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Aligned Zee-Grimus-Neufeld model for (g−2)μ

R. E. A. Bringas1,*, A. L. Cherchiglia2,†, G. De Conto1,‡, and C. C. Nishi3,§

  • *Contact author: ruben.bringas@ufabc.edu.br
  • †Contact author: alche@unicamp.br
  • ‡Contact author: george.de.conto@gmail.com
  • §Contact author: celso.nishi@ufabc.edu.br

Phys. Rev. D 112, 075046 – Published 27 October, 2025

DOI: https://doi.org/10.1103/t5jf-fb3q

Abstract

The recent result of the Fermilab Muon g-2 experiment is still in conflict with the standard model (SM) prediction if dispersive methods are used as input for the hadronic vacuum polarization. We seek models where the same set of mediators around the weak scale or above contribute to neutrino masses and to the muon g−2 through a chiral enhanced contribution. As family lepton number violation is inherent to the former, non-negligible charged lepton flavor violation will be induced. We arrive at the following field content additional to the SM: one Higgs doublet, one singly charged scalar, and one right-handed neutrino. Neutrino masses will be generated by a combination of mechanisms: the tree-level seesaw, Zee mechanism, and Grimus-Neufeld mechanism, while lepton flavor violation will be minimized by considering Yukawa-aligned Higgs doublets. The setting is flexible enough to account for (g−2)μ, the Cabibbo angle anomaly, and the W mass deviation, while avoiding dangerous charged lepton flavor violation.

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Physics Subject Headings (PhySH)

Corrections

29 July, 2026

Correction: Minor errors in Eqs. (31) and (55) and in the text following Eqs. (33), (79), and (99) have been fixed.

Article Text

References (92)

  1. T. Ohlsson, Nucl. Phys. B908, 1 (2016).
  2. M. Aoki et al. (COMET Collaboration, MEG Collaboration, Mu2e Collaboration, and Mu3e Collaboration), arXiv:2503.22461; A. Baldini, D. Glenzinski, F. Kapusta, Y. Kuno, M. Lancaster, J. Miller, S. Miscetti, T. Mori, A. Papa, A. Schoning et al. (Mu3e Collaboration), arXiv:1812.06540.
  3. A. Zee, Phys. Lett. 93B, 389 (1980); 95B, 461 (1980).
  4. T. P. Cheng and L. F. Li, Phys. Rev. D 22, 2860 (1980).
  5. A. Zee, Nucl. Phys. B264, 99 (1986).
  6. K. S. Babu, Phys. Lett. B 203, 132 (1988).
  7. E. Ma, Phys. Rev. Lett. 81, 1171 (1998).
  8. R. N. Mohapatra and P. B. Pal, Massive Neutrinos in Physics and Astrophysics 3rd ed. (World Scientific, Singapore, 2004).
  9. Y. Cai, J. Herrero-García, M. A. Schmidt, A. Vicente, and R. R. Volkas, Front. Phys. 5, 63 (2017).
  10. W. Grimus and H. Neufeld, Nucl. Phys. B325, 18 (1989).
  11. E. Ma, Phys. Rev. D 73, 077301 (2006).
  12. N. Rojas, R. Srivastava, and J. W. F. Valle, Phys. Lett. B 789, 132 (2019).
  13. A. Crivellin and B. Mellado, Nat. Rev. Phys. 6, 294 (2024).
  14. D. P. Aguillard et al. (Muon g-2 Collaboration), Phys. Rev. Lett. 135, 101802 (2025).
  15. G. W. Bennett et al. (Muon g-2 Collaboration), Phys. Rev. D 73, 072003 (2006).
  16. R. Aliberti, T. Aoyama, E. Balzani, A. Bashir, G. Benton, J. Bijnens, V. Biloshytskyi, T. Blum, D. Boito, M. Bruno et al., Phys. Rep. 1143, 1 (2025).
  17. T. Aoyama, N. Asmussen, M. Benayoun, J. Bijnens, T. Blum, M. Bruno, I. Caprini, C. M. Carloni Calame, M. Cè, G. Colangelo et al., Phys. Rep. 887, 1 (2020).
  18. T. Aoyama, M. Hayakawa, T. Kinoshita, and M. Nio, Phys. Rev. Lett. 109, 111808 (2012); T. Aoyama, T. Kinoshita, and M. Nio, Atoms 7, 28 (2019); A. Czarnecki, W. J. Marciano, and A. Vainshtein, Phys. Rev. D 67, 073006 (2003); 73, 119901(E) (2006); C. Gnendiger, D. Stöckinger, and H. Stöckinger-Kim, 88, 053005 (2013); M. Hoferichter, J. Lüdtke, L. Naterop, M. Procura, and P. Stoffer, Phys. Rev. Lett. 134, 201801 (2025); M. Davier, A. Hoecker, B. Malaescu, and Z. Zhang, Eur. Phys. J. C 77, 827 (2017); A. Keshavarzi, D. Nomura, and T. Teubner, Phys. Rev. D 97, 114025 (2018); G. Colangelo, M. Hoferichter, and P. Stoffer, J. High Energy Phys. 02 (2019) 006; M. Hoferichter, B. L. Hoid, and B. Kubis, 08 (2019) 137; M. Davier, A. Hoecker, B. Malaescu, and Z. Zhang, Eur. Phys. J. C 80, 241 (2020); 80, 410(E) (2020); A. Keshavarzi, D. Nomura, and T. Teubner, Phys. Rev. D 101, 014029 (2020); A. Kurz, T. Liu, P. Marquard, and M. Steinhauser, Phys. Lett. B 734, 144 (2014); G. Colangelo, M. Hoferichter, A. Nyffeler, M. Passera, and P. Stoffer, 735, 90 (2014); K. Melnikov and A. Vainshtein, Phys. Rev. D 70, 113006 (2004); P. Masjuan and P. Sanchez-Puertas, 95, 054026 (2017); G. Colangelo, M. Hoferichter, M. Procura, and P. Stoffer, J. High Energy Phys. 04 (2017) 161; M. Hoferichter, B. L. Hoid, B. Kubis, S. Leupold, and S. P. Schneider, 10 (2018) 141. A. Gérardin, H. B. Meyer, and A. Nyffeler, Phys. Rev. D 100, 034520 (2019); J. Bijnens, N. Hermansson-Truedsson, and A. Rodríguez-Sánchez, Phys. Lett. B 798, 134994 (2019); G. Colangelo, F. Hagelstein, M. Hoferichter, L. Laub, and P. Stoffer, J. High Energy Phys. 03 (2020) 101; T. Blum, N. Christ, M. Hayakawa, T. Izubuchi, L. Jin, C. Jung, and C. Lehner, Phys. Rev. Lett. 124, 132002 (2020); S. Borsanyi, Z. Fodor, J. N. Guenther, C. Hoelbling, S. D. Katz, L. Lellouch, T. Lippert, K. Miura, L. Parato, K. K. Szabo et al., Nature (London) 593, 51 (2021); S. Kuberski, M. Cè, G. von Hippel, H. B. Meyer, K. Ottnad, A. Risch, and H. Wittig, J. High Energy Phys. 03 (2024) 172; A. Boccaletti, S. Borsanyi, M. Davier, Z. Fodor, F. Frech, A. Gerardin, D. Giusti, A. Y. Kotov, L. Lellouch, T. Lippert et al., arXiv:2407.10913; T. Blum et al. (RBC Collaboration and UKQCD Collaboration), Phys. Rev. Lett. 134, 201901 (2025); D. Djukanovic, G. von Hippel, S. Kuberski, H. B. Meyer, N. Miller, K. Ottnad, J. Parrino, A. Risch, and H. Wittig, J. High Energy Phys. 04 (2025) 098; C. Alexandrou et al. (Extended Twisted Mass Collaboration), Phys. Rev. D 111, 054502 (2025); A. Bazavov et al. (MILC Collaboration, Fermilab Lattice Collaboration, and HPQCD Collaboration), 111, 094508 (2025).
  19. F. V. Ignatov et al. (CMD-3 Collaboration), Phys. Rev. D 109, 112002 (2024); Phys. Rev. Lett. 132, 231903 (2024).
  20. A. Crivellin, M. Hoferichter, C. A. Manzari, and M. Montull, Phys. Rev. Lett. 125, 091801 (2020).
  21. R. Capdevilla, D. Curtin, Y. Kahn, and G. Krnjaic, Phys. Rev. D 105, 015028 (2022).
  22. D. Buttazzo and P. Paradisi, Phys. Rev. D 104, 075021 (2021); W. Yin and M. Yamaguchi, 106, 033007 (2022).
  23. K. Kannike, M. Raidal, D. M. Straub, and A. Strumia, J. High Energy Phys. 02 (2012) 106; 10 (2012) 136(E).
  24. A. Freitas, J. Lykken, S. Kell, and S. Westhoff, J. High Energy Phys. 05 (2014) 145; 09 (2014) 155(E).
  25. A. Crivellin, M. Hoferichter, and P. Schmidt-Wellenburg, Phys. Rev. D 98, 113002 (2018).
  26. L. Calibbi, R. Ziegler, and J. Zupan, J. High Energy Phys. 07 (2018) 046.
  27. P. Athron, C. Balázs, D. H. J. Jacob, W. Kotlarski, D. Stöckinger, and H. Stöckinger-Kim, J. High Energy Phys. 09 (2021) 080.
  28. M. Lindner, M. Platscher, and F. S. Queiroz, Phys. Rep. 731, 1 (2018).
  29. A. Broggio, E. J. Chun, M. Passera, K. M. Patel, and S. K. Vempati, J. High Energy Phys. 11 (2014) 058.
  30. V. Ilisie, J. High Energy Phys. 04 (2015) 077.
  31. T. Han, S. K. Kang, and J. Sayre, J. High Energy Phys. 02 (2016) 097.
  32. A. Cherchiglia, P. Kneschke, D. Stöckinger, and H. Stöckinger-Kim, J. High Energy Phys. 01 (2017) 007; 10 (2021) 242(E).
  33. A. Cherchiglia, D. Stöckinger, and H. Stöckinger-Kim, Phys. Rev. D 98, 035001 (2018).
  34. R. K. Barman, R. Dcruz, and A. Thapa, J. High Energy Phys. 03 (2022) 183.
  35. A. L. Cherchiglia, G. De Conto, and C. C. Nishi, J. High Energy Phys. 08 (2023) 170.
  36. A. Crivellin, F. Kirk, C. A. Manzari, and L. Panizzi, Phys. Rev. D 103, 073002 (2021).
  37. T. Felkl, J. Herrero-Garcia, and M. A. Schmidt, J. High Energy Phys. 05 (2021) 122; 05 (2022) 73.
  38. D. A. Dicus, H. J. He, and J. N. Ng, Phys. Rev. Lett. 87, 111803 (2001).
  39. E. Ma and M. Raidal, Phys. Rev. Lett. 87, 011802 (2001); 87, 159901(E) (2001).
  40. P. Escribano, J. Terol-Calvo, and A. Vicente, Phys. Rev. D 103, 115018 (2021); C. H. Chen, C. W. Chiang, and T. Nomura, 104, 055011 (2021); A. E. C. Hernández, S. F. King, and H. Lee, 103, 115024 (2021); A. E. C. Hernández, D. T. Huong, and I. Schmidt, Eur. Phys. J. C 82, 63 (2022); L. T. Hue, A. E. Cárcamo Hernández, H. N. Long, and T. T. Hong, Nucl. Phys. B984, 115962 (2022); A. E. Cárcamo Hernández, Y. H. Velásquez, S. Kovalenko, N. A. Pérez-Julve, and I. Schmidt, Prog. Theor. Exp. Phys. 2024, 103B02 (2024).
  41. R. Dcruz and A. Thapa, Phys. Rev. D 107, 015002 (2023).
  42. K. S. Babu, P. S. B. Dev, S. Jana, and A. Thapa, J. High Energy Phys. 03 (2021) 179; D. Zhang, 07 (2021) 069; S. L. Chen, W. w. Jiang, and Z. K. Liu, Eur. Phys. J. C 82, 959 (2022).
  43. A. Pich and P. Tuzon, Phys. Rev. D 80, 091702 (2009).
  44. H. Georgi and D. V. Nanopoulos, Phys. Lett. 82B, 95 (1979).
  45. F. J. Botella and J. P. Silva, Phys. Rev. D 51, 3870 (1995).
  46. G. C. Branco, L. Lavoura, and J. P. Silva, Int. Ser. Monogr. Phys. 103, 1 (1999).
  47. S. Davidson and H. E. Haber, Phys. Rev. D 72, 035004 (2005); 72, 099902(E) (2005).
  48. ATLAS Collaboration, pp collisions at s=13  TeV, Report No. ATLAS-CONF-2023-052, 2023.
  49. V. Dudėnas and T. Gajdosik, Acta Phys. Pol. B Proc. Suppl. 15, 1 (2022).
  50. P. S. Bhupal Dev and A. Pilaftsis, J. High Energy Phys. 12 (2014) 024; 11 (2015) 147(E).
  51. T. P. Cheng and L. F. Li, Phys. Rev. D 22, 2860 (1980).
  52. S. T. Petcov, Phys. Lett. 115B, 401 (1982); A. Zee, Nucl. Phys. B264, 99 (1986).
  53. J. Herrero-García, T. Ohlsson, S. Riad, and J. Wirén, J. High Energy Phys. 04 (2017) 130.
  54. L. Wolfenstein, Nucl. Phys. B175, 93 (1980).
  55. X. G. He, Eur. Phys. J. C 34, 371 (2004); Y. Koide, Phys. Rev. D 64, 077301 (2001).
  56. V. Dudėnas, T. Gajdosik, U. Khasianevich, W. Kotlarski, and D. Stöckinger, J. High Energy Phys. 09 (2022) 174.
  57. P. H. Frampton, S. L. Glashow, and D. Marfatia, Phys. Lett. B 536, 79 (2002); B. R. Desai, D. P. Roy, and A. R. Vaucher, Mod. Phys. Lett. A 18, 1355 (2003).
  58. S. Dev, S. Kumar, S. Verma, and S. Gupta, Phys. Rev. D 76, 013002 (2007).
  59. I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, T. Schwetz, and A. Zhou, J. High Energy Phys. 09 (2020) 178; NuFIT 5.3, (2024), http://www.nu-fit.org.
  60. R. Coy and M. Frigerio, Phys. Rev. D 99, 095040 (2019).
  61. S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024).
  62. H. Augustin et al. (Mu3e Collaboration), IEEE Trans. Nucl. Sci. 68, 1833 (2021).
  63. Y. S. Amhis et al. (HFLAV Collaboration), Eur. Phys. J. C 81, 226 (2021).
  64. E. Kou et al. (Belle-II Collaboration), Prog. Theor. Exp. Phys. 2019, 123C01 (2019); 2020, 029201(E) (2020).
  65. K. Afanaciev et al. (MEG II Collaboration), arXiv:2504.15711.
  66. A. M. Baldini et al. (MEG II Collaboration), Eur. Phys. J. C 78, 380 (2018).
  67. A. Abdesselam et al. (Belle Collaboration), J. High Energy Phys. 10 (2021) 019.
  68. W. H. Bertl et al. (SINDRUM II Collaboration), Eur. Phys. J. C 47, 337 (2006).
  69. M. Yucel et al. (Mu2e Collaboration), Proc. Sci. ICHEP2020 (2021) 439; R. J. Abrams et al. (Mu2e Collaboration), arXiv:1211.7019.
  70. A. Kurup (COMET Collaboration), Nucl. Phys. B, Proc. Suppl. 218, 38 (2011); R. Abramishvili et al. (COMET Collaboration), Prog. Theor. Exp. Phys. 2020, 033C01 (2020); M. Lee et al. (COMET Collaboration and Mu2e Collaboration), arXiv:2203.07089.
  71. R. J. Barlow, Nucl. Phys. B, Proc. Suppl. 218, 44 (2011).
  72. M. Ardu, S. Davidson, and S. Lavignac, Eur. Phys. J. C 84, 458 (2024); E. Fernández-Martínez, X. Marcano, and D. Naredo-Tuero, 84, 666 (2024); V. Cirigliano, R. Kitano, Y. Okada, and P. Tuzon, Phys. Rev. D 80, 013002 (2009); R. Kitano, M. Koike, and Y. Okada, 66, 096002 (2002); 76, 059902(E) (2007); M. Raidal and A. Santamaria, Phys. Lett. B 421, 250 (1998).
  73. Y. Kuno and Y. Okada, Rev. Mod. Phys. 73, 151 (2001).
  74. E. Mituda and K. Sasaki, Phys. Lett. B 516, 47 (2001).
  75. M. Nebot, J. F. Oliver, D. Palao, and A. Santamaria, Phys. Rev. D 77, 093013 (2008).
  76. E. E. Jenkins, A. V. Manohar, and P. Stoffer, J. High Energy Phys. 03 (2018) 016; 12 (2023) 43.
  77. B. Belfatto, R. Beradze, and Z. Berezhiani, Eur. Phys. J. C 80, 149 (2020); Y. Grossman, E. Passemar, and S. Schacht, J. High Energy Phys. 07 (2020) 068.
  78. A. Crivellin, M. Kirk, T. Kitahara, and F. Mescia, J. High Energy Phys. 03 (2023) 234; G. C. Branco, J. T. Penedo, P. M. F. Pereira, M. N. Rebelo, and J. I. Silva-Marcos, 07 (2021) 099; A. Crivellin, M. Hoferichter, and C. A. Manzari, Phys. Rev. Lett. 127, 071801 (2021).
  79. A. Pich, Prog. Part. Nucl. Phys. 75, 41 (2014).
  80. E. Gersabeck and A. Pich, C.R. Phys. 21, 75 (2020).
  81. A. Adelmann et al. (PIONEER Collaboration), arXiv:2504.06375.
  82. M. E. Peskin and T. Takeuchi, Phys. Rev. Lett. 65, 964 (1990); Phys. Rev. D 46, 381 (1992).
  83. I. Maksymyk, C. P. Burgess, and D. London, Phys. Rev. D 50, 529 (1994).
  84. T. Abe, R. Sato, and K. Yagyu, J. High Energy Phys. 07 (2017) 012.
  85. J. Heeck and A. Thapa, Phys. Lett. B 841, 137910 (2023).
  86. T. Aaltonen et al. (CDF Collaboration), Science 376, 170 (2022).
  87. M. S. Bilenky and A. Santamaria, Nucl. Phys. B420, 47 (1994).
  88. Y. Farzan and M. Tortola, Front. Phys. 6, 10 (2018); P. Coloma, M. C. Gonzalez-Garcia, M. Maltoni, J. P. Pinheiro, and S. Urrea, J. High Energy Phys. 08 (2023) 032.
  89. T. Ohlsson, T. Schwetz, and H. Zhang, Phys. Lett. B 681, 269 (2009); J. Tang and W. Winter, Phys. Rev. D 80, 053001 (2009).
  90. ALEPH Collaboration, DELPHI Collaboration, L3 Collaboration, OPAL Collaboration, and LEP Collaboration, Eur. Phys. J. C 73, 2463 (2013).
  91. G. Aad et al. (ATLAS Collaboration), J. High Energy Phys. 07 (2025) 196.
  92. A. M. Sirunyan et al. (CMS Collaboration), J. High Energy Phys. 01 (2019) 122.

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