]

    Pith/arXiv arXiv 2022

  12. [12]

    and how neutrino mass can be explained within it. The original problem addressed by this theory is the hi- erarchy problem, which is generated by the sensitivity of the Higgs mass to the cutoff of the SM and the required fine-tuning to realise the light Higgs boson observed at LHC. The starting point ofN-naturalness is the realisation that the fine-tuning...

  13. [13]

    Phenomenology, astrophysics and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity,

    N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, “Phenomenology, astrophysics and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity,”Phys. Rev. D59(1999) 086004, arXiv:hep-ph/9807344

    Pith/arXiv arXiv 1999

  14. [14]

    Dark Matter via Many Copies of the Standard Model,

    G. Dvali, I. Sawicki, and A. Vikman, “Dark Matter via Many Copies of the Standard Model,”JCAP08(2009) 009,arXiv:0903.0660 [hep-th]

    Pith/arXiv arXiv 2009

  15. [15]

    Solving the Hierarchy Problem at Reheating with a Large Number of Degrees of Freedom,

    N. Arkani-Hamed, T. Cohen, R. T. D’Agnolo, A. Hook, H. D. Kim, and D. Pinner, “Solving the Hierarchy Problem at Reheating with a Large Number of Degrees of Freedom,”Phys. Rev. Lett.117no. 25, (2016) 251801,arXiv:1607.06821 [hep-ph]

    Pith/arXiv arXiv 2016

  16. [16]

    Dark dimension, the swampland, and the dark matter fraction composed of primordial black holes,

    L. A. Anchordoqui, I. Antoniadis, and D. Lust, “Dark dimension, the swampland, and the dark matter fraction composed of primordial black holes,”Phys. Rev. D106 no. 8, (2022) 086001,arXiv:2206.07071 [hep-th]

    Pith/arXiv arXiv 2022

  17. [17]

    Dark dimension gravitons as dark matter,

    E. Gonzalo, M. Montero, G. Obied, and C. Vafa, “Dark dimension gravitons as dark matter,”JHEP11(2023) 109,arXiv:2209.09249 [hep-ph]

    Pith/arXiv arXiv 2023

  18. [18]

    Primordial black hole dark matter in the context of extra dimensions,

    A. Friedlander, K. J. Mack, S. Schon, N. Song, and A. C. Vincent, “Primordial black hole dark matter in the context of extra dimensions,”Phys. Rev. D105 no. 10, (2022) 103508,arXiv:2201.11761 [hep-ph]

    Pith/arXiv arXiv 2022

  19. [19]

    Micro Black Hole Dark Matter,

    M. Ettengruber and F. Kuhnel, “Micro Black Hole Dark Matter,”arXiv:2506.14871 [hep-th]

    Pith/arXiv arXiv

  20. [20]

    The dark dimension and the Swampland,

    M. Montero, C. Vafa, and I. Valenzuela, “The dark dimension and the Swampland,”JHEP02(2023) 022, arXiv:2205.12293 [hep-th]

    Pith/arXiv arXiv 2023

  21. [21]

    The dark universe: Primordial black hole⇋dark graviton gas connection,

    L. A. Anchordoqui, I. Antoniadis, and D. Lust, “The dark universe: Primordial black hole⇋dark graviton gas connection,”Phys. Lett. B840(2023) 137844, arXiv:2210.02475 [hep-th]

    Pith/arXiv arXiv 2023

  22. [22]

    Kinematical Test of Large Extra Dimension in Beta Decay Experiments,

    V. S. Basto-Gonzalez, A. Esmaili, and O. L. G. Peres, “Kinematical Test of Large Extra Dimension in Beta Decay Experiments,”Phys. Lett. B718(2013) 1020–1023,arXiv:1205.6212 [hep-ph]

    Pith/arXiv arXiv 2013

  23. [23]

    Constraining new physics scenarios in neutrino oscillations from Daya Bay data,

    I. Girardi and D. Meloni, “Constraining new physics scenarios in neutrino oscillations from Daya Bay data,” 13 Phys. Rev. D90no. 7, (2014) 073011,arXiv:1403.5507 [hep-ph]

    Pith/arXiv arXiv 2014

  24. [24]

    Testing for Large Extra Dimensions with Neutrino Oscillations,

    P. A. N. Machado, H. Nunokawa, and R. Zukanovich Funchal, “Testing for Large Extra Dimensions with Neutrino Oscillations,”Phys. Rev. D 84(2011) 013003,arXiv:1101.0003 [hep-ph]

    Pith/arXiv arXiv 2011

  25. [25]

    Updated Constraints on Large Extra Dimensions from Reactor Antineutrino Experiments,

    T. G. Ela¸ cmaz, I. Martinez-Soler, and Y. F. Perez-Gonzalez, “Updated Constraints on Large Extra Dimensions from Reactor Antineutrino Experiments,” arXiv:2510.12900 [hep-ph]

    arXiv

  26. [26]

    Dark Dimension Right-handed Neutrinos Confronted with Long-Baseline Oscillation Experiments,

    A.-Y. Bai, A. Chatrabhuti, Y.-Y. Huang, H. Isono, and J. Tang, “Dark Dimension Right-handed Neutrinos Confronted with Long-Baseline Oscillation Experiments,”arXiv:2601.00790 [hep-ph]

    Pith/arXiv arXiv

  27. [27]

    Neutrino data analysis of extra-dimensional theories with massive bulk fields,

    P. Eller, M. Ettengruber, and A. Zander, “Neutrino data analysis of extra-dimensional theories with massive bulk fields,”Phys. Rev. D112no. 5, (2025) 055009, arXiv:2508.04274 [hep-ph]

    Pith/arXiv arXiv 2025

  28. [28]

    Neutrino masses and phenomenology in N-naturalness,

    M. Ettengruber, “Neutrino masses and phenomenology in N-naturalness,”Phys. Rev. D112no. 5, (2025) 055015,arXiv:2502.09538 [hep-ph]

    Pith/arXiv arXiv 2025

  29. [29]

    Consistent origin of neutrino mass and freeze-in dark matter in large N theories,

    Z.-L. Han, B. Zhu, L. Bian, and R. Ding, “Consistent origin of neutrino mass and freeze-in dark matter in large N theories,”arXiv:1812.00637 [hep-ph]

    Pith/arXiv arXiv

  30. [30]

    Testing the number of neutrino species with a global fit of neutrino data,

    M. Ettengruber, A. Zander, and P. Eller, “Testing the number of neutrino species with a global fit of neutrino data,”Phys. Rev. D109no. 9, (2024) 095016, arXiv:2402.00490 [hep-ph]

    Pith/arXiv arXiv 2024

  31. [31]

    i-ncidental N-naturalness,

    B. Batell, A. Ghalsasi, W. Huang, and M. Low, “i-ncidental N-naturalness,”JHEP05(2026) 127, arXiv:2512.14841 [hep-ph]

    arXiv 2026

  32. [32]

    Black Holes and Large N Species Solution to the Hierarchy Problem,

    G. Dvali, “Black Holes and Large N Species Solution to the Hierarchy Problem,”Fortsch. Phys.58(2010) 528–536,arXiv:0706.2050 [hep-th]

    Pith/arXiv arXiv 2010

  33. [33]

    A cosmological case study of a tower of warm dark matter states:Nnaturalness,

    S. Bansal, S. Ghosh, M. Low, and Y. Tsai, “A cosmological case study of a tower of warm dark matter states:Nnaturalness,”arXiv:2410.19224 [astro-ph.CO]

    Pith/arXiv arXiv

  34. [34]

    Newtrinos.jl: Julia package for global analysis of neutrino data

    P. Eller, “Newtrinos.jl: Julia package for global analysis of neutrino data.” https://github.com/philippeller/Newtrinos.jl, 2025

    2025

  35. [35]

    Constraints on non-unitary neutrino mixing in light of atmospheric and reactor neutrino data,

    T. Kozynets, P. Eller, A. Zander, M. Ettengruber, and D. J. Koskinen, “Constraints on non-unitary neutrino mixing in light of atmospheric and reactor neutrino data,”JHEP05(2025) 130,arXiv:2407.20388 [hep-ph]

    Pith/arXiv arXiv 2025

  36. [36]

    Black Hole Bound on the Number of Species and Quantum Gravity at LHC,

    G. Dvali and M. Redi, “Black Hole Bound on the Number of Species and Quantum Gravity at LHC,” Phys. Rev. D77(2008) 045027,arXiv:0710.4344 [hep-th]

    Pith/arXiv arXiv 2008

  37. [37]

    The detector system of the daya bay reactor neutrino experiment,

    D. Collaboration, “The detector system of the daya bay reactor neutrino experiment,”Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment811 (03, 2016) 133–161,arXiv:1508.03943 [physics]

    Pith/arXiv arXiv 2016

  38. [38]

    A side-by-side comparison of daya bay antineutrino detectors,

    D. B. Collaboration, “A side-by-side comparison of daya bay antineutrino detectors,”Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment685 (09, 2012) 78–97,arXiv:1202.6181 [physics]

    Pith/arXiv arXiv 2012

  39. [39]

    Atmospheric Neutrino Oscillations: the Full Picture,

    P. Eller, “Atmospheric Neutrino Oscillations: the Full Picture,”arXiv:2606.09714 [hep-ex]

    Pith/arXiv arXiv

  40. [40]

    Potential to identify neutrino mass ordering with reactor antineutrinos at JUNO*,

    JUNO Collaboration, “Potential to identify neutrino mass ordering with reactor antineutrinos at JUNO*,” Chinese Physics C49no. 3, (03, 2025) 033104

    2025

  41. [41]

    Sub-percent precision measurement of neutrino oscillation parameters with JUNO*,

    JUNO Collaboration, “Sub-percent precision measurement of neutrino oscillation parameters with JUNO*,”Chinese Physics C46no. 12, (12, 2022) 123001

    2022

  42. [42]

    Precision measurement of reactor antineutrino oscillation at kilometer-scale baselines by daya bay,

    Daya Bay Collaboration, “Precision measurement of reactor antineutrino oscillation at kilometer-scale baselines by daya bay,”Physical Review Letters130 no. 16, (04, 2023) 161802

    2023

  43. [43]

    Final results of GERDA on the search for neutrinoless double-beta decay,

    GERDA Collaboration, “Final results of GERDA on the search for neutrinoless double-beta decay,”Physical Review Letters125no. 25, (12, 2020) 252502

    2020

  44. [44]

    First results from LEGEND-200 on the search for neutrinoless double beta decay,

    G. Saleh, “First results from LEGEND-200 on the search for neutrinoless double beta decay,”Nuovo Cim. C49no. 1-2, (2026) 5,arXiv:2509.21166 [nucl-ex]

    arXiv 2026

  45. [45]

    Measurement of reactor neutrino oscillation with the first juno data,

    T. J. Collaboration, “Measurement of reactor neutrino oscillation with the first juno data,”Nature654(June,

  46. [46]

    Neutrino masses and mixing: Entering the era of subpercent precision,

    F. Capozzi, W. Giar` e, E. Lisi, A. Marrone, A. Melchiorri, and A. Palazzo, “Neutrino masses and mixing: Entering the era of subpercent precision,” Phys. Rev. D111no. 9, (2025) 093006, arXiv:2503.07752 [hep-ph]. [47]Particle Data GroupCollaboration, S. Navaset al., “Review of particle physics,”Phys. Rev. D110no. 3, (2024) 030001

    Pith/arXiv arXiv 2025

  47. [48]

    First results on the search for lepton number violating neutrinoless double-βdecay with the LEGEND-200 experiment,

    LEGEND Collaboration, “First results on the search for lepton number violating neutrinoless double-βdecay with the LEGEND-200 experiment,”Physical Review Letters136no. 2, (01, 2026) 022701

    2026

  48. [49]

    Nufit-6.0: updated global analysis of three-flavor neutrino oscillations,

    I. Esteban, M. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler, J. P. Pinheiro, and T. Schwetz, “Nufit-6.0: updated global analysis of three-flavor neutrino oscillations,”Journal of High Energy Physics 2024no. 12, (2024) 216

    2024

  49. [50]

    Discovering neutrinoless double-beta decay in the era of precision neutrino cosmology,

    M. Ettengruber, M. Agostini, A. Caldwell, P. Eller, and O. Schulz, “Discovering neutrinoless double-beta decay in the era of precision neutrino cosmology,”Phys. Rev. D106no. 7, (2022) 073004,arXiv:2208.09954 [hep-ph]

    Pith/arXiv arXiv 2022

  50. [51]

    Impact of nuclear matrix element calculations for current and future neutrinoless double beta decay searches,

    F. Pompa, T. Schwetz, and J.-Y. Zhu, “Impact of nuclear matrix element calculations for current and future neutrinoless double beta decay searches,”Journal of High Energy Physics2023no. 6, (06, 2023) 104

    2023

  51. [52]

    Status and future of nuclear matrix elements for neutrinoless double-beta decay: a review,

    J. Engel and J. Men´ endez, “Status and future of nuclear matrix elements for neutrinoless double-beta decay: a review,”Reports on Progress in Physics80 no. 4, (2017) 046301. arXiv:1610.06548 [nucl-th]

    Pith/arXiv arXiv 2017

  52. [55]

    Probing the nature of heavy neutral leptons in direct searches and neutrinoless double beta decay,

    P. D. Bolton, F. F. Deppisch, M. Rai, and Z. Zhang, “Probing the nature of heavy neutral leptons in direct searches and neutrinoless double beta decay,”Nuclear Physics B1010(2025) 116785

    2025

  53. [100]

    In the region 500≤N≤10 4, the theory remains viable only if a fine- tuning of at leastr≤0.1 is introduced

    Considering the JUNO+TAO projected sensitivity and the corresponding global constraints, all values of N <500 are excluded for any choice ofr. In the region 500≤N≤10 4, the theory remains viable only if a fine- tuning of at leastr≤0.1 is introduced. FIG. 7. Excluded regions at 90% C.L. in the (r, N) plane from all the experiments considered for the Majora...

  54. [1000]

    Other experiments, such as MINOS and KamLand have been taken into consideration, but since they are not sensitive enough to the theory parameters, at least at the analysis level performed, they are not reported here. A. Oscillation experiments We make use of two reactor neutrino experiments: Daya Bay and JUNO+TAO. The Daya Bay Reactor Neutrino Experiment ...

    2025

  55. [2026]

    Published: 10 June 2026

    343–348. Published: 10 June 2026

    2026