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Exact parametrization of a minimal seesaw model

Zi-Qiang Chen1,2,3,*, Xi-He Hu1,2,3,†, and Ye-Ling Zhou1,‡

  • *Contact author: chenziqiang22@mails.ucas.ac.cn
  • †Contact author: huxihe23@mails.ucas.ac.cn
  • ‡Contact author: zhouyeling@ucas.ac.cn
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Phys. Rev. D 112, 115032 – Published 18 December, 2025

DOI: https://doi.org/10.1103/tc8x-2lp5

Abstract

We propose a parametrization of neutrino masses and mixing in the minimal seesaw model (MSM). The MSM, which introduces two heavy sterile neutrinos, is the minimal extension of the Standard Model in addressing the tiny masses of active neutrinos. The parametrization includes 11 free parameters: six neutrino oscillation parameters (two mass-squared differences Δm212, Δm312 three mixing angles θ12, θ13, θ23, and one Dirac phase δCP), one mass parameter in 0ν2β decay mee, and four additional parameters: two heavy neutrino masses M1 and M2, one active-sterile mixing angle θ14, and one CP-violating phase δ14. This parametrization is derived exactly from the most general neutrino mass matrix in the MSM without any approximation. We further discuss its implications in phenomenological studies.

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References (58)

  1. S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024).
  2. P. Minkowski, Phys. Lett. 67B, 421 (1977).
  3. T. Yanagida, Conf. Proc. C 7902131, 95 (1979).
  4. M. Gell-Mann, P. Ramond, and R. Slansky, Conf. Proc. C 790927, 315 (1979).
  5. S. L. Glashow, NATO Sci. Ser. B 61, 687 (1980).
  6. R. N. Mohapatra and G. Senjanovic, Phys. Rev. Lett. 44, 912 (1980).
  7. Z. z. Xing, Phys. Rev. D 85, 013008 (2012).
  8. S. M. Bilenky, S. T. Petcov, and B. Pontecorvo, Phys. Lett. 67B, 309 (1977).
  9. B. W. Lee, S. Pakvasa, R. E. Shrock, and H. Sugawara, Phys. Rev. Lett. 38, 937 (1977); 38, 1230(E) (1977).
  10. W. J. Marciano and A. I. Sanda, Phys. Lett. 67B, 303 (1977).
  11. T. P. Cheng and L. F. Li, Phys. Rev. Lett. 45, 1908 (1980).
  12. F. del Aguila, J. A. Aguilar-Saavedra, and R. Pittau, J. High Energy Phys. 10 (2007) 047.
  13. A. Atre, T. Han, S. Pascoli, and B. Zhang, J. High Energy Phys. 05 (2009) 030.
  14. M. Fukugita and T. Yanagida, Phys. Lett. B 174, 45 (1986).
  15. N. Aghanim et al. (Planck Collaboration), Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  16. J. A. Casas and A. Ibarra, Nucl. Phys. B618, 171 (2001).
  17. S. Davidson and A. Ibarra, Phys. Lett. B 535, 25 (2002).
  18. S. F. King, Nucl. Phys. B576, 85 (2000).
  19. S. F. King, J. High Energy Phys. 09 (2002) 011.
  20. P. H. Frampton, S. L. Glashow, and T. Yanagida, Phys. Lett. B 548, 119 (2002).
  21. W. l. Guo, Z. z. Xing, and S. Zhou, Int. J. Mod. Phys. E 16, 1 (2007).
  22. V. Barger, D. A. Dicus, H. J. He, and T. j. Li, Phys. Lett. B 583, 173 (2004).
  23. D. L. Fang, Y. F. Li, and Y. Y. Zhang, Phys. Lett. B 833, 137346 (2022).
  24. Z. z. Xing, Phys. Lett. B 660, 515 (2008).
  25. A. Ibarra and G. G. Ross, Phys. Lett. B 591, 285 (2004).
  26. I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler, J. P. Pinheiro, and T. Schwetz, J. High Energy Phys. 12 (2024) 216.
  27. S. Antusch, C. Biggio, E. Fernandez-Martinez, M. B. Gavela, and J. Lopez-Pavon, J. High Energy Phys. 10 (2006) 084.
  28. M. Blennow, E. Fernández-Martínez, J. Hernández-García, J. López-Pavón, X. Marcano, and D. Naredo-Tuero, J. High Energy Phys. 08 (2023) 030.
  29. C. S. Lim and T. Inami, Prog. Theor. Phys. 67, 1569 (1982).
  30. P. Langacker and D. London, Phys. Rev. D 38, 907 (1988).
  31. A. Ilakovac and A. Pilaftsis, Nucl. Phys. B437, 491 (1995).
  32. R. Alonso, M. Dhen, M. B. Gavela, and T. Hambye, J. High Energy Phys. 01 (2013) 118.
  33. R. Kitano, M. Koike, and Y. Okada, Phys. Rev. D 66, 096002 (2002); 76, 059902(E) (2007).
  34. T. Suzuki, D. F. Measday, and J. P. Roalsvig, Phys. Rev. C 35, 2212 (1987).
  35. K. Afanaciev et al. (MEG II Collaboration), Eur. Phys. J. C 84, 216 (2024); 84, 1042(E) (2024).
  36. A. M. Baldini et al. (MEG II Collaboration), Eur. Phys. J. C 78, 380 (2018).
  37. U. Bellgardt et al. (SINDRUM Collaboration), Nucl. Phys. B299, 1 (1988).
  38. K. Arndt et al. (Mu3e Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 1014, 165679 (2021).
  39. C. Dohmen et al. (SINDRUM II Collaboration), Phys. Lett. B 317, 631 (1993).
  40. E. V. Hungerford (COMET Collaboration), AIP Conf. Proc. 1182, 694 (2009).
  41. Y. G. Cui et al. (COMET Collaboration), Report No. KEK-2009-10.
  42. P. D. Bolton, F. F. Deppisch, and P. S. Bhupal Dev, J. High Energy Phys. 03 (2020) 170.
  43. F. J. Escrihuela, D. V. Forero, O. G. Miranda, M. Tortola, and J. W. F. Valle, Phys. Rev. D 92, 053009 (2015); 93, 119905(E) (2016).
  44. Y. F. Li and S. Luo, Phys. Rev. D 93, 033008 (2016).
  45. D. V. Forero, C. Giunti, C. A. Ternes, and M. Tortola, Phys. Rev. D 104, 075030 (2021).
  46. R. Barbieri, P. Creminelli, A. Strumia, and N. Tetradis, Nucl. Phys. B575, 61 (2000).
  47. W. Buchmuller, P. Di Bari, and M. Plumacher, Ann. Phys. (Amsterdam) 315, 305 (2005).
  48. E. Nardi, Y. Nir, E. Roulet, and J. Racker, J. High Energy Phys. 01 (2006) 164.
  49. A. Abada, S. Davidson, A. Ibarra, F. X. Josse-Michaux, M. Losada, and A. Riotto, J. High Energy Phys. 09 (2006) 010.
  50. S. Y. Khlebnikov and M. E. Shaposhnikov, Nucl. Phys. B308, 885 (1988).
  51. J. A. Harvey and M. S. Turner, Phys. Rev. D 42, 3344 (1990).
  52. A. Granelli, K. Moffat, Y. F. Perez-Gonzalez, H. Schulz, and J. Turner, Comput. Phys. Commun. 262, 107813 (2021).
  53. A. Granelli, C. Leslie, Y. F. Perez-Gonzalez, H. Schulz, B. Shuve, J. Turner, and R. Walker, Comput. Phys. Commun. 291, 108834 (2023).
  54. The data can be found in the source files of the arXiv version of this article, arXiv:2505.04279.
  55. M. Blennow and E. Fernandez-Martinez, Phys. Lett. B 704, 223 (2011).
  56. A. Ibarra, J. High Energy Phys. 01 (2006) 064.
  57. T. Endoh, S. Kaneko, S. K. Kang, T. Morozumi, and M. Tanimoto, Phys. Rev. Lett. 89, 231601 (2002).
  58. T. Fujihara, S. Kaneko, S. K. Kang, D. Kimura, T. Morozumi, and M. Tanimoto, Phys. Rev. D 72, 016006 (2005).

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Phys. Rev. D 112, 115032– Published 18 December, 2025
  • Received 15 May 2025
  • Accepted 19 November 2025
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