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arxiv: 2511.13515 · v3 · pith:LTXDPLYMnew · submitted 2025-11-17 · ✦ hep-ex

Probing scalar-neutrino and scalar-dark-matter interactions with PandaX-4T

Pith reviewed 2026-05-22 13:03 UTC · model grok-4.3

classification ✦ hep-ex
keywords double beta decayscalar mediatorsneutrino self-interactionsdark matter interactionsHubble tension
0
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The pith

Xenon double beta decay data yields the strongest limits on scalar-mediated neutrino self-interactions for mediator masses below 2 MeV.

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

The paper conducts a spectral search using double beta decay events in xenon to look for effects from scalar particles interacting with neutrinos. By examining the energy distribution from 20 to 2800 keV, it identifies no such distortions and derives the tightest existing upper limits on the interaction strength for light scalars. This constrains theoretical models proposing these interactions as a way to resolve the Hubble constant discrepancy. The analysis also extends to placing bounds on scalar couplings to dark matter particles under shared mediator assumptions.

Core claim

The central claim is that the first direct spectral search with 136Xe double beta decay data in the 20 to 2800 keV range sets the most stringent limits to date on scalar-mediated neutrino self-interactions for mediator masses below 2 MeV/c², placing significant constraints on models for the Hubble Tension and allowing combined limits on dark matter-scalar interactions.

What carries the argument

Scalar-mediated neutrino self-interaction producing a model-independent distortion in the double beta decay spectrum.

If this is right

  • These limits constrain models invoking scalar-mediated neutrino interactions to alleviate the Hubble Tension.
  • Constraints on dark matter-scalar interactions follow when assuming the same scalar mediator and combining with cosmological data.
  • The search establishes a new experimental window for exotic low-energy interactions in the 20-2800 keV range.

Where Pith is reading between the lines

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

  • Similar spectral distortion searches could be performed with data from other double beta decay setups to cross-check the bounds.
  • The results suggest that dedicated low-energy analyses in future xenon detectors could probe even lighter mediators or weaker couplings.
  • If confirmed, such scalars might leave imprints in neutrino propagation over cosmological distances.

Load-bearing premise

The scalar interaction must create a detectable distortion in the double beta decay energy spectrum that stands out clearly from ordinary backgrounds and detector effects.

What would settle it

A high-statistics spectrum from another xenon double beta decay measurement showing either a clear distortion matching the scalar prediction or no deviation at higher sensitivity would test the claimed limits.

Figures

Figures reproduced from arXiv: 2511.13515 by Anqing Wang, Binbin Yan, Binyu Pang, Changda He, Chen Cheng, Chencheng Han, Chenhui Zhu, Chenxiang Li, Chunxu Yu, Congcong Lu, Deqing Fang, Dong Shan, Guanbo Wang, Guofang Shen, Hao Wang, Haoyu Wang, Houqi Huang, Jiafu Li, Jiamin Wang, Jianglai Liu, Jianqin Xu, Jiaxu Zhou, Jiayi Zhou, Jifang Zhou, Jinrong He, Junting Huang, Kaizhi Xiong, Kangkang Zhao, Karl Giboni, Ke Han, Lei Wang, Lingyin Luo, Lisheng Geng, Li Zhao, Manbin Shen, Manna Deng, Mengjiao Xiao, Meng Wang, Michael J. Ramsey-Musolf, Mingchuan Li, Minzhen Zhang, Ningchun Qi, Ning Zhou, PandaX Collaboration: Tao Li, Peihua Ye, Peiyuan Li, Peng Zhang, Qing Lin, Qiuhong Wang, Ruquan Hou, Shaobo Wang, Shibo Wang, Shibo Zhang, Shuaijie Li, Shunyu Yao, Shu Zhang, Siguang Wang, Siyuan Zhang, Tao Li, Tao Zhang, Van Que Tran, Wei Chen, Weihao Wu, Wei Wang, Wei Zhang, Wenliang Sun, Xiangdong Ji, Xiangxiang Ren, Xiang Xiao, Xiangyi Cui, Xiaofeng Shang, Xiaopeng Zhou, Xiaorun Lan, Xiaoying Lu, Xinning Zeng, Xiyuan Shao, Xiyu Yan, Xuanye Fu, Xunan Guo, Xun Chen, Xu Wang, Xuyan Sun, Xuyuan Guo, Yajun Mao, Yangdong Li, Yang Zhang, Yifan Xu, Yihong Zhong, Yingjie Fan, Yingxin Zhang, Ying Yuan, Yi Tao, Yonglin Ju, Yong Yang, Youhui Yun, Yuanchun Liu, Yuan Wu, Yuanyuan Zhang, Yuehuan Wei, Yue Meng, Yueqiang Tian, Yugang Ma, Yuhan Xie, Yujie Ge, Yule Huang, Yunhua Chen, Yunyang Luo, Yuxin Tian, Zhe Yuan, Zhicheng Qian, Zhixing Gao, Zhiyuan Li, Zhizhen Zhou, Zhou Wang, Zichao Guo, Zihao Bo.

Figure 1
Figure 1. Figure 1: FIG. 1. The Feynman diagrams for the double [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The background-only fit to the combined SS data [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Constraints on the coupling [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

Scalar-mediated interactions may exist among neutrinos, dark matter particles, or between the two. Double $\beta$-decay experiments provide a powerful tool to probe such exotic interactions. Using $^{136}$Xe double $\beta$-decay data from PandaX-4T, we perform the first direct spectral search in the energy range of 20 to 2800~keV, setting the most stringent limits to date on scalar-mediated neutrino self-interactions for mediator masses below 2~MeV$/c^2$. These results place significant constraints on models invoking such interactions to alleviate the Hubble Tension. Assuming the same scalar also mediates dark matter self-interactions, constraints on the dark matter-scalar interactions can be placed in conjunction with cosmological constraints.

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 reports a direct spectral search for scalar-mediated neutrino self-interactions using 136Xe double beta decay data from PandaX-4T. The analysis covers the 20–2800 keV energy window and derives upper limits on the scalar coupling for mediator masses below 2 MeV/c², presented as the most stringent to date. The work also combines these results with cosmological constraints to bound scalar-mediated dark matter self-interactions and discusses implications for models addressing the Hubble tension.

Significance. If the spectral separation and systematic control are robust, the result would meaningfully tighten constraints on light scalar mediators in neutrino and dark matter sectors. The repurposing of existing double beta decay data for this purpose is a useful methodological contribution, and the explicit linkage to Hubble-tension models provides a clear physics motivation.

major comments (2)
  1. The headline limits rest on the assumption that a scalar-induced distortion remains distinguishable from the standard 2νββ spectrum, background components, and detector-response variations across the full 20–2800 keV window. The manuscript provides no quantitative demonstration—such as a correlation matrix, principal-component analysis of systematic templates, or profiled likelihood scan with floated energy-scale and resolution parameters—that the signal template is sufficiently orthogonal to these variations. Without this, the derived upper limits risk being weakened by partial absorption into background or response adjustments.
  2. Section describing the fit procedure (and associated figures): the paper should explicitly show how the scalar signal template is constructed for m_φ ≲ 2 MeV and how it is simultaneously fitted with the 2νββ shape and background normalizations. The absence of such a demonstration leaves the central claim vulnerable to the degeneracy concern raised in the stress-test note.
minor comments (2)
  1. Clarify the precise data selection criteria and live-time exposure used for the 20–2800 keV analysis; these details are needed to assess the statistical power of the search.
  2. Add a brief comparison plot or table placing the new limits against existing constraints from other experiments or cosmological probes for mediator masses below 2 MeV/c².

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and constructive review. The comments correctly identify areas where the presentation of the analysis robustness can be strengthened. We address each major point below and will incorporate the suggested clarifications and additional demonstrations in a revised manuscript.

read point-by-point responses
  1. Referee: The headline limits rest on the assumption that a scalar-induced distortion remains distinguishable from the standard 2νββ spectrum, background components, and detector-response variations across the full 20–2800 keV window. The manuscript provides no quantitative demonstration—such as a correlation matrix, principal-component analysis of systematic templates, or profiled likelihood scan with floated energy-scale and resolution parameters—that the signal template is sufficiently orthogonal to these variations. Without this, the derived upper limits risk being weakened by partial absorption into background or response adjustments.

    Authors: We agree that an explicit quantitative demonstration of orthogonality strengthens the result. The scalar-induced distortion for m_φ ≲ 2 MeV/c² modifies the low-energy portion of the 2νββ spectrum through an altered phase-space factor and propagator, producing a shape that is not fully degenerate with standard backgrounds or linear energy-scale shifts. In the current analysis the likelihood already profiles over energy-scale and resolution nuisance parameters; post-fit correlation matrices show the signal normalization remains largely uncorrelated with these systematics. We will add a dedicated subsection with the correlation matrix, a principal-component decomposition of the systematic templates, and a profiled-likelihood scan in which energy-scale and resolution parameters are floated, confirming that the upper limits are not materially weakened. revision: yes

  2. Referee: Section describing the fit procedure (and associated figures): the paper should explicitly show how the scalar signal template is constructed for m_φ ≲ 2 MeV and how it is simultaneously fitted with the 2νββ shape and background normalizations. The absence of such a demonstration leaves the central claim vulnerable to the degeneracy concern raised in the stress-test note.

    Authors: We accept that the construction of the signal template and its simultaneous fit with the 2νββ component and backgrounds should be shown more explicitly. The template is obtained by numerically integrating the differential double-beta decay rate that includes the scalar-mediated interaction term (with the mediator propagator evaluated at low momentum transfer for m_φ ≲ 2 MeV/c²) and then folding with the detector response. This shape is fitted simultaneously with a free normalization for the standard 2νββ spectrum and independent normalizations for each background component. We will expand the fit-procedure section with a step-by-step description of template generation, an equation for the modified spectrum, and a new figure displaying the individual fit components together with the best-fit scalar signal for a representative mass point. revision: yes

Circularity Check

0 steps flagged

No significant circularity: limits derived from direct spectral fit to experimental data.

full rationale

The paper reports upper limits on scalar-mediated neutrino self-interactions obtained by fitting the observed 136Xe double-beta decay spectrum in the 20-2800 keV range with standard 2νββ templates plus additive signal distortion shapes for different mediator masses. No equation or result is shown to reduce by construction to a fitted parameter that is then relabeled as a prediction, nor does any load-bearing step invoke a self-citation chain or uniqueness theorem whose validity depends on the present work. The central claim is an empirical constraint extracted from PandaX-4T data; external cosmological references are cited only for context and do not substitute for the spectral analysis itself. The derivation chain is therefore self-contained against the experimental dataset.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the assumption that a light scalar mediator exists and couples to neutrinos (and possibly dark matter) in a way that distorts the double beta decay spectrum; no independent evidence for the scalar is supplied beyond the null result.

axioms (1)
  • domain assumption The standard 2νββ spectrum shape is known and can be subtracted or modeled accurately in the 20–2800 keV range.
    Invoked implicitly when claiming any new scalar interaction would produce a detectable spectral distortion.
invented entities (1)
  • light scalar mediator no independent evidence
    purpose: Mediates neutrino self-interactions and possibly dark matter self-interactions
    Postulated to explain possible new physics; no direct detection or independent evidence provided in the abstract.

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Works this paper leans on

69 extracted references · 69 canonical work pages · 35 internal anchors

  1. [1]

    Galaxies in LCDM with Halo Abundance Matching: luminosity-velocity relation, baryonic mass-velocity relation, velocity function and clustering

    S. Trujillo-Gomez, A. Klypin, J. Primack, and A. J. Romanowsky, Astrophys. J.742, 16 (2011), arXiv:1005.1289 [astro-ph.CO]

  2. [2]

    The large-scale structure of the Universe

    V. Springel, C. S. Frenk, and S. D. M. White, Nature 440, 1137 (2006), arXiv:astro-ph/0604561

  3. [3]

    N. A. Bahcall, J. P. Ostriker, S. Perlmutter, and P. J. Steinhardt, Science284, 1481 (1999), arXiv:astro- ph/9906463

  4. [4]

    A. G. Riess, S. Casertano, D. Kenworthy, D. Scolnic, and L. Macri, (2018), arXiv:1810.03526 [astro-ph.CO]

  5. [5]

    Planck 2018 results. VI. Cosmological parameters

    N. Aghanim et al. (Planck), Astron. Astrophys.641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]

  6. [6]

    A. G. Riess, S. Casertano, W. Yuan, L. M. Macri, and D. Scolnic, Astrophys. J.876, 85 (2019), arXiv:1903.07603 [astro-ph.CO]

  7. [7]

    GAIA Cepheid parallaxes and 'Local Hole' relieve $H_0$ tension

    T. Shanks, L. Hogarth, and N. Metcalfe, Mon. Not. Roy. Astron. Soc.484, L64 (2019), arXiv:1810.02595 [astro- ph.CO]

  8. [8]

    A. G. Riess et al., Astrophys. J.826, 56 (2016), arXiv:1604.01424 [astro-ph.CO]

  9. [9]

    Limits on Neutrino-Neutrino Scattering in the Early Universe

    F.-Y. Cyr-Racine and K. Sigurdson, Phys. Rev. D90, 123533 (2014), arXiv:1306.1536 [astro-ph.CO]

  10. [10]

    C. D. Kreisch, F.-Y. Cyr-Racine, and O. Dor´ e, Phys. Rev. D101, 123505 (2020), arXiv:1902.00534 [astro- ph.CO]

  11. [11]

    A tale of two modes: Neutrino free-streaming in the early universe

    L. Lancaster, F.-Y. Cyr-Racine, L. Knox, and Z. Pan, JCAP07, 033 (2017), arXiv:1704.06657 [astro-ph.CO]

  12. [12]

    I. M. Oldengott, T. Tram, C. Rampf, and Y. Y. Y. Wong, JCAP11, 027 (2017), arXiv:1706.02123 [astro-ph.CO]

  13. [13]

    H. M. Georgi, S. L. Glashow, and S. Nussinov, Nucl. Phys. B193, 297 (1981)

  14. [14]

    Yanagida, Conf

    T. Yanagida, Conf. Proc. C7902131, 95 (1979)

  15. [15]

    S. L. Glashow, NATO Sci. Ser. B61, 687 (1980)

  16. [16]

    R. N. Mohapatra and G. Senjanovic, Phys. Rev. Lett. 44, 912 (1980)

  17. [17]

    Schechter and J

    J. Schechter and J. W. F. Valle, Phys. Rev. D22, 2227 (1980)

  18. [18]

    J. L. Feng, M. Kaplinghat, and H.-B. Yu, Phys. Rev. Lett.104, 151301 (2010), arXiv:0911.0422 [hep-ph]

  19. [19]

    Beyond Collisionless Dark Matter: Particle Physics Dynamics for Dark Matter Halo Structure

    S. Tulin, H.-B. Yu, and K. M. Zurek, Phys. Rev. D87, 115007 (2013), arXiv:1302.3898 [hep-ph]

  20. [20]

    Self-interacting scalar dark matter with local $Z_{3}$ symmetry

    P. Ko and Y. Tang, JCAP05, 047 (2014), arXiv:1402.6449 [hep-ph]

  21. [21]

    K. K. Boddy, J. L. Feng, M. Kaplinghat, and T. M. P. Tait, Phys. Rev. D89, 115017 (2014), arXiv:1402.3629 [hep-ph]

  22. [22]

    Dark Matter Self-interactions and Small Scale Structure

    S. Tulin and H.-B. Yu, Phys. Rept.730, 1 (2018), arXiv:1705.02358 [hep-ph]

  23. [23]

    Thermal Dark Matter Through the Dirac Neutrino Portal

    B. Batell, T. Han, D. McKeen, and B. Shams Es Haghi, Phys. Rev. D97, 075016 (2018), arXiv:1709.07001 [hep- ph]

  24. [24]

    Dark matter-neutrino interactions through the lens of their cosmological implications

    A. Olivares-Del Campo, C. Bœhm, S. Palomares-Ruiz, and S. Pascoli, Phys. Rev. D97, 075039 (2018), arXiv:1711.05283 [hep-ph]

  25. [25]

    Blennow, E

    M. Blennow, E. Fernandez-Martinez, A. Olivares- Del Campo, S. Pascoli, S. Rosauro-Alcaraz, and A. V. Titov, Eur. Phys. J. C79, 555 (2019), arXiv:1903.00006 [hep-ph]

  26. [26]

    M. R. Buckley and P. J. Fox, Phys. Rev. D81, 083522 (2010), arXiv:0911.3898 [hep-ph]

  27. [27]

    Cores in Dwarf Galaxies from Dark Matter with a Yukawa Potential

    A. Loeb and N. Weiner, Phys. Rev. Lett.106, 171302 (2011), arXiv:1011.6374 [astro-ph.CO]

  28. [28]

    M. Doi, T. Kotani, and E. Takasugi, Prog. Theor. Phys. Suppl.83, 1 (1985)

  29. [29]

    M. Doi, T. Kotani, and E. Takasugi,37, 2575

  30. [30]

    Mohapatra and E

    R. Mohapatra and E. Takasugi,211, 192

  31. [31]

    K. A. Olive et al. (Particle Data Group), Chin. Phys. C 38, 090001 (2014)

  32. [32]

    J. B. Albert et al. (EXO-200), Phys. Rev. D90, 092004 (2014), arXiv:1409.6829 [hep-ex]

  33. [33]

    Limits on Majoron-emitting double-beta decays of Xe-136 in the KamLAND-Zen experiment

    A. Gando et al. (KamLAND-Zen), Phys. Rev. C86, 021601 (2012), arXiv:1205.6372 [hep-ex]

  34. [34]

    M. T. Mustonen and J. Engel, Phys. Rev. C87, 064302 (2013), arXiv:1301.6997 [nucl-th]

  35. [35]

    The 0nbb-decay nuclear matrix elements with self-consistent short-range correlations

    F. Simkovic, A. Faessler, H. Muther, V. Rodin, and M. Stauf, Phys. Rev. C79, 055501 (2009), arXiv:0902.0331 [nucl-th]

  36. [36]

    Si et al

    L. Si et al. (PandaX), Research2022, 9798721 (2022), arXiv:2205.12809 [nucl-ex]

  37. [37]

    Meng et al

    Y. Meng et al. (PandaX-4T), Phys. Rev. Lett.127, 261802 (2021), arXiv:2107.13438 [hep-ex]

  38. [38]

    Bo et al

    Z. Bo et al. (PandaX), Phys. Rev. Lett.134, 011805 (2025), arXiv:2408.00664 [hep-ex]

  39. [39]

    Li et al

    T. Li et al. (PandaX), Phys. Rev. Lett.134, 071004 (2025), arXiv:2409.00773 [hep-ex]

  40. [40]

    Zhang et al

    S. Zhang et al. (PandaX), (2024), arXiv:2412.13979 [nucl-ex]

  41. [41]

    Majoron Dark Matter and Constraints on the Majoron-Neutrino Coupling

    T. Brune and H. P¨ as, Phys. Rev. D99, 096005 (2019), arXiv:1808.08158 [hep-ph]

  42. [42]

    Blinov, K

    N. Blinov, K. J. Kelly, G. Z. Krnjaic, and S. D. McDermott, Phys. Rev. Lett.123, 191102 (2019), arXiv:1905.02727 [astro-ph.CO]

  43. [43]

    J. M. Berryman, A. De Gouvˆ ea, K. J. Kelly, and Y. Zhang, Phys. Rev. D97, 075030 (2018), arXiv:1802.00009 [hep-ph]

  44. [44]

    E. W. Kolb and M. S. Turner, Phys. Rev. D36, 2895 (1987)

  45. [45]

    Shalgar, I

    S. Shalgar, I. Tamborra, and M. Bustamante, Phys. Rev. D103, 123008 (2021), arXiv:1912.09115 [astro-ph.HE]

  46. [46]

    J. M. Hyde, (2023), arXiv:2307.02361 [hep-ph]

  47. [47]

    Abbasi et al

    R. Abbasi et al. (IceCube), Science378, 538 (2022), arXiv:2211.09972 [astro-ph.HE]

  48. [48]

    Luo et al

    L. Luo et al. (PandaX-4T, PandaX), JHEP05, 089 (2025), arXiv:2502.03017 [nucl-ex]

  49. [49]

    Bo et al

    Z. Bo et al. (PandaX-4T, PandaX), JHEP05, 119 (2025), arXiv:2411.14355 [nucl-ex]

  50. [50]

    Low-energy electronic recoil in xenon detectors by solar neutrinos

    J.-W. Chen, H.-C. Chi, C. P. Liu, and C.-P. Wu, Phys. 7 Lett. B774, 656 (2017), arXiv:1610.04177 [hep-ex]

  51. [51]

    Bellini et al

    G. Bellini et al. (BOREXINO), Nature512, 383 (2014)

  52. [52]

    F. F. Deppisch, L. Graf, W. Rodejohann, and X.-J. Xu, Phys. Rev. D102, 051701 (2020), arXiv:2004.11919 [hep- ph]

  53. [53]

    Bleau, J

    K. Bleau, J. Bramante, and C. Cappiello, JCAP01, 021 (2024), arXiv:2309.06482 [hep-ph]

  54. [54]

    D. N. Spergel and P. J. Steinhardt, Phys. Rev. Lett.84, 3760 (2000), arXiv:astro-ph/9909386

  55. [55]

    Cosmological Simulations with Self-Interacting Dark Matter I: Constant Density Cores and Substructure

    M. Rocha, A. H. G. Peter, J. S. Bullock, M. Kapling- hat, S. Garrison-Kimmel, J. Onorbe, and L. A. Mous- takas, Mon. Not. Roy. Astron. Soc.430, 81 (2013), arXiv:1208.3025 [astro-ph.CO]

  56. [56]

    Subhaloes in Self-Interacting Galactic Dark Matter Haloes

    M. Vogelsberger, J. Zavala, and A. Loeb, Mon. Not. Roy. Astron. Soc.423, 3740 (2012), arXiv:1201.5892 [astro- ph.CO]

  57. [57]

    Non-Perturbative Effect on Dark Matter Annihilation and Gamma Ray Signature from Galactic Center

    J. Hisano, S. Matsumoto, M. M. Nojiri, and O. Saito, Phys. Rev. D71, 063528 (2005), arXiv:hep-ph/0412403

  58. [58]

    A Theory of Dark Matter

    N. Arkani-Hamed, D. P. Finkbeiner, T. R. Slatyer, and N. Weiner, Phys. Rev. D79, 015014 (2009), arXiv:0810.0713 [hep-ph]

  59. [59]

    Colquhoun, S

    B. Colquhoun, S. Heeba, F. Kahlhoefer, L. Sagun- ski, and S. Tulin, Phys. Rev. D103, 035006 (2021), arXiv:2011.04679 [hep-ph]

  60. [60]

    J. M. Cline, S. Gao, F. Guo, Z. Lin, S. Liu, M. Puel, P. Todd, and T. Xiao, Phys. Rev. Lett.130, 091402 (2023), arXiv:2209.02713 [hep-ph]

  61. [61]

    Cosmological bounds on dark matter-neutrino interactions

    G. Mangano, A. Melchiorri, P. Serra, A. Cooray, and M. Kamionkowski, Phys. Rev. D74, 043517 (2006), arXiv:astro-ph/0606190

  62. [62]

    R. J. Wilkinson, C. Boehm, and J. Lesgourgues, JCAP 05, 011 (2014), arXiv:1401.7597 [astro-ph.CO]

  63. [63]

    M. R. Mosbech, C. Boehm, S. Hannestad, O. Mena, J. Stadler, and Y. Y. Y. Wong, JCAP03, 066 (2021), arXiv:2011.04206 [astro-ph.CO]

  64. [64]

    A. Paul, A. Chatterjee, A. Ghoshal, and S. Pal, JCAP 10, 017 (2021), arXiv:2104.04760 [hep-ph]

  65. [65]

    Agostini, E

    M. Agostini, E. Bossio, A. Ibarra, and X. Marcano, Phys. Lett. B815, 136127 (2021), arXiv:2012.09281 [hep-ph]

  66. [66]

    Probing Dark Sector Particles Coupling to Neutrinos with Double Beta Decay

    N.-I. Boudjema, F. F. Deppisch, A. Herrero- Brocal, C. Majumdar, and S. Senapati, (2025), arXiv:2511.13606 [hep-ph]

  67. [67]

    Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review

    J. Engel and J. Men´ endez, Rept. Prog. Phys.80, 046301 (2017), arXiv:1610.06548 [nucl-th]

  68. [68]

    M. Doi, T. Kotani, and E. Takasugi, Phys. Rev. D37, 2575 (1988)

  69. [69]

    W. C. Haxton and G. J. Stephenson, Prog. Part. Nucl. Phys.12, 409 (1984). 8 Supplementary material I. THE PHASE SP ACE F ACTOR The factorG νχ is defined as Gνϕ = a0ν (meR0)2 Z F0(Zf , p1)F0(Zf , p2)dΩνϕ.(6) Here the normalization factora 0ν is given by: a0ν = (GF cosθ CgA)4m9 e 64π5 ,(7) whereG F is the Fermi constant,θ C is the Cabibbo angle,g A is the a...