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  • Access by Xinjiang University

Minimal dark matter: Generalized framework and direct-detection sensitivity

Spencer Griffith1,2,*, Juri Smirnov3,†, Laura Lopez-Honorez4,5,‡, and John F. Beacom1,2,6,§

  • *Contact author: griffith.1037@osu.edu
  • Contact author: juri.smirnov@liverpool.ac.uk
  • Contact author: Laura.Lopez.Honorez@ulb.be
  • §Contact author: beacom.7@osu.edu

Phys. Rev. D 114, 035016 – Published 10 August, 2026

DOI: https://doi.org/10.1103/jv6s-76s9

Abstract

Minimal electroweak dark matter models are compelling due to their simplicity, though calculations of their freeze-out abundance are complicated by nonperturbative effects due to Sommerfeld enhancement and bound-state formation. It has been shown that all individual multiplet scenarios beyond the doublet lead to direct-detection signals above the neutrino floor and thus within the reach of next-generation experiments. If no signals are found, would minimal dark matter be excluded? Yes for the simplest models, but it has been unknown for the important extension of two multiplets coupled by Higgs interactions (Higgs-coupled minimal dark matter). We present a generalized framework for calculating nonperturbative effects for such models that also covers the case of individual multiplets. In this framework, we calculate nonperturbative effects on freeze-out as well as the prospects for direct detection, correcting shortcomings and omissions in the literature. Importantly, for the mixed Majorana (odd) and Dirac (even) multiplet combination 3M2D (and marginally the 5M4D), we find that the predicted direct-detection signals can extend below the neutrino floor. Fully testing minimal dark matter will thus require more than direct-detection experiments.

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References (75)

  1. G. Bertone and D. Hooper, Rev. Mod. Phys. 90, 045002 (2018).
  2. B. Carr, M. Raidal, T. Tenkanen, V. Vaskonen, and H. Veermäe, Phys. Rev. D 96, 023514 (2017).
  3. S. Ge, K. Lawson, and A. Zhitnitsky, Phys. Rev. D 99, 116017 (2019).
  4. M. Cirelli, Y. Gouttenoire, K. Petraki, and F. Sala, J. Cosmol. Astropart. Phys. 02 (2019) 014.
  5. J. Berges, A. Chatrchyan, and J. Jaeckel, J. Cosmol. Astropart. Phys. 08 (2019) 020.
  6. M. Blennow, E. Fernandez-Martinez, A. Olivares-Del Campo, S. Pascoli, S. Rosauro-Alcaraz, and A. V. Titov, Eur. Phys. J. C 79, 555 (2019).
  7. G. Arcadi, A. Djouadi, and M. Raidal, Phys. Rep. 842, 1 (2020).
  8. S. W. Allen, A. E. Evrard, and A. B. Mantz, Annu. Rev. Astron. Astrophys. 49, 409 (2011).
  9. P. Salucci, Astron. Astrophys. Rev. 27, 2 (2019).
  10. N. Aghanim et al. (Planck Collaboration), Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  11. J. D. Simon, Annu. Rev. Astron. Astrophys. 57, 375 (2019).
  12. M. Cirelli, A. Strumia, and J. Zupan, arXiv:2406.01705.
  13. M. Cirelli, N. Fornengo, and A. Strumia, Nucl. Phys. B753, 178 (2006).
  14. M. Cirelli, A. Strumia, and M. Tamburini, Nucl. Phys. B787, 152 (2007).
  15. G. Steigman and M. S. Turner, Nucl. Phys. B253, 375 (1985).
  16. G. Bertone, D. Hooper, and J. Silk, Phys. Rep. 405, 279 (2005).
  17. G. Steigman, B. Dasgupta, and J. F. Beacom, Phys. Rev. D 86, 023506 (2012).
  18. G. Arcadi, M. Dutra, P. Ghosh, M. Lindner, Y. Mambrini, M. Pierre, S. Profumo, and F. S. Queiroz, Eur. Phys. J. C 78, 203 (2018).
  19. L. Roszkowski, E. M. Sessolo, and S. Trojanowski, Rep. Prog. Phys. 81, 066201 (2018).
  20. J. Smirnov, SciPost Phys. Proc. 12, 003 (2023).
  21. J. Hisano, S. Matsumoto, and M. M. Nojiri, Phys. Rev. Lett. 92, 031303 (2004).
  22. J. Hisano, S. Matsumoto, M. M. Nojiri, and O. Saito, Phys. Rev. D 71, 063528 (2005).
  23. J. Hisano, S. Matsumoto, M. Nagai, O. Saito, and M. Senami, Phys. Lett. B 646, 34 (2007).
  24. N. Arkani-Hamed, D. P. Finkbeiner, T. R. Slatyer, and N. Weiner, Phys. Rev. D 79, 015014 (2009).
  25. S. Cassel, J. Phys. G 37, 105009 (2010).
  26. J. D. March-Russell and S. M. West, Phys. Lett. B 676, 133 (2009).
  27. B. von Harling and K. Petraki, J. Cosmol. Astropart. Phys. 12 (2014) 033.
  28. H. An, M. B. Wise, and Y. Zhang, Phys. Rev. D 93, 115020 (2016).
  29. A. Mitridate, M. Redi, J. Smirnov, and A. Strumia, J. Cosmol. Astropart. Phys. 05 (2017) 006.
  30. S. Bottaro, D. Buttazzo, M. Costa, R. Franceschini, P. Panci, D. Redigolo, and L. Vittorio, Eur. Phys. J. C 82, 31 (2022).
  31. I. M. Bloch, S. Bottaro, D. Redigolo, and L. Vittorio, J. High Energy Phys. 08 (2025) 216.
  32. L. Baudis, Nucl. Phys. B1003, 116473 (2024).
  33. A. Abdukerim et al. (PANDA-X and PandaX Collaboration), Sci. China Phys. Mech. Astron. 68, 221011 (2025).
  34. M. W. Goodman and E. Witten, Phys. Rev. D 31, 3059 (1985).
  35. D. S. Akerib et al. (CDMS Collaboration), Phys. Rev. Lett. 96, 011302 (2006).
  36. R. Mahbubani and L. Senatore, Phys. Rev. D 73, 043510 (2006).
  37. F. D’Eramo, Phys. Rev. D 76, 083522 (2007).
  38. R. Enberg, P. J. Fox, L. J. Hall, A. Y. Papaioannou, and M. Papucci, J. High Energy Phys. 11 (2007) 014.
  39. T. Cohen, J. Kearney, A. Pierce, and D. Tucker-Smith, Phys. Rev. D 85, 075003 (2012).
  40. C. Cheung and D. Sanford, J. Cosmol. Astropart. Phys. 02 (2014) 011.
  41. L. Calibbi, A. Mariotti, and P. Tziveloglou, J. High Energy Phys. 10 (2015) 116.
  42. A. Freitas, S. Westhoff, and J. Zupan, J. High Energy Phys. 09 (2015) 015.
  43. S. Banerjee, S. Matsumoto, K. Mukaida, and Y.-L. S. Tsai, J. High Energy Phys. 11 (2016) 070.
  44. A. Dedes and D. Karamitros, Phys. Rev. D 89, 115002 (2014).
  45. M. Beneke, A. Bharucha, A. Hryczuk, S. Recksiegel, and P. Ruiz-Femenia, J. High Energy Phys. 01 (2017) 002.
  46. T. M. P. Tait and Z.-H. Yu, J. High Energy Phys. 03 (2016) 204.
  47. L. Lopez Honorez, M. H. G. Tytgat, P. Tziveloglou, and B. Zaldivar, J. High Energy Phys. 04 (2018) 011.
  48. R. Oncala and K. Petraki, J. High Energy Phys. 06 (2021) 124.
  49. R. Oncala and K. Petraki, J. High Energy Phys. 08 (2021) 069.
  50. P. Asadi, M. Baumgart, P. J. Fitzpatrick, E. Krupczak, and T. R. Slatyer, J. Cosmol. Astropart. Phys. 02 (2017) 005.
  51. J. Smirnov and J. F. Beacom, Phys. Rev. D 100, 043029 (2019).
  52. T. Hambye, F. S. Ling, L. Lopez Honorez, and J. Rocher, J. High Energy Phys. 07 (2009) 090; 05 (2010) 66.
  53. J. Billard, L. Strigari, and E. Figueroa-Feliciano, Phys. Rev. D 89, 023524 (2014).
  54. J. Fan and M. Reece, J. High Energy Phys. 10 (2013) 124.
  55. T. Cohen, M. Lisanti, A. Pierce, and T. R. Slatyer, J. Cosmol. Astropart. Phys. 10 (2013) 061.
  56. N. L. Rodd, B. R. Safdi, and W. L. Xu, Phys. Rev. D 110, 043003 (2024).
  57. B. R. Safdi and W. L. Xu, arXiv:2507.15934.
  58. M. Aghaie, A. Dondarini, G. Marino, and P. Panci, arXiv:2507.17607.
  59. M. Baumgart, S. Bottaro, D. Redigolo, N. L. Rodd, and T. R. Slatyer, J. High Energy Phys. 02 (2026) 213.
  60. J. Hisano, K. Ishiwata, and N. Nagata, J. High Energy Phys. 06 (2015) 097.
  61. A. Mitridate, M. Redi, J. Smirnov, and A. Strumia, J. High Energy Phys. 10 (2017) 210.
  62. N. A. Dondi, F. Sannino, and J. Smirnov, Phys. Rev. D 101, 103010 (2020).
  63. M. Garny and J. Heisig, Phys. Rev. D 105, 055004 (2022).
  64. S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024).
  65. J. Sakurai, Advanced Quantum Mechanics (Addison-Wesley Publishing Company, New York, 1967).
  66. V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Quantum Electrodynamics, Course of Theoretical Physics Vol. 4 (Pergamon Press, Oxford, 1982).
  67. M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, Reading, MA, 1995).
  68. L. Schiff, Quantum Mechanics: 3rd Edition (McGraw Hill, New York, 1968).
  69. C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics, Volume 2: Angular Momentum, Spin, and Approximation Methods (Wiley, New York, 2019).
  70. H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One and Two-Electron Atoms (Springer, Berlin, Heidelberg, 1957).
  71. K. Griest and D. Seckel, Phys. Rev. D 43, 3191 (1991).
  72. J. Aalbers et al. (LZ Collaboration), Phys. Rev. Lett. 135, 011802 (2025).
  73. Z. Bo et al. (PandaX Collaboration), Phys. Rev. Lett. 134, 011805 (2025).
  74. J. Billard, F. Mayet, and D. Santos, Phys. Rev. D 85, 035006 (2012).
  75. S. Griffith, J. Smirnov, L. Lopez-Honorez, and J. F. Beacom (2026), https://github.com/skgriffith/MixedMultipletDM.

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