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  • Open Access

Texture-zeros in minimal seesaw from noninvertible symmetry fusion rules

Zheng Jiang1,*, Bu-Yao Qu1,†, and Gui-Jun Ding1,2,‡

  • *Contact author: jzdyx@mail.ustc.edu.cn
  • †Contact author: qubuyao@mail.ustc.edu.cn
  • ‡Contact author: dinggj@ustc.edu.cn
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Phys. Rev. D 112, 115029 – Published 17 December, 2025

DOI: https://doi.org/10.1103/d29s-cw34

Abstract

The Z2 gauging of ZN symmetry can enforce the vanishing of certain elements of the fermion Yukawa couplings. We have performed a systematical study of texture-zero patterns of lepton mass matrices in the minimal seesaw model, and we have presented all the possible patterns of the charged-lepton Yukawa coupling YE, neutrino Yukawa coupling Yν, right-handed neutrino mass matrix MR, and the light neutrino mass matrix Mν, which can be derived from the Z2 gauging of ZN symmetry. The realization of the textures with the maximum number of zeros and the second maximum number of zeros from noninvertible symmetry is studied, and the phenomenological implications in neutrino oscillation are discussed.

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References (59)

  1. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  2. F. Capozzi, W. Giarè, E. Lisi, A. Marrone, A. Melchiorri, and A. Palazzo, Neutrino masses and mixing: Entering the era of subpercent precision, Phys. Rev. D 111, 093006 (2025).
  3. I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler, J. P. Pinheiro, and T. Schwetz, nufit-6.0: Updated global analysis of three-flavor neutrino oscillations, J. High Energy Phys. 12 (2024) 216.
  4. P. F. de Salas, D. V. Forero, S. Gariazzo, P. Martínez-Miravé, O. Mena, C. A. Ternes, M. Tórtola, and J. W. F. Valle, 2020 global reassessment of the neutrino oscillation picture, J. High Energy Phys. 02 (2021) 071.
  5. F. Feruglio and A. Romanino, Lepton flavor symmetries, Rev. Mod. Phys. 93, 015007 (2021).
  6. Z.-z. Xing, Flavor structures of charged fermions and massive neutrinos, Phys. Rep. 854, 1 (2020).
  7. G.-J. Ding and S. F. King, Neutrino mass and mixing with modular symmetry, Rep. Prog. Phys. 87, 084201 (2024).
  8. G.-J. Ding and J. W. F. Valle, The symmetry approach to quark and lepton masses and mixing, Phys. Rep. 1109, 1 (2025).
  9. F. Feruglio and S. Ramos-Sanchez, Quark and lepton masses, arXiv:2506.20755.
  10. S. Weinberg, The problem of mass, Trans. N.Y. Acad. Sci. 38, 185 (1977).
  11. H. Fritzsch, Calculating the Cabibbo angle, Phys. Lett. 70B, 436 (1977).
  12. P. H. Frampton, S. L. Glashow, and D. Marfatia, Zeroes of the neutrino mass matrix, Phys. Lett. B 536, 79 (2002).
  13. Z.-z. Xing, Texture zeros and Majorana phases of the neutrino mass matrix, Phys. Lett. B 530, 159 (2002).
  14. H. Fritzsch and Z.-z. Xing, Mass and flavor mixing schemes of quarks and leptons, Prog. Part. Nucl. Phys. 45, 1 (2000).
  15. M. Gupta and G. Ahuja, Flavor mixings and textures of the fermion mass matrices, Int. J. Mod. Phys. A 27, 1230033 (2012).
  16. W. Grimus, A. S. Joshipura, L. Lavoura, and M. Tanimoto, Symmetry realization of texture zeros, Eur. Phys. J. C 36, 227 (2004).
  17. R. González Felipe and H. Serôdio, Abelian realization of phenomenological two-zero neutrino textures, Nucl. Phys. B886, 75 (2014).
  18. S. S. Correia, R. G. Felipe, and F. R. Joaquim, Dirac neutrinos in the 2HDM with restrictive Abelian symmetries, Phys. Rev. D 100, 115008 (2019).
  19. H. B. Camara, R. G. Felipe, and F. R. Joaquim, Minimal inverse-seesaw mechanism with Abelian flavour symmetries, J. High Energy Phys. 05 (2021) 021.
  20. D. Zhang, A modular A4 symmetry realization of two-zero textures of the Majorana neutrino mass matrix, Nucl. Phys. B952, 114935 (2020).
  21. J.-N. Lu, X.-G. Liu, and G.-J. Ding, Modular symmetry origin of texture zeros and quark lepton unification, Phys. Rev. D 101, 115020 (2020).
  22. S. Kikuchi, T. Kobayashi, M. Tanimoto, and H. Uchida, Texture zeros of quark mass matrices at fixed point τ=ω in modular flavor symmetry, Eur. Phys. J. C 83, 591 (2023).
  23. G.-J. Ding, F. R. Joaquim, and J.-N. Lu, Texture-zero patterns of lepton mass matrices from modular symmetry, J. High Energy Phys. 03 (2023) 141.
  24. D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, Generalized global symmetries, J. High Energy Phys. 02 (2015) 172.
  25. C. Cordova, T. T. Dumitrescu, K. Intriligator, and S.-H. Shao, Snowmass white paper: Generalized symmetries in quantum field theory and beyond, in Snowmass 2021 (2022), arXiv:2205.09545.
  26. S. Schafer-Nameki, ICTP lectures on (non-)invertible generalized symmetries, Phys. Rep. 1063, 1 (2024).
  27. T. D. Brennan and S. Hong, Introduction to generalized global symmetries in QFT and particle physics, arXiv:2306.00912.
  28. L. Bhardwaj, L. E. Bottini, L. Fraser-Taliente, L. Gladden, D. S. W. Gould, A. Platschorre, and H. Tillim, Lectures on generalized symmetries, Phys. Rep. 1051, 1 (2024).
  29. S.-H. Shao, What’s done cannot be undone: TASI lectures on non-invertible symmetries, arXiv:2308.00747.
  30. T. Kobayashi, H. Otsuka, and M. Tanimoto, Yukawa textures from non-invertible symmetries, J. High Energy Phys. 12 (2024) 117.
  31. T. Kobayashi, Y. Nishioka, H. Otsuka, and M. Tanimoto, More about quark Yukawa textures from selection rules without group actions, J. High Energy Phys. 05 (2025) 177.
  32. T. Kobayashi, H. Otsuka, M. Tanimoto, and H. Uchida, Lepton mass textures from non-invertible multiplication rules, J. High Energy Phys. 08 (2025) 189.
  33. T. Kobayashi, H. Okada, and H. Otsuka, Radiative neutrino mass models from non-invertible selection rules, arXiv:2505.14878.
  34. J. Chen, C.-Q. Geng, H. Okada, and J.-J. Wu, A radiative lepton model in a non-invertible fusion rule, arXiv:2507.11951.
  35. Q. Liang and T. T. Yanagida, Non-invertible symmetry as an axion-less solution to the strong CP problem, Phys. Lett. B 868, 139706 (2025).
  36. T. Kobayashi, H. Otsuka, and T. T. Yanagida, Non-invertible symmetry as a solution to the strong CP problem in a GUT-inspired standard model, arXiv:2508.12287.
  37. T. Kobayashi, H. Otsuka, M. Tanimoto, and T. T. Yanagida, GUT-motivated non-invertible symmetry as a solution to the strong CP problem and the neutrino CP-violating phase, arXiv:2510.01680.
  38. S. F. King, Large mixing angle MSW and atmospheric neutrinos from single right-handed neutrino dominance and U(1) family symmetry, Nucl. Phys. B576, 85 (2000).
  39. P. H. Frampton, S. L. Glashow, and T. Yanagida, Cosmological sign of neutrino CP violation, Phys. Lett. B 548, 119 (2002).
  40. A. Kageyama, S. Kaneko, N. Shimoyama, and M. Tanimoto, Seesaw realization of the texture zeros in the neutrino mass matrix, Phys. Lett. B 538, 96 (2002).
  41. D. M. Barreiros, R. G. Felipe, and F. R. Joaquim, Minimal type-I seesaw model with maximally restricted texture zeros, Phys. Rev. D 97, 115016 (2018).
  42. L. Bhardwaj, L. E. Bottini, S. Schafer-Nameki, and A. Tiwari, Non-invertible higher-categorical symmetries, SciPost Phys. 14, 007 (2023).
  43. T. Bartsch, M. Bullimore, A. E. V. Ferrari, and J. Pearson, Non-invertible symmetries and higher representation theory I, SciPost Phys. 17, 015 (2024).
  44. T. Kobayashi and H. Otsuka, Non-invertible flavor symmetries in magnetized extra dimensions, J. High Energy Phys. 11 (2024) 120.
  45. J. Dong, T. Jeric, T. Kobayashi, R. Nishida, and H. Otsuka, On discrete gauging and non-invertible selection rules, arXiv:2507.02375.
  46. Z.-z. Xing and Z.-h. Zhao, The minimal seesaw and leptogenesis models, Rep. Prog. Phys. 84, 066201 (2021).
  47. G. C. Branco, L. Lavoura, and F. Mota, Nearest neighbor interactions and the physical content of Fritzsch mass matrices, Phys. Rev. D 39, 3443 (1989).
  48. G. C. Branco and J. I. Silva-Marcos, NonHermitian Yukawa couplings?, Phys. Lett. B 331, 390 (1994).
  49. G. C. Branco, D. Emmanuel-Costa, and R. Gonzalez Felipe, Texture zeros and weak basis transformations, Phys. Lett. B 477, 147 (2000).
  50. I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler, J. P. Pinheiro, and T. Schwetz, nufit-6.0: Updated global analysis of three-flavor neutrino oscillations, J. High Energy Phys. 12 (2024) 216.
  51. F. An et al. (JUNO Collaboration), Neutrino physics with JUNO, J. Phys. G 43, 030401 (2016).
  52. K. Abe et al. (Hyper-Kamiokande Collaboration), Hyper-Kamiokande design report, arXiv:1805.04163.
  53. B. Abi et al. (DUNE Collaboration), Deep underground neutrino experiment (DUNE), far detector technical design report, volume II: DUNE physics, arXiv:2002.03005.
  54. J. Kaidi, Y. Tachikawa, and H. Y. Zhang, On a class of selection rules without group actions in field theory and string theory, SciPost Phys. 17, 169 (2024).
  55. J. J. Heckman, J. McNamara, M. Montero, A. Sharon, C. Vafa, and I. Valenzuela, Fate of stringy noninvertible symmetries, Phys. Rev. D 110, 106001 (2024).
  56. S. Funakoshi, T. Kobayashi, and H. Otsuka, Quantum aspects of non-invertible flavor symmetries in intersecting/magnetized D-brane models, J. High Energy Phys. 04 (2025) 183.
  57. J. A. Casas, J. R. Espinosa, A. Ibarra, and I. Navarro, General RG equations for physical neutrino parameters and their phenomenological implications, Nucl. Phys. B573, 652 (2000).
  58. P. H. Chankowski and S. Pokorski, Quantum corrections to neutrino masses and mixing angles, Int. J. Mod. Phys. A 17, 575 (2002).
  59. S. Antusch, J. Kersten, M. Lindner, M. Ratz, and M. A. Schmidt, Running neutrino mass parameters in see-saw scenarios, J. High Energy Phys. 03 (2005) 024.

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Phys. Rev. D 112, 115029– Published 17 December, 2025
  • Received 23 October 2025
  • Accepted 18 November 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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