- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Testing the Froggatt-Nielsen mechanism with lepton flavor and number violating processes

Claudia Cornella1,*, David Curtin2,†, Gordan Krnjaic3,4,5,‡, and Micah Mellors2,§

  • *Contact author: claudia.cornella@cern.ch
  • †Contact author: dcurtin@physics.utoronto.ca
  • ‡Contact author: krnjaicg@fnal.gov
  • §Contact author: m.mellors@mail.utoronto.ca
PDF

Phys. Rev. D 112, 115010 – Published 3 December, 2025

DOI: https://doi.org/10.1103/c2ws-hx4h

Abstract

The Froggatt-Nielsen (FN) mechanism offers an elegant explanation for the observed masses and mixings of Standard Model fermions. In this work, we systematically study FN models in the lepton sector, identifying a broad range of charge assignments (“textures”) that naturally yield viable masses and mixings for various neutrino mass generation mechanisms. Using these textures, we consider higher-dimensional operators consistent with a FN origin and find that natural realizations predict distinct patterns in lepton flavor- and number-violating observables. For Dirac and Majorana neutrinos, FN-related correlations can lead to detectable rates of charged lepton flavor violation at next-generation low-energy experiments. Majorana and type-I seesaw models predict measurable rates of neutrinoless double beta decay. Determination of inverted neutrino mass ordering would exclude the Dirac neutrino FN scenario. Only a small minority of purely leptonic FN models predict detectable flavor violation at future muon colliders, though it is possible that a combined analysis with the quark sector will reveal motivated signals. These findings highlight the power of the FN mechanism to link neutrino mass generation to testable leptonic observables, offering new pathways for the experimental exploration of lepton number and underscoring the importance of next-generation low-energy probes.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (77)

  1. C. Froggatt and H. Nielsen, Hierarchy of quark masses, Cabibbo angles and CP violation, Nucl. Phys. B147, 277 (1979).
  2. M. Leurer, Y. Nir, and N. Seiberg, Mass matrix models, Nucl. Phys. B398, 319 (1993).
  3. M. Leurer, Y. Nir, and N. Seiberg, Mass matrix models: The sequel, Nucl. Phys. B420, 468 (1994).
  4. E. Dudas, C. Grojean, S. Pokorski, and C. A. Savoy, Abelian flavour symmetries in supersymmetric models, Nucl. Phys. B481, 85 (1996).
  5. N. Irges, S. Lavignac, and P. Ramond, Predictions from an anomalous U(1) model of Yukawa hierarchies, Phys. Rev. D 58, 035003 (1998).
  6. J. Sato and K. Tobe, Neutrino masses and lepton flavor violation in supersymmetric models with lopsided Froggatt-Nielsen charges, Phys. Rev. D 63, 116010 (2001).
  7. J. Sato and T. Yanagida, Low-energy predictions of lopsided family charges, Phys. Lett. B 493, 356 (2000).
  8. D. Suematsu, The Origin of quark and lepton mixings, Phys. Rev. D 64, 073013 (2001).
  9. H. K. Dreiner and M. Thormeier, Supersymmetric Froggatt-Nielsen models with baryon and lepton number violation, Phys. Rev. D 69, 053002 (2004).
  10. Y. Nir and Y. Shadmi, The Importance of being majorana: Neutrinos versus charged fermions in flavor models, J. High Energy Phys. 11 (2004) 055.
  11. H. Kamikado, T. Shindou, and E. Takasugi, Froggatt-Nielsen hierarchy and the neutrino mass matrix, arXiv:0805.1338.
  12. F. Plentinger, G. Seidl, and W. Winter, Group space scan of flavor symmetries for nearly tribimaximal lepton mixing, J. High Energy Phys. 04 (2008) 077.
  13. W. Buchmuller, V. Domcke, and K. Schmitz, Predicting Θ13 and the neutrino mass scale from quark lepton mass hierarchies, J. High Energy Phys. 03 (2012) 008.
  14. S. Krippendorf, S. Schafer-Nameki, and J.-M. Wong, Froggatt-Nielsen meets Mordell-Weil: A phenomenological survey of Global F-theory GUTs with U(1)s, J. High Energy Phys. 11 (2015) 008.
  15. M. Bauer, T. Schell, and T. Plehn, Hunting the flavon, Phys. Rev. D 94, 056003 (2016).
  16. Y. Ema, K. Hamaguchi, T. Moroi, and K. Nakayama, Flaxion: A minimal extension to solve puzzles in the standard model, J. High Energy Phys. 01 (2017) 096.
  17. L. Calibbi, F. Goertz, D. Redigolo, R. Ziegler, and J. Zupan, Minimal axion model from flavor, Phys. Rev. D 95, 095009 (2017).
  18. K. Nishiwaki, Y. Shimizu, and Y. Tatsuta, Double Froggatt–Nielsen mechanism, Prog. Theor. Exp. Phys. 2016, 083B05 (2016).
  19. V. V. Vien, H. N. Long, and A. E. Cárcamo Hernández, Fermion mass and mixing in a low-scale Seesaw model based on the S4 flavor symmetry, Prog. Theor. Exp. Phys. 2019, 113B04 (2019).
  20. F. Feruglio and A. Romanino, Lepton flavour symmetries, Rev. Mod. Phys. 93, 015007 (2021).
  21. M. S. Berger and M. Dawid, A Froggatt–Nielsen flavor model for neutrino physics, Int. J. Mod. Phys. A 34, 1950102 (2019).
  22. M. Bordone, O. Catà, and T. Feldmann, Effective theory approach to new physics with flavour: General framework and a leptoquark example, J. High Energy Phys. 01 (2020) 067.
  23. A. Smolkovič, M. Tammaro, and J. Zupan, Anomaly free Froggatt-Nielsen models of flavor, J. High Energy Phys. 10 (2019) 188.
  24. M. Fedele, A. Mastroddi, and M. Valli, Minimal Froggatt-Nielsen textures, J. High Energy Phys. 03 (2021) 135.
  25. S. Nishimura, C. Miyao, and H. Otsuka, Exploring the flavor structure of quarks and leptons with reinforcement learning, J. High Energy Phys. 12 (2023) 021.
  26. D. Aloni, P. Asadi, Y. Nakai, M. Reece, and M. Suzuki, Spontaneous CP violation and horizontal symmetry in the MSSM: toward lepton flavor naturalness, J. High Energy Phys. 09 (2021) 031.
  27. D. Ringe, Probing intermediate scale Froggatt-Nielsen models at future gravitational wave observatories, Phys. Rev. D 107, 015030 (2023).
  28. P. Asadi, A. Bhattacharya, K. Fraser, S. Homiller, and A. Parikh, Wrinkles in the Froggatt-Nielsen mechanism and flavorful new physics, J. High Energy Phys. 10 (2023) 069.
  29. Y.-C. Qiu, J.-W. Wang, and T. T. Yanagida, Predictions of mee and neutrino mass from a consistent Froggatt-Nielsen model, Phys. Rev. D 108, 115021 (2023).
  30. C. Cornella, D. Curtin, E. T. Neil, and J. O. Thompson, Mapping and probing Froggatt-Nielsen solutions to the quark flavor puzzle, Phys. Rev. D 111, 015042 (2025).
  31. S. Nishimura, C. Miyao, and H. Otsuka, Reinforcement learning-based statistical search strategy for an axion model from flavor, J. High Energy Phys. 10 (2025) 043.
  32. M. Ibe, S. Shirai, and K. Watanabe, Comprehensive bayesian exploration of Froggatt-Nielsen mechanism, J. High Energy Phys. 03 (2025) 150.
  33. S. Weinberg, Baryon- and lepton-nonconserving processes, Phys. Rev. Lett. 43, 1566 (1979).
  34. P. Minkowski, M→eγ at a rate of one out of 109 muon decays?, Phys. Lett. 67B, 421 (1977).
  35. T. Yanagida, Horizontal symmetry and masses of neutrinos, Prog. Theor. Phys. 64, 1103 (1980).
  36. M. Gell-Mann, P. Ramond, and R. Slansky, Complex spinors and unified theories, Conf. Proc. C 790927, 315 (1979).
  37. R. N. Mohapatra and G. Senjanović, Neutrino mass and spontaneous parity nonconservation, Phys. Rev. Lett. 44, 912 (1980).
  38. See Supplemental Material at http://link.aps.org/supplemental/10.1103/c2ws-hx4h for technical details, generalizations, and supplemental plots, which also includes Refs. [39–61].
  39. I. M. Oldengott, G. Barenboim, S. Kahlen, J. Salvado, and D. J. Schwarz, How to relax the cosmological neutrino mass bound, J. Cosmol. Astropart. Phys. 04 (2019) 049.
  40. Z. Chacko, A. Dev, P. Du, V. Poulin, and Y. Tsai, Cosmological limits on the neutrino mass and lifetime, J. High Energy Phys. 04 (2020) 020.
  41. M. Escudero, T. Schwetz, and J. Terol-Calvo, A seesaw model for large neutrino masses in concordance with cosmology, J. High Energy Phys. 02 (2023) 142.
  42. Z.-z. Xing, H. Zhang, and S. Zhou, Impacts of the Higgs mass on vacuum stability, running fermion masses and two-body Higgs decays, Phys. Rev. D 86, 013013 (2012).
  43. I. Esteban, M. Gonzalez-Garcia, M. Maltoni, T. Schwetz, and A. Zhou, The fate of hints: Updated global analysis of three-flavor neutrino oscillations, J. High Energy Phys. 09 (2020) 178.
  44. A. M. Baldini et al., MEG upgrade proposal, arXiv:1301.7225.
  45. U. Bellgardt, G. Otter et al. (SINDRUM Collaboration), Search for the decay μ+→e+e+e−, Nucl. Phys. B299, 1 (1988).
  46. A. Blondel et al., Research Proposal for an experiment to search for the decay μ→eee, arXiv:1301.6113.
  47. B. Aubert et al. (BABAR Collaboration), Searches for lepton flavor violation in the decays T+→e+γ and τ+→M+γ, Phys. Rev. Lett. 104, 021802 (2010).
  48. E. Kou, P. Urquijo et al. (Belle-II Collaboration), The Belle II physics book, Prog. Theor. Exp. Phys. 2019, 123C01 (2019).
  49. K. Uno, K. Hayasaka et al. (Belle Collaboration), Search for lepton-flavor-violating tau-lepton decays to ℓγ at Belle, J. High Energy Phys. 10 (2021) 019.
  50. K. Hayasaka et al., Search for lepton flavor violating Tau decays into three leptons with 719 million produced τ+τ− pairs, Phys. Lett. B 687, 139 (2010).
  51. P. Wintz, Results of the SINDRUM-II experiment, Conf. Proc. C 980420, 534 (1998).
  52. W. Honecker et al. (SINDRUM II Collaboration), Improved limit on the branching ratio of μ−e conversion on lead, Phys. Rev. Lett. 76, 200 (1996).
  53. B. Grzadkowski, M. Iskrzynski, M. Misiak, and J. Rosiek, Dimension-six terms in the standard model Lagrangian, J. High Energy Phys. 10 (2010) 085.
  54. M. Paraskevas, Dirac and Majorana Feynman rules with four-fermions, arXiv:1802.02657.
  55. M. Heikinheimo, K. Huitu, V. Keus, and N. Koivunen, Cosmological constraints on light flavons, J. High Energy Phys. 06 (2019) 065.
  56. C. Accettura et al., Towards a muon collider, Eur. Phys. J. C 83, 864 (2023).
  57. V. Shiltsev and F. Zimmermann, Modern and future colliders, Rev. Mod. Phys. 93, 015006 (2021).
  58. Z. Chacko, N. Craig, P. J. Fox, and R. Harnik, Cosmology in mirror twin Higgs and neutrino masses, J. High Energy Phys. 07 (2017) 023.
  59. G. Alonso-Álvarez, D. Curtin, A. Rasovic, and Z. Yuan, Baryogenesis through asymmetric reheating in the mirror twin Higgs, J. High Energy Phys. 05 (2024) 069.
  60. A. Dedes, S. Rimmer, and J. Rosiek, Neutrino masses in the lepton number violating MSSM, J. High Energy Phys. 08 (2006) 005.
  61. E. Ma and U. Sarkar, Neutrino masses and leptogenesis with heavy Higgs triplets, Phys. Rev. Lett. 80, 5716 (1998).
  62. M. Magg and C. Wetterich, Neutrino mass problem and gauge hierarchy, Phys. Lett. 94B, 61 (1980).
  63. J. Schechter and J. W. F. Valle, Neutrino masses in SU(2)×U(1) theories, Phys. Rev. D 22, 2227 (1980).
  64. G. Lazarides, Q. Shafi, and C. Wetterich, Proton lifetime and fermion masses in an SO(10) model, Nucl. Phys. B181, 287 (1981).
  65. R. N. Mohapatra and G. Senjanovic, Neutrino masses and mixings in gauge models with spontaneous parity violation, Phys. Rev. D 23, 165 (1981).
  66. C. Wetterich, Neutrino masses and the scale of B-L violation, Nucl. Phys. B187, 343 (1981).
  67. D. M. Straub, flavio: A python package for flavour and precision phenomenology in the standard model and beyond, arXiv:1810.08132.
  68. J. Aebischer, J. Kumar, and D. M. Straub, wilson: A python package for the running and matching of Wilson coefficients above and below the electroweak scale, Eur. Phys. J. C 78, 1026 (2018).
  69. A. M. Baldini et al. (MEG Collaboration), Search for the lepton flavour violating decay M+→e+  γ with the full dataset of the MEG experiment, Eur. Phys. J. C 76, 434 (2016).
  70. W. Bertl, R. Engfer et al. (SINDRUM II Collaboration), A search for μ−e conversion in muonic gold, Eur. Phys. J. C 47, 337 (2006).
  71. L. Bartoszek, E. Barnes et al. (Mu2e Collaboration), Mu2e technical design report, arXiv:1501.05241.
  72. A. Aghamousa et al. (DESI Collaboration), The DESI experiment part I: Science, targeting, and survey design, arXiv:1611.00036.
  73. R. L. Workman et al. (Particle Data Group), Review of particle physics, Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
  74. M. Aker et al. (Katrin Collaboration), Direct neutrino-mass measurement based on 259 days of KATRIN data, Science 388, adq9592 (2025).
  75. G. Adhikari et al. (nEXO Collaboration), NEXO: Neutrinoless double beta decay search beyond 1028 year half-life sensitivity, J. Phys. G 49, 015104 (2021).
  76. A. Armatol, C. Augier et al. (CUPID Collaboration), Toward CUPID-1T, arXiv:2203.08386.
  77. C. Cornella, D. Curtin, G. Krnjaic, and M. Mellors, Testing the Froggatt-Nielsen mechanism with lepton violation, arXiv:2501.00629.

Outline

Information

Phys. Rev. D 112, 115010– Published 3 December, 2025
  • Received 10 February 2025
  • Accepted 31 October 2025
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation