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Dark light shining on B→K(*)Emiss

Patrick D. Bolton*

Jernej F. Kamenik†

Martín Novoa-Brunet‡

  • *Contact author: patrick.bolton@ijs.si
  • †Contact author: jernej.kamenik@cern.ch
  • ‡Contact author: martin.novoa@ific.uv.es
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Phys. Rev. D 113, 115001 – Published 2 June, 2026

DOI: https://doi.org/10.1103/68gt-2nlf

Abstract

Recent Belle II data on B+→K+Emiss show an excess consistent with a two-body decay involving a light invisible particle with mass around 2.1 GeV. We present a UV-complete explanation based on a Higgsed U(1)′ gauge symmetry with a light vector boson Z′ and a vectorlike top partner, which naturally enhances b→s transitions. While the minimal model can reproduce the required B→K(*)Z′ rate, it is excluded by LHCb searches for resonant dimuon decays due to unavoidable loop-induced couplings of Z′ to charged leptons. We show that a minimal extension with an additional light U(1)′-charged singlet fermion allows Z′ to decay dominantly invisibly, evades existing constraints coming also from dark photon and collider searches as well as Higgs measurements, and can simultaneously account for the Belle II excess and the observed dark matter abundance through resonant thermal freeze-out.

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References (108)

  1. I. Adachi et al. (Belle-II Collaboration), Phys. Rev. D 109, 112006 (2024).
  2. P. D. Bolton, S. Fajfer, J. F. Kamenik, and M. Novoa-Brunet, Phys. Rev. D 110, 055001 (2024).
  3. G. de Marino and L. E. Gaertner, in 2025 Belle II Physics Week (KEK, Tsukuba, 2025) conference contribution.
  4. P. D. Bolton, S. Fajfer, J. F. Kamenik, and M. Novoa-Brunet, Phys. Rev. D 112, 035010 (2025).
  5. J. F. Kamenik and C. Smith, Phys. Lett. B 680, 471 (2009).
  6. K. Fridell, M. Ghosh, T. Okui, and K. Tobioka, Phys. Rev. D 109, 115006 (2024).
  7. G. Guedes and P. Olgoso, arXiv:2412.14253.
  8. A. J. Buras, J. Harz, and M. A. Mojahed, J. High Energy Phys. 10 (2024) 087.
  9. S. Rosauro-Alcaraz and L. P. S. Leal, Eur. Phys. J. C 84, 795 (2024).
  10. D. Marzocca, M. Nardecchia, A. Stanzione, and C. Toni, Eur. Phys. J. C 84, 1217 (2024).
  11. B.-F. Hou, X.-Q. Li, M. Shen, Y.-D. Yang, and X.-B. Yuan, J. High Energy Phys. 06 (2024) 172.
  12. J. F. Kamenik, Y. Soreq, and J. Zupan, Phys. Rev. D 97, 035002 (2018).
  13. V. Gherardi, D. Marzocca, M. Nardecchia, and A. Romanino, J. High Energy Phys. 10 (2019) 112.
  14. G. D’Ambrosio, G. F. Giudice, G. Isidori, and A. Strumia, Nucl. Phys. B645, 155 (2002).
  15. R. Barbieri, G. Isidori, J. Jones-Perez, P. Lodone, and D. M. Straub, Eur. Phys. J. C 71, 1725 (2011).
  16. R. Barbieri, D. Buttazzo, F. Sala, and D. M. Straub, J. High Energy Phys. 07 (2012) 181.
  17. D. McKeen, J. N. Ng, and D. Tuckler, Phys. Rev. D 109, 075006 (2024).
  18. W. Altmannshofer, A. Crivellin, H. Haigh, G. Inguglia, and J. Martin Camalich, Phys. Rev. D 109, 075008 (2024).
  19. A. Berezhnoy and D. Melikhov, Europhys. Lett. 145, 14001 (2024).
  20. W. Altmannshofer and S. Roy, Phys. Rev. D 111, 075029 (2025).
  21. S.-Y. Ho, J. Kim, and P. Ko, Phys. Rev. D 111, 055029 (2025).
  22. L. Calibbi, T. Li, L. Mukherjee, and M. A. Schmidt, Phys. Rev. D 112, 075020 (2025).
  23. A. Berezhnoy, W. Lucha, and D. Melikhov, Phys. Rev. D 111, 075035 (2025).
  24. L. Di Luzio, M. Nardecchia, and C. Toni, Phys. Rev. D 112, 055031 (2025).
  25. J. Kim and P. Ko, arXiv:2511.20430.
  26. T. M. Aliev, A. Elpe, L. Selbuz, and I. Turan, Phys. Rev. D 112, 015025 (2025).
  27. A. Datta, D. Marfatia, and L. Mukherjee, Phys. Rev. D 109, L031701 (2024).
  28. C.-H. Chen and C.-W. Chiang, Phys. Rev. D 109, 075004 (2024).
  29. X.-G. He, X.-D. Ma, and G. Valencia, Phys. Rev. D 109, 075019 (2024).
  30. Z. S. Wang, H. K. Dreiner, and J. Y. Günther, Eur. Phys. J. C 85, 66 (2025).
  31. T. Felkl, A. Giri, R. Mohanta, and M. A. Schmidt, Eur. Phys. J. C 83, 1135 (2023).
  32. P. Athron, R. Martinez, and C. Sierra, J. High Energy Phys. 02 (2024) 121.
  33. B. Bhattacharya, A. Datta, G. Faisel, S. Khalil, and S. Roy, arXiv:2412.16115.
  34. A. J. Buras and P. Stangl, Eur. Phys. J. C 85, 519 (2025).
  35. D. Bečirević, S. Fajfer, N. Košnik, and L. Pavičić, Phys. Lett. B 861, 139285 (2025).
  36. C. Hati, J. Leite, N. Nath, and J. W. F. Valle, Phys. Rev. D 111, 015038 (2025).
  37. C. S. Kim, D. Sahoo, and K. N. Vishnudath, Eur. Phys. J. C 84, 882 (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. C.-H. Chen and C.-W. Chiang, Phys. Rev. D 110, 075036 (2024).
  40. E. Gabrielli, L. Marzola, K. Müürsepp, and M. Raidal, Eur. Phys. J. C 84, 460 (2024).
  41. F. Loparco, Particles 7, 161 (2024).
  42. C.-H. Chen, C.-W. Chiang, and L. M. G. de la Vega, J. High Energy Phys. 09 (2025) 055.
  43. A. Crivellin, S. Iguro, and T. Kitahara, Phys. Rev. D 112, 095016 (2025).
  44. R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 115, 161802 (2015).
  45. R. Aaij et al. (LHCb Collaboration), Phys. Rev. D 95, 071101 (2017).
  46. L. Allwicher, P. Arnan, D. Barducci, and M. Nardecchia, J. High Energy Phys. 10 (2021) 129.
  47. M. Bauer and P. Foldenauer, Phys. Rev. Lett. 129, 171801 (2022).
  48. B. W. Lee, C. Quigg, and H. B. Thacker, Phys. Rev. D 16, 1519 (1977).
  49. B. W. Lee, C. Quigg, and H. B. Thacker, Phys. Rev. Lett. 38, 883 (1977).
  50. A. Bharucha, D. M. Straub, and R. Zwicky, J. High Energy Phys. 08 (2016) 098.
  51. N. Gubernari, M. Reboud, D. van Dyk, and J. Virto, J. High Energy Phys. 12 (2023) 153; 01 (2025) 125(E).
  52. Y. Ohnishi et al., Prog. Theor. Exp. Phys. 2013, 03A011 (2013).
  53. K. G. Chetyrkin, J. H. Kuhn, and A. Kwiatkowski, Phys. Rep. 277, 189 (1996).
  54. P. A. Baikov, K. G. Chetyrkin, J. H. Kuhn, and J. Rittinger, Phys. Rev. Lett. 108, 222003 (2012).
  55. A. Freitas, J. High Energy Phys. 04 (2014) 070.
  56. P. Ilten, Y. Soreq, M. Williams, and W. Xue, J. High Energy Phys. 06 (2018) 004.
  57. M. Bauer, P. Foldenauer, and J. Jaeckel, J. High Energy Phys. 07 (2018) 094.
  58. C. Baruch, P. Ilten, Y. Soreq, and M. Williams, J. High Energy Phys. 11 (2022) 124.
  59. A. L. Foguel, P. Reimitz, and R. Z. Funchal, J. High Energy Phys. 04 (2022) 119.
  60. J. P. Lees et al. (BABAR Collaboration, Phys. Rev. D 87, 112005 (2013).
  61. M. Abumusabh et al. (Belle-II Collaboration), arXiv:2511.10980.
  62. R. Aaij et al. (LHCb Collaboration), J. High Energy Phys. 06 (2014) 133.
  63. S. Choudhury et al. (BELLE Collaboration), J. High Energy Phys. 03 (2021) 105.
  64. G. Aad et al. (ATLAS Collaboration), Phys. Lett. B 854, 138743 (2024).
  65. A. M. Sirunyan et al. (CMS Collaboration), Eur. Phys. J. C 81, 378 (2021).
  66. J. P. Lees et al. (BABAR Collaboration), Phys. Rev. Lett. 119, 131804 (2017).
  67. J. P. Lees et al. (BABAR Collaboration), Phys. Rev. Lett. 113, 201801 (2014).
  68. M. Ablikim et al. (BESIII Collaboration), Phys. Lett. B 774, 252 (2017).
  69. R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 120, 061801 (2018).
  70. R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 124, 041801 (2020).
  71. G. Aad et al. (ATLAS Collaboration), J. High Energy Phys. 03 (2024) 139.
  72. G. Aad et al. (ATLAS Collaboration), Eur. Phys. J. C 83, 561 (2023).
  73. G. Aad et al. (ATLAS Collaboration), Eur. Phys. J. C 80, 737 (2020).
  74. M. Drees, H. Dreiner, D. Schmeier, J. Tattersall, and J. S. Kim, Comput. Phys. Commun. 187, 227 (2015).
  75. A. Alloul, N. D. Christensen, C. Degrande, C. Duhr, and B. Fuks, Comput. Phys. Commun. 185, 2250 (2014).
  76. J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, H. S. Shao, T. Stelzer, P. Torrielli, and M. Zaro, J. High Energy Phys. 07 (2014) 079.
  77. P. Artoisenet, R. Frederix, O. Mattelaer, and R. Rietkerk, J. High Energy Phys. 03 (2013) 015.
  78. T. Sjostrand, S. Mrenna, and P. Z. Skands, Comput. Phys. Commun. 178, 852 (2008).
  79. M. Czakon and A. Mitov, Comput. Phys. Commun. 185, 2930 (2014).
  80. G. Aad et al. (ATLAS Collaboration), Phys. Lett. B 842, 137963 (2023).
  81. G. Aad et al. (ATLAS Collaboration), J. High Energy Phys. 08 (2024) 153.
  82. S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024).
  83. K. S. Babu, C. F. Kolda, and J. March-Russell, Phys. Rev. D 57, 6788 (1998).
  84. A. Hook, E. Izaguirre, and J. G. Wacker, Adv. High Energy Phys. 2011, 859762 (2011).
  85. D. Curtin, R. Essig, S. Gori, and J. Shelton, J. High Energy Phys. 02 (2015) 157.
  86. S. Schael et al. (ALEPH, DELPHI, L3, OPAL, SLD Collaborations, LEP Electroweak Working Group, SLD Electroweak Group, SLD Heavy Flavour Group), Phys. Rep. 427, 257 (2006).
  87. H. Davoudiasl, H.-S. Lee, and W. J. Marciano, Phys. Rev. D 85, 115019 (2012).
  88. D. P. Aguillard et al. (Muon g-2 Collaboration), Phys. Rev. Lett. 135, 101802 (2025).
  89. R. Aliberti et al., Phys. Rep. 1143, 1 (2025).
  90. J. Grygier et al. (Belle Collaboration), Phys. Rev. D 96, 091101 (2017); 97, 099902(A) (2018).
  91. S. Fajfer, A. Greljo, J. F. Kamenik, and I. Mustac, J. High Energy Phys. 07 (2013) 155.
  92. M. Bauer, M. Neubert, S. Renner, M. Schnubel, and A. Thamm, J. High Energy Phys. 09 (2022) 056.
  93. N. Aghanim et al. (Planck Collaboration), Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  94. P. Gondolo and G. Gelmini, Nucl. Phys. B360, 145 (1991).
  95. G. Alguero, G. Belanger, F. Boudjema, S. Chakraborti, A. Goudelis, S. Kraml, A. Mjallal, and A. Pukhov, Comput. Phys. Commun. 299, 109133 (2024).
  96. A. Belyaev, N. D. Christensen, and A. Pukhov, Comput. Phys. Commun. 184, 1729 (2013).
  97. G. Bélanger, S. Chakraborti, C. Delaunay, and M. Jomain, Phys. Rev. D 112, 095039 (2025).
  98. T. Binder, T. Bringmann, M. Gustafsson, and A. Hryczuk, Phys. Rev. D 96, 115010 (2017); 101, 099901(E) (2020).
  99. P. Agnes et al. (DarkSide Collaboration), Phys. Rev. Lett. 121, 081307 (2018).
  100. E. Aprile et al. (XENON Collaboration), Phys. Rev. Lett. 123, 251801 (2019).
  101. S. Li et al. (PandaX Collaboration), Phys. Rev. Lett. 130, 261001 (2023).
  102. T. R. Slatyer, Phys. Rev. D 93, 023527 (2016).
  103. R. K. Leane, T. R. Slatyer, J. F. Beacom, and K. C. Y. Ng, Phys. Rev. D 98, 023016 (2018).
  104. K. Abe et al. (Super-Kamiokande Collaboration), Phys. Rev. D 102, 072002 (2020).
  105. M. Cirelli, N. Fornengo, J. Koechler, E. Pinetti, and B. M. Roach, J. Cosmol. Astropart. Phys. 07 (2023) 026; 08 (2025) E02(E).
  106. S. Balaji, D. Cleaver, P. De la Torre Luque, and M. Michailidis, J. Cosmol. Astropart. Phys. 11 (2025) 053.
  107. W. Altmannshofer et al. (Belle-II Collaboration), Prog. Theor. Exp. Phys. 2019, 123C01 (2019); 2020, 029201(E) (2020).
  108. A. Abada et al. (FCC Collaboration), Eur. Phys. J. C 79, 474 (2019).

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Phys. Rev. D 113, 115001– Published 2 June, 2026
  • Received 9 January 2026
  • Accepted 6 April 2026
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