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  • Open Access

Natural complex plane for kaon CKM data: Framework, status, and future prospects

Avital Dery*

  • CERN, Theoretical Physics Department, Geneva, Switzerland

  • *Contact author: avital.dery@cern.ch

Phys. Rev. D 112, 053005 – Published 19 September, 2025

DOI: https://doi.org/10.1103/dz6j-q85l

Abstract

Kaon physics can be used to independently determine three out of the four parameters of the CKM matrix, without any B physics input. Treating one parameter, |Vus|, or alternatively Wolfenstein λ, as well known, we show that the natural plane for the presentation of kaon CKM information is spanned by the combinations [A2(1−ρ^),A2η^]. In this way, the use of B physics inputs is avoided, as well as the artificial inflation of errors due to parametric uncertainties, mainly due to |Vcb|. We show that the current status of kaon CKM constraints, impacted by recent advances in measurement and theory, is characterized by four allowed regions, and find that incoming data will inevitably disfavor a number of them, either confirming the CKM paradigm as dominant, or discovering a departure from the Standard Model.

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References (39)

  1. E. Cortina Gil et al. (NA62 Collaboration), J. High Energy Phys. 02 (2025) 191.
  2. M. Hoferichter, B.-L. Hoid, and J. R. de Elvira, J. High Energy Phys. 04 (2024) 071.
  3. G. D’Ambrosio and T. Kitahara, Phys. Rev. Lett. 119, 201802 (2017).
  4. A. Dery, M. Ghosh, Y. Grossman, and S. Schacht, J. High Energy Phys. 07 (2021) 103.
  5. A. Dery, M. Ghosh, Y. Grossman, T. Kitahara, and S. Schacht, J. High Energy Phys. 03 (2023) 014.
  6. E.-H. Chao and N. Christ, Phys. Rev. D 110, 054514 (2024).
  7. J. Fry et al. (KOTO Collaboration), arXiv:2501.14827.
  8. A. Dery, Y. Grossman, T. Kitahara, R. Marchevski, D. Martinez Santos, and S. Schacht, arXiv:2507.13445.
  9. L. Wolfenstein, Phys. Rev. Lett. 51, 1945 (1983).
  10. G. Buchalla and A. J. Buras, Phys. Rev. D 54, 6782 (1996).
  11. A. J. Buras, M. Gorbahn, U. Haisch, and U. Nierste, J. High Energy Phys. 11 (2006) 002; 11 (2012) 167(E).
  12. E. Blucher, B. Winstein, and T. Yamanaka, Prog. Theor. Phys. 122, 81 (2009).
  13. A. J. Buras and E. Venturini, Acta Phys. Pol. B 53, 6 (2021).
  14. C. Lehner, E. Lunghi, and A. Soni, Phys. Lett. B 759, 82 (2016).
  15. E. Lunghi and A. Soni, J. High Energy Phys. 12 (2024) 097.
  16. A. J. Buras, M. E. Lautenbacher, and G. Ostermaier, Phys. Rev. D 50, 3433 (1994).
  17. J. Charles, A. Hocker, H. Lacker, S. Laplace, F. R. Le Diberder, J. Malcles, J. Ocariz, M. Pivk, and L. Roos (CKMfitter Group), Eur. Phys. J. C 41, 1 (2005).
  18. R. F. Lebed, Phys. Rev. D 55, 348 (1997).
  19. S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024).
  20. CKMFitter Collaboration, http://ckmfitter.in2p3.fr/.
  21. R. Marchevski, J. Phys. Conf. Ser. 2446, 012035 (2023).
  22. A. Dery and M. Ghosh, J. High Energy Phys. 03 (2022) 048.
  23. R. Abbott et al. (RBC and UKQCD Collaborations), Phys. Rev. D 102, 054509 (2020).
  24. T. Blum, P. A. Boyle, D. Hoying, T. Izubuchi, L. Jin, C. Jung, C. Kelly, C. Lehner, A. Soni, and M. Tomii (RBC and UKQCD Collaborations), Phys. Rev. D 108, 094517 (2023).
  25. G. Buchalla and A. J. Buras, Nucl. Phys. B548, 309 (1999).
  26. G. Isidori, F. Mescia, and C. Smith, Nucl. Phys. B718, 319 (2005).
  27. J. Brod and M. Gorbahn, Phys. Rev. D 78, 034006 (2008).
  28. J. Brod, M. Gorbahn, and E. Stamou, Phys. Rev. D 83, 034030 (2011).
  29. A. J. Buras, D. Buttazzo, J. Girrbach-Noe, and R. Knegjens, J. High Energy Phys. 11 (2015) 033.
  30. J. Brod, M. Gorbahn, and E. Stamou, Proc. Sci. BEAUTY2020 (2021) 056 [arXiv:2105.02868].
  31. G. Buchalla, A. J. Buras, and M. E. Lautenbacher, Rev. Mod. Phys. 68, 1125 (1996).
  32. A. J. Buras, D. Guadagnoli, and G. Isidori, Phys. Lett. B 688, 309 (2010).
  33. J. Brod and M. Gorbahn, Phys. Rev. D 82, 094026 (2010).
  34. J. Brod, M. Gorbahn, and E. Stamou, Phys. Rev. Lett. 125, 171803 (2020).
  35. M. Ciuchini, E. Franco, V. Lubicz, G. Martinelli, L. Silvestrini, and C. Tarantino, J. High Energy Phys. 02 (2022) 181.
  36. J. Brod, S. Kvedaraite, Z. Polonsky, and A. Youssef, J. High Energy Phys. 12 (2022) 014.
  37. G. D’Ambrosio, G. Isidori, and J. Portoles, Phys. Lett. B 423, 385 (1998).
  38. G. Isidori and R. Unterdorfer, J. High Energy Phys. 01 (2004) 009.
  39. J. Brod and E. Stamou, J. High Energy Phys. 05 (2023) 155.

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