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  • Open Access

Is dark matter the origin of the B→Kνν¯ excess at Belle II?

Lorenzo Calibbi1,*, Tong Li1,†, Lopamudra Mukherjee1,‡, and Michael A. Schmidt2,§

  • *Contact author: calibbi@nankai.edu.cn
  • †Contact author: litong@nankai.edu.cn
  • ‡Contact author: lopamudra.physics@gmail.com
  • §Contact author: m.schmidt@unsw.edu.au

Phys. Rev. D 112, 075020 – Published 10 October, 2025

DOI: https://doi.org/10.1103/r2gw-rwzw

Abstract

We present two models of dark matter (DM) that can provide a natural explanation of the excess of B+→K++invisible events with respect to the Standard Model (SM) prediction for B+→K+νν¯, which has been reported by the Belle II Collaboration. Interactions between the dark and the visible sector are mediated by an axionlike particle in one case, by the kinetic mixing between a dark photon and the SM photon in the second case. Both models encompass a light fermion singlet as the DM candidate and can account for the observed DM relic abundance through, respectively, the freeze-in and the freeze-out production mechanism, while simultaneously explaining the Belle II excess.

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References (117)

  1. I. Adachi et al. (Belle-II Collaboration), Phys. Rev. D 109, 112006 (2024).
  2. W. G. Parrott, C. Bouchard, and C. T. H. Davies (HPQCD Collaboration), Phys. Rev. D 107, 014511 (2023); 107, 119903(E) (2023).
  3. D. Bečirević, G. Piazza, and O. Sumensari, Eur. Phys. J. C 83, 252 (2023).
  4. W. Altmannshofer, A. J. Buras, D. M. Straub, and M. Wick, J. High Energy Phys. 04 (2009) 022.
  5. A. J. Buras, J. Girrbach-Noe, C. Niehoff, and D. M. Straub, J. High Energy Phys. 02 (2015) 184.
  6. T. Blake, G. Lanfranchi, and D. M. Straub, Prog. Part. Nucl. Phys. 92, 50 (2017).
  7. P. Athron, R. Martinez, and C. Sierra, J. High Energy Phys. 02 (2024) 121.
  8. R. Bause, H. Gisbert, and G. Hiller, Phys. Rev. D 109, 015006 (2024).
  9. L. Allwicher, D. Becirevic, G. Piazza, S. Rosauro-Alcaraz, and O. Sumensari, Phys. Lett. B 848, 138411 (2024).
  10. C.-H. Chen and C.-W. Chiang, Phys. Rev. D 109, 075004 (2024).
  11. F.-Z. Chen, Q. Wen, and F. Xu, Eur. Phys. J. C 84, 1012 (2024).
  12. B.-F. Hou, X.-Q. Li, M. Shen, Y.-D. Yang, and X.-B. Yuan, J. High Energy Phys. 06 (2024) 172.
  13. D. Marzocca, M. Nardecchia, A. Stanzione, and C. Toni, Eur. Phys. J. C 84, 1217 (2024).
  14. S. Karmakar, A. Dighe, and R. S. Gupta, Phys. Rev. D 111, 055002 (2025).
  15. C. Hati, J. Leite, N. Nath, and J. W. F. Valle, Phys. Rev. D 111, 015038 (2025).
  16. L. Allwicher, M. Bordone, G. Isidori, G. Piazza, and A. Stanzione, Phys. Lett. B 861, 139295 (2025).
  17. H.-J. Tian, H.-B. Fu, T. Zhong, Y.-X. Wang, and X.-G. Wu, Phys. Rev. D 111, 076013 (2025).
  18. J. Alda, A. Mir, and S. Penaranda, arXiv:2412.15830.
  19. P. S. B. Dev, S. Goswami, C. Majumdar, and D. Pachhar, J. High Energy Phys. 01 (2025) 004.
  20. D. Bečirević, S. Fajfer, N. Košnik, and L. Pavičić, Phys. Lett. B 861, 139285 (2025).
  21. A. J. Buras and P. Stangl, Eur. Phys. J. C 85, 519 (2025).
  22. B. Bhattacharya, A. Datta, G. Faisel, S. Khalil, and S. Roy, arXiv:2412.16115.
  23. C.-H. Chen and C.-W. Chiang, Phys. Rev. D 110, 075036 (2024).
  24. C. S. Kim, D. Sahoo, and K. N. Vishnudath, Eur. Phys. J. C 84, 882 (2024).
  25. C.-Q. Zhang, J. Sun, Z.-P. Xing, and R.-L. Zhu, Phys. Rev. D 111, 113003 (2025).
  26. T. E. Browder, N. G. Deshpande, R. Mandal, and R. Sinha, Phys. Rev. D 104, 053007 (2021).
  27. X. G. He and G. Valencia, Phys. Lett. B 821, 136607 (2021).
  28. T. Felkl, S. L. Li, and M. A. Schmidt, J. High Energy Phys. 12 (2021) 118.
  29. T. Felkl, A. Giri, R. Mohanta, and M. A. Schmidt, Eur. Phys. J. C 83, 1135 (2023).
  30. M. Ovchynnikov, M. A. Schmidt, and T. Schwetz, Eur. Phys. J. C 83, 791 (2023).
  31. L. Gärtner, N. Hartmann, L. Heinrich, M. Horstmann, T. Kuhr, M. Reboud, S. Stefkova, and D. van Dyk, Eur. Phys. J. C 84, 693 (2024).
  32. S. Rosauro-Alcaraz and L. P. S. Leal, Eur. Phys. J. C 84, 795 (2024).
  33. A. J. Buras, J. Harz, and M. A. Mojahed, J. High Energy Phys. 10 (2024) 087.
  34. A. Datta, D. Marfatia, and L. Mukherjee, Phys. Rev. D 109, L031701 (2024).
  35. C. Bird, P. Jackson, R. V. Kowalewski, and M. Pospelov, Phys. Rev. Lett. 93, 201803 (2004).
  36. X.-G. He, X.-D. Ma, and G. Valencia, J. High Energy Phys. 03 (2023) 037.
  37. X.-G. He, X.-D. Ma, and G. Valencia, Phys. Rev. D 109, 075019 (2024).
  38. X.-G. He, X.-D. Ma, M. A. Schmidt, G. Valencia, and R. R. Volkas, J. High Energy Phys. 07 (2024) 168.
  39. S.-Y. Ho, J. Kim, and P. Ko, Phys. Rev. D 111, 055029 (2025).
  40. M. Abdughani and Y. Reyimuaji, Phys. Rev. D 110, 055013 (2024).
  41. A. Berezhnoy and D. Melikhov, Europhys. Lett. 145, 14001 (2024).
  42. Z. G. Berezhiani, M. Y. Khlopov, and R. R. Khomeriki, Sov. J. Nucl. Phys. 52, 344 (1990).
  43. Z. G. Berezhiani and M. Y. Khlopov, Sov. J. Nucl. Phys. 51, 935 (1990).
  44. Z. G. Berezhiani and M. Y. Khlopov, Sov. J. Nucl. Phys. 51, 739 (1990).
  45. T. Ferber, A. Filimonova, R. Schäfer, and S. Westhoff, J. High Energy Phys. 04 (2023) 131.
  46. W. Altmannshofer, A. Crivellin, H. Haigh, G. Inguglia, and J. Martin Camalich, Phys. Rev. D 109, 075008 (2024).
  47. W. Altmannshofer and S. Roy, Phys. Rev. D 111, 075029 (2025).
  48. G.-Q. Dai, C.-X. Yue, Y.-Y. Bu, and Y.-H. Wang, Commun. Theor. Phys. 76, 095202 (2024).
  49. A. Filimonova, R. Schäfer, and S. Westhoff, Phys. Rev. D 101, 095006 (2020).
  50. K. Fridell, M. Ghosh, T. Okui, and K. Tobioka, Phys. Rev. D 109, 115006 (2024).
  51. Q.-Y. Hu, Eur. Phys. J. C 85, 556 (2025).
  52. P. D. Bolton, S. Fajfer, J. F. Kamenik, and M. Novoa-Brunet, Phys. Rev. D 110, 055001 (2024).
  53. E. Gabrielli, L. Marzola, K. Müürsepp, and M. Raidal, Eur. Phys. J. C 84, 460 (2024).
  54. D. McKeen, J. N. Ng, and D. Tuckler, Phys. Rev. D 109, 075006 (2024).
  55. H. Davoudiasl and M. Schnubel, Phys. Rev. D 110, 075014 (2024).
  56. R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 115, 161802 (2015).
  57. R. Aaij et al. (LHCb Collaboration), Phys. Rev. D 95, 071101 (2017).
  58. R. Aaij et al. (LHCb Collaboration), J. High Energy Phys. 06 (2014) 133.
  59. J. P. Lees et al. (BABAR Collaboration, Phys. Rev. Lett. 113, 201801 (2014).
  60. J. P. Lees et al. (BABAR Collaboration, Phys. Rev. D 87, 112005 (2013).
  61. B. Döbrich, F. Ertas, F. Kahlhoefer, and T. Spadaro, Phys. Lett. B 790, 537 (2019).
  62. F. Bergsma et al. (CHARM Collaboration), Phys. Lett. 157B, 458 (1985).
  63. G. G. Raffelt, Phys. Rep. 198, 1 (1990).
  64. R. Alemany Fernández et al. (PBC Collaboration), arXiv:2505.00947.
  65. N. Aghanim et al. (Planck Collaboration), Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  66. A. Bharucha, F. Brümmer, N. Desai, and S. Mutzel, J. High Energy Phys. 02 (2023) 141.
  67. D. K. Ghosh, A. Ghoshal, and S. Jeesun, J. High Energy Phys. 01 (2024) 026.
  68. A. Cheek, J. K. Osiński, L. Roszkowski, and S. Trojanowski, J. High Energy Phys. 03 (2023) 149.
  69. K. S. Babu, S. Chakdar, N. Das, D. K. Ghosh, and P. Ghosh, J. High Energy Phys. 07 (2023) 143.
  70. R. Mandal and T. Tong, J. Cosmol. Astropart. Phys. 11 (2023) 074.
  71. M. Pospelov, A. Ritz, and M. B. Voloshin, Phys. Lett. B 662, 53 (2008).
  72. M. T. Frandsen, F. Kahlhoefer, S. Sarkar, and K. Schmidt-Hoberg, J. High Energy Phys. 09 (2011) 128.
  73. J. L. Feng and J. Smolinsky, Phys. Rev. D 96, 095022 (2017).
  74. S. Knapen, T. Lin, and K. M. Zurek, Phys. Rev. D 96, 115021 (2017).
  75. M. Dutra, M. Lindner, S. Profumo, F. S. Queiroz, W. Rodejohann, and C. Siqueira, J. Cosmol. Astropart. Phys. 03 (2018) 037.
  76. D.-W. Jung, S.-H. Nam, C. Yu, Y. G. Kim, and K. Y. Lee, Eur. Phys. J. C 80, 513 (2020).
  77. T. G. Rizzo, J. High Energy Phys. 01 (2021) 079.
  78. D. Borah, L. Mukherjee, and S. Nandi, J. High Energy Phys. 12 (2020) 052.
  79. T. G. Rizzo, Phys. Rev. D 110, 075037 (2024).
  80. G. D. V. Garcia, F. Kahlhoefer, M. Ovchynnikov, and T. Schwetz, J. High Energy Phys. 02 (2025) 127.
  81. G. Krnjaic, arXiv:2505.04626.
  82. D. Alonso-González, D. Cerdeño, P. Foldenauer, and J. M. No, arXiv:2507.11376.
  83. I. Brivio, M. B. Gavela, L. Merlo, K. Mimasu, J. M. No, R. del Rey, and V. Sanz, Eur. Phys. J. C 77, 572 (2017).
  84. M. Bauer, M. Neubert, S. Renner, M. Schnubel, and A. Thamm, J. High Energy Phys. 09 (2022) 056.
  85. N. Gubernari, M. Reboud, D. van Dyk, and J. Virto, J. High Energy Phys. 12 (2023) 153.
  86. N. Gubernari, A. Kokulu, and D. van Dyk, J. High Energy Phys. 01 (2019) 150.
  87. J. Lees et al. (BABAR Collaboration, Phys. Rev. D 87, 112005 (2013).
  88. W. Altmannshofer et al. (Belle-II Collaboration), Prog. Theor. Exp. Phys. 2019, 123C01 (2019); 2020, 029201(E) (2020).
  89. G. Dalla Valle Garcia, F. Kahlhoefer, M. Ovchynnikov, and A. Zaporozhchenko, Phys. Rev. D 109, 055042 (2024).
  90. S. Navas et al. (Particle Data Group Collaboration), Phys. Rev. D 110, 030001 (2024).
  91. M. Aghaie, G. Armando, A. Conaci, A. Dondarini, P. Matak, P. Panci, Z. Sinska, and R. Ziegler, Phys. Lett. B 856, 138923 (2024).
  92. J. McDonald, Phys. Rev. Lett. 88, 091304 (2002).
  93. L. J. Hall, K. Jedamzik, J. March-Russell, and S. M. West, J. High Energy Phys. 03 (2010) 080.
  94. O. Wantz and E. P. S. Shellard, Phys. Rev. D 82, 123508 (2010).
  95. G. Ballesteros, M. A. G. Garcia, and M. s. Pierre, J. Cosmol. Astropart. Phys. 03 (2021) 101.
  96. F. D’Eramo and A. Lenoci, J. Cosmol. Astropart. Phys. 10 (2021) 045.
  97. Q. Decant, J. Heisig, D. C. Hooper, and L. Lopez-Honorez, J. Cosmol. Astropart. Phys. 03 (2022) 041.
  98. F. Wilczek, Phys. Rev. Lett. 49, 1549 (1982).
  99. Y. Ema, K. Hamaguchi, T. Moroi, and K. Nakayama, J. High Energy Phys. 01 (2017) 096.
  100. L. Calibbi, F. Goertz, D. Redigolo, R. Ziegler, and J. Zupan, Phys. Rev. D 95, 095009 (2017).
  101. H. Davoudiasl, H.-S. Lee, and W. J. Marciano, Phys. Rev. D 85, 115019 (2012).
  102. A. Datta, A. Hammad, D. Marfatia, L. Mukherjee, and A. Rashed, J. High Energy Phys. 03 (2023) 108.
  103. B. Holdom, Phys. Lett. 166B, 196 (1986).
  104. K. S. Babu, C. F. Kolda, and J. March-Russell, Phys. Rev. D 57, 6788 (1998).
  105. J. P. Lees et al. (BABAR Collaboration, Phys. Rev. Lett. 119, 131804 (2017).
  106. G. Steigman, B. Dasgupta, and J. F. Beacom, Phys. Rev. D 86, 023506 (2012).
  107. E. W. Kolb and M. S. Turner, The Early Universe (Taylor and Francis, London, 2019), Vol. 69.
  108. J. Grygier et al. (Belle Collaboration), Phys. Rev. D 96, 091101 (2017); 97, 099902(A) (2018).
  109. E. Cortina Gil et al. (NA62 Collaboration), J. High Energy Phys. 06 (2021) 093.
  110. D. Gorbunov, I. Krasnov, and S. Suvorov, Phys. Lett. B 820, 136524 (2021).
  111. T. Ferber, A. Grohsjean, and F. Kahlhoefer, Prog. Part. Nucl. Phys. 136, 104105 (2024).
  112. M. W. Winkler, Phys. Rev. D 99, 015018 (2019).
  113. D. Huang et al. (PandaX Collaboration), Phys. Rev. Lett. 131, 191002 (2023).
  114. M. Cirelli, A. Strumia, and J. Zupan, arXiv:2406.01705.
  115. S. W. Randall, M. Markevitch, D. Clowe, A. H. Gonzalez, and M. Bradac, Astrophys. J. 679, 1173 (2008).
  116. L. Aggarwal et al. (Belle-II Collaboration), arXiv:2207.06307.
  117. E. Cortina Gil et al. (NA62 Collaboration), J. High Energy Phys. 02 (2025) 191.

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