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arxiv: 2509.05233 · v2 · pith:7D436GCAnew · submitted 2025-09-05 · ✦ hep-ph · astro-ph.CO· hep-th

Searching for a Dark Dimension Right-handed Neutrino in KATRIN

Ignatios Antoniadis , Auttakit Chatrabhuti , Hiroshi Isono This is my paper

Pith reviewed 2026-05-21 21:52 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COhep-th
keywords right-handed neutrinodark dimensionKATRINbeta decayKaluza-Klein excitationsextra dimensionssterile neutrino
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The pith

A right-handed neutrino in a micron-scale extra dimension could produce detectable kinks in the KATRIN tritium beta-decay spectrum.

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

The paper examines the possibility that the right-handed neutrino is a five-dimensional field traveling along the extra dimension proposed in the dark dimension scenario. It calculates how this neutrino and its Kaluza-Klein excitations would distort the electron energy spectrum in tritium beta decay, creating one or more kinks at characteristic energies. The analysis shows that a substantial portion of the viable parameter space for the compactification scale, bulk mass, and Yukawa coupling falls inside the sensitivity reach of the KATRIN experiment. Depending on whether the bulk mass is small or large compared with the compactification scale, the spectrum may exhibit several distinct kinks or collapse to a single effective kink.

Core claim

We show that a large part of the allowed parameter space of the compactification scale and the R-neutrino bulk mass versus the Yukawa coupling is within KATRIN's sensitivity. When the bulk mass is much smaller than the compactification scale, several kinks could be observed corresponding to the positions of the R-neutrino Kaluza-Klein excitations, while for large bulk mass there will be effectively one kink at the position of the bulk mass.

What carries the argument

Five-dimensional right-handed neutrino bulk field with bulk mass and Yukawa coupling to active neutrinos, whose Kaluza-Klein tower imprints kinks on the tritium beta-decay electron spectrum.

If this is right

  • Multiple distinct kinks appear in the spectrum when the bulk mass is much smaller than the compactification scale.
  • A single effective kink occurs at the bulk mass position when the bulk mass is large compared with the compactification scale.
  • A substantial fraction of the parameter space in compactification scale, bulk mass, and Yukawa coupling lies within current KATRIN reach.
  • The signatures differ from those of a simple four-dimensional sterile neutrino by the possible presence of a tower of excitations.

Where Pith is reading between the lines

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

  • This model offers a way to connect extra-dimension proposals directly to low-energy neutrino experiments without requiring high-energy colliders.
  • Non-observation in KATRIN data would tighten bounds on the allowed size of the extra dimension in this framework.
  • The predicted spectral features could help distinguish bulk neutrino scenarios from conventional sterile neutrino models in future analyses.

Load-bearing premise

The right-handed neutrino propagates as a five-dimensional bulk field in a micron-size extra dimension and couples to active neutrinos with a Yukawa strength large enough to create an observable distortion in the beta-decay spectrum.

What would settle it

No kink-like features appearing in the KATRIN electron energy spectrum at the energies predicted by the allowed range of bulk masses and compactification scales would rule out observable effects from this scenario.

Figures

Figures reproduced from arXiv: 2509.05233 by Auttakit Chatrabhuti, Hiroshi Isono, Ignatios Antoniadis.

Figure 1
Figure 1. Figure 1: The two panels illustrate the roots of the mass equation ( [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: For an extra dimension with radius R = 0.2 µm, the region near the endpoint of the spectrum is distorted due to the KK modes. In this case, KK modes with n = 1, 2 contribute. We can see the two characteristic “kink” signatures on the spectrum. our convenience, we show only two kinks of the two lowest KK modes n = 1, 2. Note that not all KK modes can be included in the KATRIN observational window (0 − 40 eV… view at source ↗
Figure 3
Figure 3. Figure 3: The left panel depicts a general structure of the mass spectrum. The right panel [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Sterile neutrino exclusion contour and the simulated sensitivity contour from KATRIN [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Exclusion contours for R = 1.0 and 10.0 µm in the (¯c, µ¯1)-plane are shown in the black dashed and solid curves respectively. The blue curve represents the sin2 (θ max eff ) = 0.050 boundary. Since R2 |∆m2 i3 |/(2π|c¯|) ≲ O(1), all ¯µ 2 i satisfy (4.15). The effective mixing sin2 θeff can then be written as sin2 θeff ≃ πµ¯ 2 1 2|c¯| [PITH_FULL_IMAGE:figures/full_fig_p025_5.png] view at source ↗
read the original abstract

We study the possibility that the Right-handed neutrino is a five-dimensional state propagating along a micron size extra dimension, as required in the dark dimension proposal. We work out the signatures of R-neutrino production in KATRIN experiment and compare them with those of a sterile neutrino which manifests by a kink in the electron energy spectrum of the beta-decay at a value corresponding to the sterile neutrino mass. We explore the allowed parameter space of the compactification scale and the R-neutrino bulk mass versus the Yukawa coupling, and show that a large part of it is within KATRIN's sensitivity. When the bulk mass is much smaller than the compactification scale, several kinks could be observed corresponding to the positions of the R-neutrino Kaluza-Klein excitations, while for large bulk mass there will be effectively one kink at the position of the bulk mass.

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 manuscript proposes that the right-handed neutrino is realized as a five-dimensional bulk field propagating along the micron-scale extra dimension of the dark dimension scenario. It derives the resulting distortions to the tritium beta-decay electron spectrum observable at KATRIN, including multiple kinks from Kaluza-Klein excitations when the bulk mass is much smaller than the compactification scale, or a single effective kink when the bulk mass is large. The authors map the three-dimensional parameter space of compactification scale, bulk mass, and Yukawa coupling and conclude that a substantial fraction lies within KATRIN reach.

Significance. If the central results hold after external constraints are applied, the work supplies a concrete, falsifiable test of the dark dimension proposal at an existing precision experiment. The diagnostic distinction between multi-kink and single-kink regimes is a useful phenomenological feature. The connection between the 5D Dirac equation and beta-decay kinematics is a clear strength.

major comments (2)
  1. [§4] §4 (parameter-space exploration): the claim that a large part of the (compactification scale, bulk mass, Yukawa) space yields an observable KATRIN signal does not fold in cosmological bounds on N_eff and structure formation or existing laboratory limits from reactor, tritium, and meson-decay searches. These constraints may exclude most of the region flagged as accessible, directly undermining the headline sensitivity statement.
  2. [Signatures section] Signatures section: the mixing-angle formulas, the explicit reduction of the 5D Dirac equation to the effective 4D spectrum, and the numerical evaluation of the kink positions and heights are not shown. Without these derivations the quantitative sensitivity claims cannot be independently verified.
minor comments (2)
  1. [Abstract] The abstract and introduction should explicitly define the three free parameters and their allowed ranges before stating the sensitivity conclusion.
  2. Notation for the bulk mass m_b and compactification radius R should be introduced at first use and kept consistent throughout the equations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and have revised the manuscript to strengthen the presentation and qualify our claims.

read point-by-point responses

  1. Referee: [§4] §4 (parameter-space exploration): the claim that a large part of the (compactification scale, bulk mass, Yukawa) space yields an observable KATRIN signal does not fold in cosmological bounds on N_eff and structure formation or existing laboratory limits from reactor, tritium, and meson-decay searches. These constraints may exclude most of the region flagged as accessible, directly undermining the headline sensitivity statement.

    Authors: We agree that a complete discussion of the viable parameter space requires consideration of external constraints. The submitted manuscript concentrated on deriving the KATRIN signatures specific to the dark-dimension realization of the right-handed neutrino and on mapping the three-dimensional parameter space for KATRIN sensitivity. In the revised version we will add a dedicated subsection in §4 that summarizes the relevant cosmological bounds on N_eff and structure formation as well as existing laboratory limits from reactor, tritium, and meson-decay searches. We will indicate which portions of the KATRIN-accessible region survive these constraints and which are already excluded, thereby qualifying the headline statement about the fraction of parameter space that remains testable. revision: yes

  2. Referee: [Signatures section] Signatures section: the mixing-angle formulas, the explicit reduction of the 5D Dirac equation to the effective 4D spectrum, and the numerical evaluation of the kink positions and heights are not shown. Without these derivations the quantitative sensitivity claims cannot be independently verified.

    Authors: We acknowledge that the derivations underlying the mixing angles, the reduction of the five-dimensional Dirac equation, and the numerical determination of kink locations and heights were not presented in sufficient detail. In the revised manuscript we will expand the Signatures section (or add a short appendix) to provide the explicit mixing-angle formulas, the step-by-step reduction from the 5D Dirac equation to the effective four-dimensional spectrum, and the numerical procedure used to evaluate kink positions and heights. This addition will allow independent verification of the quantitative results. revision: yes

Circularity Check

0 steps flagged

No significant circularity in KATRIN signature derivation

full rationale

The paper derives observable kinks in the tritium beta-decay spectrum by solving the 5D Dirac equation for a bulk right-handed neutrino and applying standard beta-decay kinematics to the resulting Kaluza-Klein modes or effective bulk mass. These steps are independent of the dark dimension proposal's motivations and use the compactification scale, bulk mass, and Yukawa coupling as free inputs whose observable consequences are computed explicitly. No self-definitional loops, fitted parameters renamed as predictions, or load-bearing self-citations that reduce the central claim to unverified inputs are present. The analysis remains self-contained and falsifiable against KATRIN data regardless of external cosmological bounds.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 1 invented entities

The central claim rests on the dark dimension framework and standard 5D field theory; the three parameters are varied rather than derived, and the 5D right-handed neutrino is introduced without independent evidence.

free parameters (3)
  • compactification scale
    Micron-size extra dimension taken from the dark dimension proposal; sets the KK mass spacing.
  • bulk mass
    Additional 5D mass parameter for the right-handed neutrino field; controls the location of the effective kink.
  • Yukawa coupling
    Determines the mixing strength with active neutrinos and therefore the size of the spectral distortion.
axioms (2)
  • domain assumption The right-handed neutrino propagates as a 5D bulk field in a compactified extra dimension of micron size.
    Core premise imported from the dark dimension proposal.
  • standard math Each massive neutrino eigenstate produces a kink in the beta-decay electron spectrum at energy Q minus its mass.
    Standard kinematic result used in all neutrino-mass searches.
invented entities (1)
  • 5D right-handed neutrino with Kaluza-Klein tower no independent evidence
    purpose: To generate neutrino masses while realizing the dark dimension scenario.
    Postulated 5D field whose KK modes are the source of the predicted kinks; no independent falsifiable signature outside this model is given.

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Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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

    hep-ph 2026-01 unverdicted novelty 3.0

    Dark dimension right-handed neutrino models are confronted with T2K and NOvA long-baseline oscillation data, yielding exclusion limits on model parameters while remaining compatible with standard three-neutrino oscillations.

  3. Do neutrinos dream in 5D? Towards a comprehensive extra-dimensional neutrino phenomenology

    hep-ph 2025-12 unverdicted novelty 3.0

    Surveys neutrino masses and mixing in 5D large extra dimension scenarios across four mass-generation cases and derives constraints from oscillation data.

Reference graph

Works this paper leans on

31 extracted references · 31 canonical work pages · cited by 3 Pith papers · 19 internal anchors

  1. [1]

    Green, J.H

    M.B. Green, J.H. Schwarz and E. Witten,SUPERSTRING THEORY, Vols I and II, Cambridge Monographs on Mathematical Physics (1988)

    work page 1988

  2. [2]

    Antoniadis,A Possible new dimension at a few TeV,Phys

    I. Antoniadis,A Possible new dimension at a few TeV,Phys. Lett. B246(1990) 377

    work page 1990

  3. [3]

    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 [hep-ph/9803315]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  4. [4]

    New Dimensions at a Millimeter to a Fermi and Superstrings at a TeV

    I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali,New dimensions at a millimeter to a Fermi and superstrings at a TeV,Phys. Lett. B436(1998) 257 [hep-ph/9804398]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  5. [5]

    Light Neutrinos without Heavy Mass Scales: A Higher-Dimensional Seesaw Mechanism

    K.R. Dienes, E. Dudas and T. Gherghetta,Neutrino oscillations without neutrino masses or heavy mass scales: A Higher dimensional seesaw mechanism,Nucl. Phys. B557 (1999) 25 [hep-ph/9811428]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  6. [6]

    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 [hep-ph/9811448]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  7. [7]

    Probing Large Extra Dimensions with Neutrinos

    G.R. Dvali and A.Y. Smirnov,Probing large extra dimensions with neutrinos,Nucl. Phys. B563(1999) 63 [hep-ph/9904211]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  8. [8]

    MSLED: A Minimal Supersymmetric Large Extra Dimensions Scenario

    C.P. Burgess, J. Matias and F. Quevedo,MSLED: A Minimal supersymmetric large extra dimensions scenario,Nucl. Phys. B706(2005) 71 [hep-ph/0404135]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  9. [9]

    Montero, C

    M. Montero, C. Vafa and I. Valenzuela,The dark dimension and the Swampland,JHEP 02(2023) 022 [2205.12293]

    work page arXiv 2023

  10. [10]

    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 [0706.2050]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  11. [11]

    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 [0710.4344]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  12. [12]

    Lee, E.G

    J.G. Lee, E.G. Adelberger, T.S. Cook, S.M. Fleischer and B.R. Heckel,New Test of the Gravitational1/r 2 Law at Separations down to 52µm,Phys. Rev. Lett.124(2020) 101101 [2002.11761]

    work page arXiv 2020

  13. [13]

    The String Landscape and the Swampland

    C. Vafa,The String landscape and the swampland,hep-th/0509212. 29

    work page internal anchor Pith review Pith/arXiv arXiv

  14. [14]

    On the Geometry of the String Landscape and the Swampland

    H. Ooguri and C. Vafa,On the Geometry of the String Landscape and the Swampland, Nucl. Phys. B766(2007) 21 [hep-th/0605264]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  15. [15]

    L¨ ust, E

    D. L¨ ust, E. Palti and C. Vafa,AdS and the Swampland,Phys. Lett. B797(2019) 134867 [1906.05225]

    work page arXiv 2019

  16. [16]

    Anchordoqui, I

    L.A. Anchordoqui, I. Antoniadis and D. Lust,Two Micron-Size Dark Dimensions, Fortsch. Phys.73(2025) e70015 [2501.11690]

    work page arXiv 2025

  17. [17]

    Anchordoqui, I

    L.A. Anchordoqui, I. Antoniadis and D. L¨ ust,Landscape, Swampland, and Extra Dimensions,PoSCORFU2023(2024) 215 [2405.04427]

    work page arXiv 2024

  18. [18]

    Anchordoqui, I

    L.A. Anchordoqui, I. Antoniadis and D. Lust,Aspects of the dark dimension in cosmology,Phys. Rev. D107(2023) 083530 [2212.08527]

    work page arXiv 2023

  19. [19]

    Constraining Neutrino Masses, the Cosmological Constant and BSM Physics from the Weak Gravity Conjecture

    L.E. Ibanez, V. Martin-Lozano and I. Valenzuela,Constraining Neutrino Masses, the Cosmological Constant and BSM Physics from the Weak Gravity Conjecture,JHEP11 (2017) 066 [1706.05392]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  20. [20]

    Anchordoqui, I

    L.A. Anchordoqui, I. Antoniadis and J. Cunat,Dark dimension and the standard model landscape,Phys. Rev. D109(2024) 016028 [2306.16491]

    work page arXiv 2024

  21. [21]

    Non-supersymmetric AdS and the Swampland

    H. Ooguri and C. Vafa,Non-supersymmetric AdS and the Swampland,Adv. Theor. Math. Phys.21(2017) 1787 [1610.01533]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  22. [22]

    Quantum Horizons of the Standard Model Landscape

    N. Arkani-Hamed, S. Dubovsky, A. Nicolis and G. Villadoro,Quantum Horizons of the Standard Model Landscape,JHEP06(2007) 078 [hep-th/0703067]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  23. [23]

    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. D84(2011) 013003 [1101.0003]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  24. [24]

    Forero, C

    D.V. Forero, C. Giunti, C.A. Ternes and O. Tyagi,Large extra dimensions and neutrino experiments,Phys. Rev. D106(2022) 035027 [2207.02790]

    work page arXiv 2022

  25. [25]

    Solar neutrino oscillation from large extra dimensions

    A. Lukas, P. Ramond, A. Romanino and G.G. Ross,Solar neutrino oscillation from large extra dimensions,Phys. Lett. B495(2000) 136 [hep-ph/0008049]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  26. [26]

    Neutrino Masses and Mixing in Brane-World Theories

    A. Lukas, P. Ramond, A. Romanino and G.G. Ross,Neutrino Masses and Mixing in Brane World Theories,JHEP04(2001) 010 [hep-ph/0011295]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  27. [27]

    Neutrinos in Large Extra Dimensions and Short-Baseline $\nu_e$ Appearance

    M. Carena, Y.-Y. Li, C.S. Machado, P.A.N. Machado and C.E.M. Wagner,Neutrinos in Large Extra Dimensions and Short-Baselineν e Appearance,Phys. Rev. D96(2017) 095014 [1708.09548]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  28. [28]

    Eller, M

    P. Eller, M. Ettengruber and A. Zander,A neutrino data analysis of extra-dimensional theories with massive bulk fields,2508.04274. [29]KATRINcollaboration,Improved eV-scale sterile-neutrino constraints from the second KATRIN measurement campaign,Phys. Rev. D105(2022) 072004 [2201.11593]. [30]KATRINcollaboration,First Constraints on General Neutrino Intera...

    work page arXiv 2022

  29. [29]

    NuFit-6.0: Updated global analysis of three-flavor neutrino oscillations

    I. Esteban, M.C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler, J.a.P. Pinheiro and T. Schwetz,NuFit-6.0: updated global analysis of three-flavor neutrino oscillations,JHEP 12(2024) 216 [2410.05380]. [33]KATRINcollaboration,The design, construction, and commissioning of the KATRIN experiment,JINST16(2021) T08015 [2103.04755]. [34]KATRINcollaboration,Dire...

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  30. [30]

    $\beta$-Decay Spectrum, Response Function and Statistical Model for Neutrino Mass Measurements with the KATRIN Experiment

    M. Kleesiek et al.,β-Decay Spectrum, Response Function and Statistical Model for Neutrino Mass Measurements with the KATRIN Experiment,Eur. Phys. J. C79(2019) 204 [1806.00369]. [36]Planckcollaboration,Planck 2018 results. I. Overview and the cosmological legacy of Planck,Astron. Astrophys.641(2020) A1 [1807.06205]. [37]Planckcollaboration,Planck 2018 resu...

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  31. [31]

    Siegmann et al.,Development of a silicon drift detector array to search for keV-scale sterile neutrinos with the KATRIN experiment,J

    D. Siegmann et al.,Development of a silicon drift detector array to search for keV-scale sterile neutrinos with the KATRIN experiment,J. Phys. G51(2024) 085202 [2401.14114]. 31

    work page arXiv 2024