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  • Open Access

Photomeson-threshold origin of the TeV break in astrophysical neutrinos: Spectrum, flavor, resolved sources, and the ultrahigh-energy landscape

Vernon Barger*

  • *Contact author: barger@pheno.wisc.edu
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APS Open Sci. 1, 000175 – Published 19 October, 2026

DOI: https://doi.org/10.1103/l9sf-3yht

Abstract

IceCube observes a break near 30 TeV in the diffuse astrophysical neutrino spectrum. We interpret it as the photomeson (pγ) threshold. Accelerated protons interact with the soft x rays of accreting black holes through the Δ(1232) resonance. One kinematic relation sets the break energy from the target field’s lowest photon energy, the seed scale ɛ0. The measured break fixes ɛ0≃0.13keV and supplies the low-energy suppression no sum of falling power laws can produce. Building on the Δ(1232) identification of Khatee Zathul, Fang, Halzen, and Hooper and the single-source-class photo-pion fit of Winter, Fiorillo, and Buson, we give closed-form relations that invert the four broken-power-law fit parameters to the source physics with no remaining freedom, namely, γ2=s and γ1=s−(αx−1) (s, αx the proton and target photon indices), and Ebr∝[(1+z¯)ɛ0]−1. The break width then measures the population’s uniformity. The total smearing is bounded to σs≤0.235dex (68% confidence level), no broader than redshift alone must make it, and the seed scale is the same across the sources to within a factor ≲1.5, a constraint mean-spectrum fits do not provide. The model also predicts that below-break neutrinos come on average from higher redshifts than those above. The threshold also fixes the flavor and neutrino-antineutrino composition, including the energy-dependent ν¯e fraction and the Glashow-resonance discriminator computed in detail by Winter et al., matching current flavor data. Inverted source by source, the relation gives each resolved IceCube source its target photon scale, from the keV coronae of NGC 1068 and PKS 1424+240 to the ∼20eV jet of TXS 0506+056. That two-decade spread means they cannot supply the homogeneous break. It requires a separate, fainter population. KM3-230213A points to a warm-dust target, ɛ0≃0.02eV, unless cosmogenic.

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References (41)

  1. M. G. Aartsen, R. Abbasi, Y. Abdou, M. Ackermann, J. Adams, J. A. Aguilar, M. Ahlers, D. Altmann, J. Auffenberg, X. Bai, et al. (IceCube Collaboration), Evidence for high-energy extraterrestrial neutrinos at the IceCube detector, Science 342, 1242856 (2013).
  2. R. Abbasi, M. Ackermann, J. Adams, S. K. Agarwalla, J. A. Aguilar, M. Ahlers, J. M. Alameddine, S. Ali, N. M. Amin, K. Andeen, et al. (IceCube Collaboration), Evidence for a spectral break or curvature in the spectrum of astrophysical neutrinos from 5 TeV to 10 PeV, Phys. Rev. Lett. 136, 121002 (2026).
  3. A. Khatee Zathul, K. Fang, F. Halzen, and D. Hooper, The Delta resonance in the neutrino sky, arXiv:2606.00249.
  4. W. Winter, D. F. G. Fiorillo, and S. Buson, Single-source-class interpretation of the diffuse astrophysical neutrino flux, Phys. Rev. D 113, 123043 (2026).
  5. S. L. Glashow, Resonant scattering of antineutrinos, Phys. Rev. 118, 316 (1960).
  6. V. Barger, L. Fu, J. G. Learned, D. Marfatia, S. Pakvasa, and T. J. Weiler, Glashow resonance as a window into cosmic neutrino sources, Phys. Rev. D 90, 121301 (2014).
  7. L. Wolfenstein, Neutrino oscillations in matter, Phys. Rev. D 17, 2369 (1978).
  8. S. P. Mikheyev and A. Yu. Smirnov, Resonance amplification of oscillations in matter and spectroscopy of solar neutrinos, Yad. Fiz. 42, 1441 (1985) [Sov. J. Nucl. Phys. 42, 913 (1985)].
  9. V. Barger, K. Whisnant, S. Pakvasa, and R. J. N. Phillips, Matter effects on three-neutrino oscillations, Phys. Rev. D 22, 2718 (1980).
  10. A. M. Dziewonski and D. L. Anderson, Preliminary reference Earth model, Phys. Earth Planet. Inter. 25, 297 (1981).
  11. B. Feldstein, A. Kusenko, S. Matsumoto, and T. T. Yanagida, Neutrinos at IceCube from heavy decaying dark matter, Phys. Rev. D 88, 015004 (2013).
  12. A. Esmaili and P. D. Serpico, Are IceCube neutrinos unveiling PeV-scale decaying dark matter? J. Cosmol. Astropart. Phys. 11 (2013) 054.
  13. K. Ioka and K. Murase, IceCube PeV–EeV neutrinos and secret interactions of neutrinos, Prog. Theor. Exp. Phys. 2014, 061E01 (2014).
  14. K. C. Y. Ng and J. F. Beacom, Cosmic neutrino cascades from secret neutrino interactions, Phys. Rev. D 90, 065035 (2014); 90, 089904(E) (2014).
  15. S. Hümmer, M. Rüger, F. Spanier, and W. Winter, Simplified models for photohadronic interactions in cosmic accelerators, Astrophys. J. 721, 630 (2010).
  16. A. Mücke, R. Engel, J. P. Rachen, R. J. Protheroe, and T. Stanev, sophia: Monte Carlo simulations of photohadronic processes in astrophysics, Comput. Phys. Commun. 124, 290 (2000).
  17. M. G. Aartsen, R. Abbasi, M. Ackermann, J. Adams, J. A. Aguilar, M. Ahlers, M. Ahrens, C. Alispach, N. M. Amin, K. Andeen, et al. (IceCube Collaboration), Detection of a particle shower at the Glashow resonance with IceCube, Nature (London) 591, 220 (2021).
  18. K. Murase, D. Guetta, and M. Ahlers, Hidden cosmic-ray accelerators as an origin of TeV-PeV cosmic neutrinos, Phys. Rev. Lett. 116, 071101 (2016).
  19. K. Murase, S. S. Kimura, and P. Mészáros, Hidden cores of active galactic nuclei as the origin of medium-energy neutrinos: Critical tests with the MeV gamma-ray connection, Phys. Rev. Lett. 125, 011101 (2020).
  20. R. Abbasi, M. Ackermann, J. Adams, J. A. Aguilar, M. Ahlers, M. Ahrens, J. M. Alameddine, C. Alispach, A. A. Alves Jr., N. M. Amin, et al. (IceCube Collaboration), Evidence for neutrino emission from the nearby active galaxy NGC 1068, Science 378, 538 (2022).
  21. R. Abbasi, M. Ackermann, J. Adams, S. K. Agarwalla, J. A. Aguilar, M. Ahlers, J. M. Alameddine, S. Ali, N. M. Amin, K. Andeen, et al. (IceCube Collaboration), Improved measurements of the TeV–PeV extragalactic neutrino spectrum from joint analyses of IceCube tracks and cascades, Phys. Rev. D 113, 062002 (2026), companion to Ref. [2].
  22. N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020).
  23. P. Madau and M. Dickinson, Cosmic star-formation history, Annu. Rev. Astron. Astrophys. 52, 415 (2014).
  24. Y. Ueda, M. Akiyama, G. Hasinger, T. Miyaji, and M. G. Watson, Toward the standard population synthesis model of the X-ray background: Evolution of X-ray luminosity and absorption functions of active galactic nuclei, Astrophys. J. 786, 104 (2014).
  25. K. Carloni, Y. Porto, C. A. Argüelles, P. S. B. Dev, and S. Jana, Signatures of quasi-Dirac neutrinos in diffuse high-energy astrophysical neutrino data, Phys. Rev. D 113, 115004 (2026).
  26. V. B. Valera, D. F. G. Fiorillo, I. Esteban, and M. Bustamante, New limits on neutrino decay from high-energy astrophysical neutrinos, Phys. Rev. D 110, 043004 (2024).
  27. A. Cooper-Sarkar, P. Mertsch, and S. Sarkar, The high energy neutrino cross-section in the Standard Model and its uncertainty, J. High Energy Phys. 08 (2011) 042.
  28. J. Stachurska (IceCube Collaboration), First double cascade tau neutrino candidates in IceCube and a new measurement of the flavor composition, Proc. Sci. ICRC2019, 1015 (2020); R. Abbasi, M. Ackermann, J. Adams, J. A. Aguilar, M. Ahlers, M. Ahrens, C. Alispach, A. A. Alves Jr., N. M. Amin, K. Andeen, et al. (IceCube Collaboration), Detection of astrophysical tau neutrino candidates in IceCube, Eur. Phys. J. C 82, 1031 (2022).
  29. N. Lad, T. J. van Eeden, and M. Ackermann (IceCube Collaboration), Neutrino flavor composition using high energy starting events with IceCube, Proc. Sci. ICRC2025, 1198 (2025).
  30. R. Abbasi, M. Ackermann, J. Adams, S. K. Agarwalla, J. A. Aguilar, M. Ahlers, J. M. Alameddine, N. M. Amin, K. Andeen, G. Anton, et al. (IceCube Collaboration), Observation of seven astrophysical tau neutrino candidates with IceCube, Phys. Rev. Lett. 132, 151001 (2024).
  31. S. Aiello, A. Albert, A. R. Alhebsi, M. Alshamsi, S. Alves Garre, A. Ambrosone, F. Ameli, M. Andre, M. Anghinolfi, L. Aphecetche, et al. (KM3NeT Collaboration), Observation of an ultra-high-energy cosmic neutrino with KM3NeT, Nature (London) 638, 376 (2025); 640, E3(E) (2025).
  32. R. Abbasi, M. Ackermann, J. Adams, S. K. Agarwalla, J. A. Aguilar, M. Ahlers, J. M. Alameddine, N. M. Amin, K. Andeen, C. Argüelles, et al. (IceCube Collaboration), Search for extremely-high-energy neutrinos and first constraints on the ultrahigh-energy cosmic-ray proton fraction with IceCube, Phys. Rev. Lett. 135, 031001 (2025).
  33. O. Adriani, S. Aiello, A. Albert, A. R. Alhebsi, M. Alshamsi, S. Alves Garre, A. Ambrosone, F. Ameli, M. Andre, L. Aphecetche, et al. (KM3NeT Collaboration), Ultra-high-energy event KM3-230213A within the global neutrino landscape, Phys. Rev. X 15, 031016 (2025).
  34. K. Kotera, D. Allard, and A. V. Olinto, Cosmogenic neutrinos: Parameter space and detectability from PeV to ZeV, J. Cosmol. Astropart. Phys. 10 (2010) 013.
  35. O. Adriani, S. Aiello, A. Albert, A. R. Alhebsi, M. Alshamsi, S. Alves Garre, A. Ambrosone, F. Ameli, M. Andre, L. Aphecetche, et al. (KM3NeT, MessMapp Group, Fermi-LAT, Owens Valley Radio Observatory 40-m Telescope Group, and SVOM Collaborations), Characterizing candidate blazar counterparts of the ultra-high-energy event KM3-230213A, Astron. J. 172, 139 (2026).
  36. C. Yuan, L. Pfeiffer, W. Winter, J. M. S. Zaballa, S. Buson, F. Testagrossa, and A. Azzollini, An accretion flare interpretation for the ultra-high-energy neutrino event KM3-230213A, Astrophys. J. Lett. 998, L1 (2026).
  37. R. Abbasi, M. Ackermann, J. Adams, S. K. Agarwalla, J. A. Aguilar, M. Ahlers, J. M. Alameddine, S. Ali, N. M. Amin, K. Andeen, et al. (IceCube Collaboration), Evidence for neutrino emission from X-ray-bright active galactic nuclei with IceCube, Astrophys. J. Lett. 1000, L26 (2026).
  38. IceCube, Fermi-LAT, MAGIC, AGILE, ASAS-SN, HAWC, H.E.S.S., INTEGRAL, Kanata, Kiso, Kapteyn, Liverpool Telescope, Subaru, Swift/NuSTAR, VERITAS, and VLA/17B-403 Teams, Multimessenger observations of a flaring blazar coincident with high-energy neutrino IceCube-170922A, Science 361, eaat1378 (2018).
  39. M. G. Aartsen, M. Ackermann, J. Adams, J. A. Aguilar, M. Ahlers, M. Ahrens, I. Al Samarai, D. Altmann, K. Andeen, T. Anderson, et al. (IceCube Collaboration), Neutrino emission from the direction of the blazar TXS 0506+056 prior to the IceCube-170922A alert, Science 361, 147 (2018).
  40. A. Zegarelli, A. Franckowiak, G. Sommani, N. Valtonen-Mattila, and T. Yuan (IceCube Collaboration), IceCat-2: Updated IceCube event catalog of alert tracks, Proc. Sci. ICRC2025, 1224 (2025).
  41. R. Kuze, K. Ioka, K. Murase, S. S. Kimura, and K. Inayoshi, Little red dots as hidden neutrino sources, Phys. Rev. D 113, 083048 (2026).

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APS Open Sci. 1, 000175– Published 19 October, 2026
Vol. 1
  • Received 14 June 2026
  • Accepted 29 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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