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Long-baseline neutrino data are compatible with standard oscillations, placing a lower bound of about 0.1 eV on the bulk mass of dark-dimension right-handed neutrinos for a 10-micron extra dimension.

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2026-08-03 12:59 UTC pith:LLFK3HKJ

load-bearing objection A competent first pass at long-baseline constraints on dark-dimension neutrino bulk masses, but the headline bounds lean on an implausibly tight T2K calibration pull and need a more realistic systematics treatment before they can be trusted. the 4 major comments →

arxiv 2601.00790 v2 pith:LLFK3HKJ submitted 2026-01-02 hep-ph astro-ph.COgr-qchep-th

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

Ai-Yu Bai , Auttakit Chatrabhuti , Yin-Yuan Huang , Hiroshi Isono , Jian Tang This is my paper
classification hep-ph astro-ph.COgr-qchep-th
keywords dark dimensionright-handed neutrinosextra dimensionsneutrino oscillationslong-baseline experimentsKaluza-Klein modesbulk massneutrino mass constraints
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 tests a quantum-gravity-motivated scenario in which right-handed neutrinos live in an extra dimension about ten micrometers thick, while ordinary particles stay on a four-dimensional brane. It computes the oscillation probabilities that such a 'dark dimension' would imprint on the two long-baseline experiments T2K and NOvA, including the effects of the full tower of Kaluza-Klein modes, and compares the predicted spectra with the published data. The central finding is that the data are fully compatible with standard three-neutrino oscillations; no statistically significant deviation appears. The absence of a signal leads the authors to exclude physical bulk masses below roughly 0.1 eV for a compactification radius of 10 µm, which in dimensionless units corresponds to |¯c1|≳5.2 for normal hierarchy and |¯c3|≳4 for inverted hierarchy at 90% confidence. This matters because it is a direct laboratory handle on a microscopic size scale suggested by quantum gravity, complementary to collider and cosmological constraints.

Core claim

The paper's central claim is that the dark-dimension model with right-handed neutrinos in the bulk is not needed to explain any observed neutrino oscillation data: the T2K and NOvA spectra are consistent with the standard three-flavor hypothesis. On the model parameter space, this consistency translates into an exclusion region in the plane of the dimensionless bulk mass |¯c| and the brane coupling ¯µ (or ¯µ for the relevant hierarchy). For a fixed compactification radius R=10 µm and small brane coupling ¯µ=0.1, the excluded region implies lower bounds |¯c1|≳5.2 in normal hierarchy and |¯c3|≳4 in inverted hierarchy at 90% CL, corresponding to physical bulk masses |c1|≳0.10 eV and |c3|≳0.08 e

What carries the argument

The central mechanism is the five-dimensional dark-dimension model: three right-handed neutrino fields propagate along an interval of length πR, while standard-model fields are confined to a 4D brane at one end. The key object that carries the calculation is the Kaluza-Klein mass matrix M_i, whose square eigenvalues m_i(ℓ) and eigenvectors L_i(n)(ℓ) determine the neutrino masses and mixings. In the infinite-KK limit the characteristic equation reduces to a 3×3 determinantal condition det T(x)=0 with the resummed function t_i(x) = π¯µ_i²√(x-¯c_i²) cot(π√(x-¯c_i²)) - x - π¯µ_i²¯c_i, whose roots are the mass eigenvalues. The paper evaluates the oscillation probabilities by numerically diagonali

Load-bearing premise

The analysis models T2K and NOvA systematic uncertainties with simplified pull parameters—5% signal normalization, 10% background, and for T2K a 0.01% calibration uncertainty—which are far less elaborate than the real detector systematics; if the true uncertainties are larger, the exclusion contours and the derived lower bounds on the bulk mass could shrink substantially.

What would settle it

Recompute the exclusion contours using the actual published covariance matrices from T2K and NOvA instead of the simplified pulls. If the 90% CL exclusion region no longer excludes the benchmark parameter point (R=10 µm, ¯µ=0.1, |¯c|=4) in normal hierarchy, the paper's claim of a stringent exclusion at 10 µm would be falsified.

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

If this is right

  • The bounds imply that, within the dark-dimension model, any right-handed neutrino with bulk mass below about 0.1 eV is impossible at a 10 µm radius; such light states cannot generate the observed neutrino mass pattern.
  • These constraints are complementary to those from colliders and cosmology: together they move the allowed dark-dimension parameter space toward larger bulk masses or smaller radii.
  • Future long-baseline experiments with higher statistics should be able to either discover the KK imprint or push the exclusion to larger masses.
  • The paper's construction shows that in the large-bulk-mass limit the model degenerates to the standard three-neutrino scenario, so the absence of a signal here is consistent with expectations if the bulk mass is large.
  • For sub-micrometer dark-dimension proposals, the bounds derived here weaken, so other probes (e.g., reactor experiments) are needed to constrain those scenarios.

Where Pith is reading between the lines

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

  • The 0.01% calibration uncertainty adopted for T2K is surprisingly small; if the real T2K calibration uncertainty is closer to the 2.5% used for NOvA, the exclusion contour could shift to significantly smaller |¯c| values, weakening the quoted lower bounds by roughly a factor of two.
  • A natural next step is to apply the same KK-tower likelihood machinery to short-baseline reactor antineutrino experiments, where the spectral distortion caused by the KK modes would appear at different energies and baselines; the paper's current framework could be adapted to test the same parameters.
  • The paper treats the bulk-brane couplings as real; allowing them to be complex would introduce CP violation from the KK tower, which could be probed by the difference between neutrino and antineutrino appearance probabilities in future experiments—an extension the authors flag as worth investigating.
  • Because the data are consistent with standard oscillations, any future anomalous signal in long-baseline facilities should first be checked against the dark-dimension model before interpreting it as evidence for other new physics, and the exclusion contours presented here provide the baseline for such comparisons.

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

4 major / 5 minor

Summary. The paper studies a 5D 'dark dimension' model in which three bulk right-handed neutrinos with masses c_i propagate on an interval, generating Dirac neutrino masses through brane-localized Yukawa couplings. It derives vacuum and matter oscillation probabilities including the full KK tower, with two of the µ_i fixed by the observed neutrino mass-squared differences. Using a modified GLoBES code and simplified simulations of T2K and NOvA with published data, the paper computes χ² and presents 68% and 90% exclusion contours in the |¯c_i|--¯µ_1 (NH) or |¯c_i|--¯µ_3 (IH) plane for R = 10 µm. The central quantitative claims are the lower bounds |¯c_1| ≳ 5.2 (NH) and |¯c_3| ≳ 4 (IH), equivalent to |c_1| ≳ 0.10 eV and |c_3| ≳ 0.08 eV. The abstract further states that the T2K and NOvA data are compatible with the standard neutrino oscillation hypothesis.

Significance. If the quoted bounds are robust, they constitute a direct long-baseline constraint on massive bulk right-handed neutrinos in the dark-dimension parameter region |c_i|R > 1 and are complementary to KATRIN and collider bounds. The paper has clear strengths: the analytic treatment of the KK eigenvalue problem, the extension to matter with a finite KK cutoff, the explicit cutoff-convergence check in Fig. 2, and the public code release. However, the quantitative result rests on a simplified statistical model with an unrealistically tight T2K calibration systematic and an ad hoc energy-smoothing procedure. These issues directly affect the central lower bounds and must be validated before the constraints can be accepted as quantitative.

major comments (4)
  1. [§3.3, Eq. (3.1), Figs. 7–8] The T2K calibration uncertainty is set to 0.01% for both signal and background. In the pull penalty (ξ_k/σ_k)^2, σ = 10^-4 makes a 0.1% spectral distortion cost about 100 and a 1% distortion about 10^4. The DD-induced event-rate differences visible in Fig. 5 are at the several-percent level per bin, so these differences are effectively forced to be incompatible by the pull term. Published T2K analyses use a much richer set of correlated systematics, with calibration/energy-scale uncertainties at least an order of magnitude larger; no reference or justification is given for 0.01%. Because the quoted |¯c| lower bounds come from these contours, the central quantitative claim is not secure until the analysis is repeated with realistic T2K systematics, ideally the public covariance matrices.
  2. [§3.4.1, Figs. 2–4] A low-pass filter of 0.03 GeV is applied to both standard and DD probabilities, but no full detector energy response or migration matrix is described, and the filter is not matched to T2K/NOvA reconstructed-energy resolution. If the filter is intended to remove numerical ringing from the finite-KK cutoff, the paper should show that it does not also remove physical DD oscillations. If it is intended to emulate detector resolution, 0.03 GeV appears considerably smaller than the realistic reconstructed-energy resolution of these experiments, which would preserve high-frequency sensitivity and overstate the constraints. The authors should either implement a proper detector response or demonstrate that the constraints are stable under the choice of filter.
  3. [§3.1, Table 1, §3.3] The standard oscillation parameters are taken from NuFIT 6.0, which includes T2K and NOvA data, while the same experiments are then used to derive the DD exclusion contours. Only θ_13 and Δm^2_32 are marginalized; θ_23 and δ_CP, which strongly affect ν_e appearance and ν_µ disappearance at these baselines, are held fixed. This introduces a self-referential element and can bias the Δχ² contours. The authors should either marginalize over the full set of standard oscillation parameters, or use priors from a global fit that excludes T2K/NOvA, and show that the lower bounds are stable.
  4. [§3.4.3 and Abstract] The abstract states that the data are compatible with the standard neutrino oscillation hypothesis, but the paper reports no absolute goodness-of-fit for the standard oscillation scenario. Only Δχ² contours relative to the standard fit are shown. If the standard oscillation model itself provides a poor description of the adopted data set, the exclusion contours would not constitute a meaningful test of the DD hypothesis. The authors should report χ^2_min for the standard fit and, ideally, a p-value or equivalent compatibility statement.
minor comments (5)
  1. [§4] Typo: 'secranio' should be 'scenario'.
  2. [Captions of Figs. 7–8] The captions say '68% (black line) and 90% (black line)', which is confusing. The solid/dashed line distinction is between marginalization strategies, but the line styles should be clearly defined in the caption.
  3. [§3.3] The notation λ_fit_i and λ_data_i in Eq. (3.1) is not fully specified. The text should state explicitly which parameters carry priors and which are treated as fixed.
  4. [§3.2] The matter density profile used in the GLoBES simulation and its assumed uncertainty are not stated explicitly, although ρ is mentioned as a parameter in Eq. (3.1). This should be documented for reproducibility.
  5. [§3.4.2, Figs. 5–6] The 'Data' histograms are shown without statistical or systematic error bars, which makes visual comparisons of the standard and DD curves difficult. Adding error bars or a χ^2 table would improve transparency.

Circularity Check

0 steps flagged

No significant circularity: DD exclusion limits are driven by KK-mode spectral deviations, not by fitted inputs; self-citations are non-load-bearing.

full rationale

The derivation chain is a standard model-comparison. The paper fixes µ̄2,µ̄3 to reproduce observed Δm² via Eq. (2.42), scans (|č|, µ̄1/µ̄3), computes T2K/NOvA spectra in GLoBES, and reports χ² differences. The quoted bounds |č1|≳ 5.2 (NH) and |č3|≳ 4 (IH) come from spectral shapes, i.e., the KK-mode-induced deviation from the standard curve; they are not a re-packaged input. The standard parameters are taken from NuFIT 6.0, an external global fit; although NuFIT 6.0 includes T2K/NOvA data, this is the usual null-model calibration and not a circular prediction, because the DD parameters are scanned rather than fitted to the same observables. The paper's self-citation [31] (same authors Chatrabhuti and Isono) provides notation, the c2,c3<0 parameter choice, and a 3+1/KATRIN correspondence, but the exclusion computation is self-contained and does not reduce to that citation. The 0.01% T2K calibration pull affects statistical robustness, not logical circularity. No equation in the paper sets a prediction equal to a fitted parameter by construction.

Axiom & Free-Parameter Ledger

3 free parameters · 6 axioms · 0 invented entities

The paper does not introduce new particles or forces; it tests an existing dark-dimension framework. The load-bearing inputs are the equal-mass slice, the zero-mode identification, and the simplified experimental systematics.

free parameters (3)
  • R (compactification radius) = 10 µm (fixed)
    Chosen as a representative dark-dimension scale; the exclusion limits are conditional on this value.
  • |¯c| = |c_i| R (equal bulk masses) = scanned in [2.5, 10]
    The scanned dimensionless bulk mass; excluded regions in Figs. 7-8 are the central result.
  • ¯µ1 (NH) or ¯µ3 (IH) = scanned in [0.2, 1.4]
    The free bulk-brane coupling for the lightest generation; the other two are fixed by observed Δm² via Eq. (2.42).
axioms (6)
  • domain assumption The 5D dark-dimension model with bulk right-handed neutrinos and compactification radius ~10 µm exists as described in Refs. [6, 8-10].
    The paper builds on this framework rather than justifying it.
  • domain assumption Zero-mode masses m_i(0) are identified with the observed active neutrino masses; the observed Δm² fix two of the ¯µ_i via Eq. (2.42).
    This removes two parameters but assumes the active neutrinos are exactly the zero modes.
  • domain assumption Equal absolute bulk masses |¯c1|=|¯c2|=|¯c3| with signs c1>0, c2,c3<0 (NH) or c3>0, c1,c2<0 (IH).
    Restricts the scan to a symmetric slice of parameter space; limits are not valid for general mass patterns.
  • standard math Matter effect for the active neutrinos is described by the standard weak potential in the intermediate basis.
    Standard MSW effect applied to the 5D model; see Eq. (2.18).
  • ad hoc to paper The KK mode cutoff N=40 and the 0.03 GeV low-pass filter yield converged and physical oscillation probabilities.
    The cutoff is checked in Fig. 2; the filter is introduced without formal justification.
  • ad hoc to paper Simplified systematic uncertainties (5% signal, 10% background, 0.01% T2K calibration) approximate the real experiments.
    These are much simpler than the true T2K/NOvA systematics and could bias the bounds.

pith-pipeline@v1.3.0-alltime-deepseek · 20710 in / 19819 out tokens · 282492 ms · 2026-08-03T12:59:16.053845+00:00 · methodology

0 comments
read the original abstract

Right-handed neutrinos are naturally induced by dark extra dimension models and play an essential role in neutrino oscillations. The model parameters can be examined by the long-baseline neutrino oscillation experiments. In this work, we compute the predicted neutrino oscillation spectra within/without extra dimension models and compare them with the experimental data. We find that the neutrino data in the T2K and NOvA experiments are compatible with the standard neutrino oscillation hypothesis. The results set the stringent exclusion limit on the extra dimension model parameters at a high confidence level. The derived constraints on dark dimension right-handed neutrinos are complementary to those results from the collider experiments and cosmological observations.

Figures

Figures reproduced from arXiv: 2601.00790 by Ai-Yu Bai, Auttakit Chatrabhuti, Hiroshi Isono, Jian Tang, Yin-Yuan Huang.

Figure 1
Figure 1. Figure 1: Panel (a) plots the values of the squared mixing coefficients in vacuum |Li 0(n) | 2 for n = 1, . . . , 40. Panels (b), (c), (d) plots the values of the squared mixing coefficients |L10(kn) | 2 , |L20(kn) | 2 , |L30(kn) | 2 , respectively. Parameters for the plots are ¯c1 = −c¯2 = −c¯3 = 4 and ¯µ1 = 0.1 with ¯µ2, µ¯3 determined by (2.42) in NH. In matter. Let us consider the case in matter. In this article… view at source ↗
Figure 2
Figure 2. Figure 2: Left panel: Difference on Pνµ→νµ with different KK modes cutoff values when {R, |c¯i |, ¯µ1} are set as {10 µm, 4, 0.1} and the baseline of NOvA is used. The low-pass filter is used to smooth the curves, which is discussed in Section 3.4.1. Right panel: the L 2 norm between Pνµ→νµ with cutoff ∈ [5, 120] and Pνµ→νµ with a fixed cutoff of 200. on the simulated neutrino oscillation spectra. The results obtain… view at source ↗
Figure 3
Figure 3. Figure 3: Neutrino oscillation probabilities for both standard oscillation and DD models at the [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Oscillation probabilities for both standard oscillation and DD models at the NOvA FD [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The reconstructed neutrino energy spectra for the FD [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The reconstructed neutrino energy spectra for the FD [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The exclusion limits at 68% (black line) and 90% (black line) C.L. in the T2K [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The exclusion limits at 68% (black line) and 90% (black line) C.L. in the NOvA [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗

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