- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Missing energy signatures of inelastic magnetic dipole DM at NA64e

Sergei N. Gninenko1,2,3, N. V. Krasnikov1,2, I. V. Voronchikhin1,4, and D. V. Kirpichnikov1,*

  • *Contact author: dmbrick@gmail.com
PDF

Phys. Rev. D 113, 115055 – Published 22 June, 2026

DOI: https://doi.org/10.1103/w86p-8mj9

Abstract

Some extensions of the Standard Model consider inelastic dark matter (iDM) as an attractive candidate for sub-GeV DM of thermal origin that could be detected at modern accelerators. In the present paper, we calculate the production rate of iDM pairs χ1χ¯0 interacting with the ordinary photon via dipole magnetic moment in the reaction of high-energy electron scattering on nuclei, e−N→e−Nχ1χ¯0, in the NA64e experiment at the CERN Super Proton Synchrotron (SPS). We derive the projected sensitivity of NA64e to such particles assuming ≃1013 100 GeV electrons on target. We also show, that incorporating heavy vector meson decays, γ*N→NV(→χ1χ¯0), alongside bremsstrahlunglike emission of inelastic dark matter pairs, e−N→e−Nγ*(→χ1χ¯0), will allow NA64e to probe previously unexplored regions of the iDM parameter space, in particular for modest mass splittings, Δ≃5×10−2, and relatively light masses, mχ0≲100  MeV.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (93)

  1. Gianfranco Bertone and Dan Hooper, History of dark matter, Rev. Mod. Phys. 90, 045002 (2018).
  2. Lars Bergstrom, Dark matter evidence, particle physics candidates and detection methods, Ann. Phys. (Amsterdam) 336, 428 (2013).
  3. Marco Cirelli, Alessandro Strumia, and Jure Zupan, Dark matter, arXiv:2406.01705.
  4. Gianfranco Bertone, Dan Hooper, and Joseph Silk, Particle dark matter: Evidence, candidates and constraints, Phys. Rep. 405, 279 (2005).
  5. Graciela B. Gelmini, The hunt for dark matter, Proc. Int. School of Physics "Enrico Fermi" 186, 189 (2016).
  6. R. Adam et al. (Planck Collaboration), Planck 2015 results. I. Overview of products and scientific results, Astron. Astrophys. 594, A1 (2016).
  7. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  8. David Tucker-Smith and Neal Weiner, Inelastic dark matter, Phys. Rev. D 64, 043502 (2001).
  9. David Tucker-Smith and Neal Weiner, The status of inelastic dark matter, Phys. Rev. D 72, 063509 (2005).
  10. Spencer Chang, Graham D. Kribs, David Tucker-Smith, and Neal Weiner, Inelastic dark matter in light of DAMA/LIBRA, Phys. Rev. D 79, 043513 (2009).
  11. R. Bernabei et al., Final model independent result of DAMA/LIBRA-phase1, Eur. Phys. J. C 73, 2648 (2013).
  12. D. Barducci, E. Bertuzzo, M. Taoso, C. A. Ternes, and C. Toni, Illuminating the dark: mono-γ signals at NA62, J. High Energy Phys. 10 (2024) 016.
  13. Krzysztof Jodłowski, Looking forward to inelastic DM with electromagnetic form factors at FASER and beam dump experiments, Phys. Rev. D 108, 115025 (2023).
  14. Keith R. Dienes, Jonathan L. Feng, Max Fieg, Fei Huang, Seung J. Lee, and Brooks Thomas, Extending the discovery potential for inelastic-dipole dark matter with FASER, Phys. Rev. D 107, 115006 (2023).
  15. Joshua Eby, Patrick J. Fox, and Graham D. Kribs, Earth-catalyzed detection of magnetic inelastic dark matter with photons in large underground detectors, J. High Energy Phys. 06 (2024) 165.
  16. I. V. Voronchikhin and D. V. Kirpichnikov, Prospects of boosted magnetic dipole inelastic fermion dark matter at ILC-BDX, arXiv:2604.20385.
  17. Giovani Dalla Valle Garcia, Felix Kahlhoefer, Maksym Ovchynnikov, and Thomas Schwetz, Not-so-inelastic dark matter, J. High Energy Phys. 02 (2025) 127.
  18. Yanou Cui, David E. Morrissey, David Poland, and Lisa Randall, Candidates for inelastic dark matter, J. High Energy Phys. 05 (2009) 076.
  19. Johnathon R. Jordan, Yonatan Kahn, Gordan Krnjaic, Matthew Moschella, and Joshua Spitz, Signatures of Pseudo-Dirac dark matter at high-intensity neutrino experiments, Phys. Rev. D 98, 075020 (2018).
  20. Asher Berlin, Stefania Gori, Philip Schuster, and Natalia Toro, Dark sectors at the Fermilab SeaQuest experiment, Phys. Rev. D 98, 035011 (2018).
  21. Brian Batell, Joshua Berger, Luc Darmé, and Claudia Frugiuele, Inelastic dark matter at the Fermilab short baseline neutrino program, Phys. Rev. D 104, 075026 (2021).
  22. Martina Mongillo, Asli Abdullahi, Benjamin Banto Oberhauser, Paolo Crivelli, Matheus Hostert, Daniele Massaro, Laura Molina Bueno, and Silvia Pascoli, Constraining light thermal inelastic dark matter with NA64, Eur. Phys. J. C 83, 391 (2023).
  23. Eder Izaguirre, Gordan Krnjaic, and Brian Shuve, Discovering inelastic thermal-relic dark matter at colliders, Phys. Rev. D 93, 063523 (2016).
  24. Ana Luisa Foguel, Peter Reimitz, and Renata Zukanovich Funchal, Unlocking the inelastic dark matter window with vector mediators, J. High Energy Phys. 05 (2025) 001.
  25. Anastasiia Filimonova, Sam Junius, Laura Lopez Honorez, and Susanne Westhoff, Inelastic Dirac dark matter, J. High Energy Phys. 06 (2022) 048.
  26. Mariana Carrillo González and Natalia Toro, Cosmology and signals of light pseudo-Dirac dark matter, J. High Energy Phys. 04 (2022) 060.
  27. Jinhui Guo, Jia Liu, Chenhao Peng, and Xiao-Ping Wang, Probing purely inelastic scalar dark matter across colliders and gravitational wave observatories, Phys. Rev. D 112, 115014 (2025).
  28. I. V. Voronchikhin and D. V. Kirpichnikov, Examining scalar portal inelastic dark matter with lepton fixed-target experiments, Phys. Rev. D 113, 015031 (2026).
  29. Zihan Wang, Scalar-mediated inelastic dark matter as a solution to small-scale structure anomalies, arXiv:2512.18959.
  30. Giovani Dalla Valle Garcia, A minimalistic model for inelastic dark matter, Phys. Lett. B 862, 139320 (2025).
  31. I. V. Voronchikhin and D. V. Kirpichnikov, Direct-detection constraints on inelastic dark matter with a scalar mediator, arXiv:2604.06929.
  32. P. Achard et al. (L3 Collaboration), Single photon and multiphoton events with missing energy in e+e− collisions at LEP, Phys. Lett. B 587, 16 (2004).
  33. Jean-Francois Fortin and Tim M. P. Tait, Collider Constraints on dipole-interacting dark matter, Phys. Rev. D 85, 063506 (2012).
  34. Brian Batell, Rouven Essig, and Ze’ev Surujon, Strong constraints on sub-GeV dark sectors from SLAC beam dump E137, Phys. Rev. Lett. 113, 171802 (2014).
  35. F. Bergsma et al. (CHARM Collaboration), Search for axion like particle production in 400-GeV proton—copper interactions, Phys. Lett. 157B, 458 (1985).
  36. S. N. Gninenko, Constraints on sub-GeV hidden sector gauge bosons from a search for heavy neutrino decays, Phys. Lett. B 713, 244 (2012).
  37. F. Bergsma et al. (CHARM Collaboration), A search for decays of heavy neutrinos, Phys. Lett. 128B, 361 (1983).
  38. J. Blumlein et al., Limits on neutral light scalar and pseudoscalar particles in a proton beam dump experiment, Z. Phys. C 51, 341 (1991).
  39. Johannes Blumlein and Jurgen Brunner, New exclusion limits for dark gauge forces from beam-dump data, Phys. Lett. B 701, 155 (2011).
  40. Sergey Alekhin et al., A facility to search for hidden particles at the CERN SPS: The SHiP physics case, Rep. Prog. Phys. 79, 124201 (2016).
  41. Jonathan L. Feng, Iftah Galon, Felix Kling, and Sebastian Trojanowski, ForwArd search experiment at the LHC, Phys. Rev. D 97, 035001 (2018).
  42. John Paul Chou, David Curtin, and H. J. Lubatti, New detectors to explore the lifetime frontier, Phys. Lett. B 767, 29 (2017).
  43. David Curtin et al., Long-lived particles at the energy frontier: The MATHUSLA physics case, Rep. Prog. Phys. 82, 116201 (2019).
  44. Brian Batell, Jonathan L. Feng, and Sebastian Trojanowski, Detecting dark matter with far-forward emulsion and liquid argon detectors at the LHC, Phys. Rev. D 103, 075023 (2021).
  45. Alexey Boyarsky, Oleksii Mikulenko, Maksym Ovchynnikov, and Lesya Shchutska, Searches for new physics at SND@LHC, J. High Energy Phys. 03 (2022) 006.
  46. Vladimir V. Gligorov, Simon Knapen, Michele Papucci, and Dean J. Robinson, Searching for long-lived particles: A compact detector for exotics at LHCb, Phys. Rev. D 97, 015023 (2018).
  47. Asher Berlin and Felix Kling, Inelastic dark matter at the LHC lifetime frontier: ATLAS, CMS, LHCb, CODEX-b, FASER, and MATHUSLA, Phys. Rev. D 99, 015021 (2019).
  48. Saeid Foroughi-Abari, Felix Kling, and Yu-Dai Tsai, Looking forward to millicharged dark sectors at the LHC, Phys. Rev. D 104, 035014 (2021).
  49. Aaron Pierce, Bibhushan Shakya, Yuhsin Tsai, and Yue Zhao, Searching for confining hidden valleys at LHCb, ATLAS, and CMS, Phys. Rev. D 97, 095033 (2018).
  50. Albert M Sirunyan et al. (CMS Collaboration), Search for disappearing tracks as a signature of new long-lived particles in proton-proton collisions at s=13  TeV, J. High Energy Phys. 08 (2018) 016.
  51. Vardan Khachatryan et al. (CMS Collaboration), Search for dark matter, extra dimensions, and unparticles in monojet events in proton–proton collisions at s=8  TeV, Eur. Phys. J. C 75, 235 (2015).
  52. Roel Aaij et al. (LHCb Collaboration), Search for dark photons produced in 13 TeV pp collisions, Phys. Rev. Lett. 120, 061801 (2018).
  53. Philip Ilten, Yotam Soreq, Jesse Thaler, Mike Williams, and Wei Xue, Proposed inclusive dark photon search at LHCb, Phys. Rev. Lett. 116, 251803 (2016).
  54. C. Cazzaniga et al. (NA64 Collaboration), Probing the explanation of the muon (g-2) anomaly and thermal light dark matter with the semi-visible dark photon channel, Eur. Phys. J. C 81, 959 (2021).
  55. Spencer Chang, Neal Weiner, and Itay Yavin, Magnetic inelastic dark matter, Phys. Rev. D 82, 125011 (2010).
  56. S. N. Gninenko, Search for MeV dark photons in a light-shining-through-walls experiment at CERN, Phys. Rev. D 89, 075008 (2014).
  57. Daniele Barducci, Wei Liu, Arsenii Titov, Zeren Simon Wang, and Yu Zhang, Probing the dipole portal to heavy neutral leptons via meson decays at the high-luminosity LHC, Phys. Rev. D 108, 115009 (2023).
  58. Yu. M. Andreev et al. (NA64 Collaboration), High efficiency veto hadron calorimeter in the NA64 experiment at CERN, Nucl. Instrum. Methods Phys. Res., Sect. A 1081, 170830 (2026).
  59. Eduard Masso, Subhendra Mohanty, and Soumya Rao, Dipolar dark matter, Phys. Rev. D 80, 036009 (2009).
  60. Xiaoyong Chu, Josef Pradler, and Lukas Semmelrock, Light dark states with electromagnetic form factors, Phys. Rev. D 99, 015040 (2019).
  61. Xiaoyong Chu, Jui-Lin Kuo, and Josef Pradler, Dark sector-photon interactions in proton-beam experiments, Phys. Rev. D 101, 075035 (2020).
  62. Chiu Man Ho and Robert J. Scherrer, Anapole dark matter, Phys. Lett. B 722, 341 (2013).
  63. Yu Gao, Chiu Man Ho, and Robert J. Scherrer, Anapole dark matter at the LHC, Phys. Rev. D 89, 045006 (2014).
  64. Eugenio Del Nobile, Graciela B. Gelmini, Paolo Gondolo, and Ji-Haeng Huh, Direct detection of light anapole and magnetic dipole DM, J. Cosmol. Astropart. Phys. 06 (2014) 002.
  65. Alexandre Alves, A. C. O. Santos, and Kuver Sinha, Collider detection of dark matter electromagnetic anapole moments, Phys. Rev. D 97, 055023 (2018).
  66. Neal Weiner and Itay Yavin, UV completions of magnetic inelastic and Rayleigh dark matter for the Fermi Line(s), Phys. Rev. D 87, 023523 (2013).
  67. Neal Weiner and Itay Yavin, How dark are Majorana WIMPs? Signals from MiDM and Rayleigh dark matter, Phys. Rev. D 86, 075021 (2012).
  68. Roshan Foadi, Mads T. Frandsen, and Francesco Sannino, Technicolor dark matter, Phys. Rev. D 80, 037702 (2009).
  69. John Bagnasco, Michael Dine, and Scott D. Thomas, Detecting technibaryon dark matter, Phys. Lett. B 320, 99 (1994).
  70. Oleg Antipin, Michele Redi, Alessandro Strumia, and Elena Vigiani, Accidental composite dark matter, J. High Energy Phys. 07 (2015) 039.
  71. Stuart Raby and Geoffrey West, Experimental consequences and constraints for magninos, Phys. Lett. B 194, 557 (1987).
  72. Maxim Pospelov and Adam Ritz, Resonant scattering and recombination of pseudo-degenerate WIMPs, Phys. Rev. D 78, 055003 (2008).
  73. D. Banerjee et al. (NA64 Collaboration), Search for invisible decays of sub-GeV dark photons in missing-energy events at the CERN SPS, Phys. Rev. Lett. 118, 011802 (2017).
  74. Yu. M. Andreev et al. (NA64 Collaboration), Search for light Dark Matter with NA64 at CERN, Phys. Rev. Lett. 131, 161801 (2023).
  75. Yu. M. Andreev et al. (NA64 Collaboration), Searching for light Dark Matter and dark sectors with the NA64 experiment at the CERN SPS, arXiv:2505.14291.
  76. Yu. M. Andreev et al., Improved exclusion limit for light dark matter from e+e− annihilation in NA64, Phys. Rev. D 104, L091701 (2021).
  77. Yu. M. Andreev et al. (NA64 Collaboration), Constraints on new physics in electron g−2 from a search for invisible decays of a scalar, pseudoscalar, vector, and axial vector, Phys. Rev. Lett. 126, 211802 (2021).
  78. D. Banerjee et al., Dark matter search in missing energy events with NA64, Phys. Rev. Lett. 123, 121801 (2019).
  79. S. N. Gninenko, D. V. Kirpichnikov, M. M. Kirsanov, and N. V. Krasnikov, The exact tree-level calculation of the dark photon production in high-energy electron scattering at the CERN SPS, Phys. Lett. B 782, 406 (2018).
  80. Nataliya Arefyeva, Sergei Gninenko, Dmitry Gorbunov, and Dmitry Kirpichnikov, Passage of millicharged particles in the electron beam-dump: Refining constraints from SLACmQ and estimating sensitivity of NA64e, Phys. Rev. D 106, 035029 (2022).
  81. Sergei N. Gninenko, N. V. Krasnikov, Sergey Kuleshov, Valery E. Lyubovitskij, P. Crivelli, D. V. Kirpichnikov, L. Molina Bueno, Alexey S. Zhevlakov, H. Sieber, and I. V. Voronchikhin, Probing millicharged particles with NA64μ and LDMX, Eur. Phys. J. C 86, 140 (2026).
  82. Sergei N. Gninenko, N. V. Krasnikov, Valery E. Lyubovitskij, Sergey Kuleshov, Alexey S. Zhevlakov, I. V. Voronchikhin, and D. V. Kirpichnikov, Constraints on dark axion portal: Missing energy and fermion EDMs, arXiv:2602.11405.
  83. Philip Schuster, Natalia Toro, and Kevin Zhou, Probing invisible vector meson decays with the NA64 and LDMX experiments, Phys. Rev. D 105, 035036 (2022).
  84. S. V. Gertsenberger, A. V. Ivanov, and A. S. Zhevlakov, Production of ρ0 meson in the target of the NA64 experiment, Phys. Part. Nucl. Lett. 22, 1129 (2025).
  85. D. Banerjee et al. (NA64 Collaboration), Search for axionlike and scalar particles with the NA64 experiment, Phys. Rev. Lett. 125, 081801 (2020).
  86. Alexander Belyaev, Neil D. Christensen, and Alexander Pukhov, calchep 3.4 for collider physics within and beyond the Standard Model, Comput. Phys. Commun. 184, 1729 (2013).
  87. C. Adloff et al. (H1 Collaboration), Elastic photoproduction of J/ψ and Upsilon mesons at HERA, Phys. Lett. B 483, 23 (2000).
  88. J. M. Laget, Photoproduction of vector mesons at large transfer, Phys. Lett. B 489, 313 (2000).
  89. T. H. Bauer, R. D. Spital, D. R. Yennie, and F. M. Pipkin, The hadronic properties of the photon in high-energy interactions, Rev. Mod. Phys. 50, 261 (1978); 51, 407(E) (1979).
  90. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  91. Yung-Su Tsai and Van Whitis, Thick target bremsstrahlung and target consideration for secondary particle production by electrons, Phys. Rev. 149, 1248 (1966).
  92. Gabriel Magill, Ryan Plestid, Maxim Pospelov, and Yu-Dai Tsai, Dipole portal to heavy neutral leptons, Phys. Rev. D 98, 115015 (2018).
  93. Yu. M. Andreev et al., Measurement of the intrinsic hadronic contamination in the NA64−e high-purity e+/e− beam at CERN, Nucl. Instrum. Methods Phys. Res., Sect. A 1057, 168776 (2023).

Outline

Information

Phys. Rev. D 113, 115055– Published 22 June, 2026
  • Received 31 March 2026
  • Accepted 19 May 2026
Crossmark - Check for updates button
Creative Commons Logo

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. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation