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Models for the electric dipole moment and anomalous magnetic moment of the tau lepton

Yuichiro Nakai1,2, Yoshihiro Shigekami3, Peng Sun1,2, and Zhihao Zhang1,2

Phys. Rev. D 113, 035001 – Published 2 February, 2026

DOI: https://doi.org/10.1103/rnrt-9gjy

Abstract

The Belle II experiment and other ongoing and projected lepton facilities are expected to greatly enhance the sensitivity to the electric dipole moment (EDM) and anomalous magnetic moment (g−2) for the tau lepton, making it timely to explore models that predict these observables. In this work, we study a class of models in which the tau mass is generated radiatively. As a result, sizable EDM and g−2 of the tau lepton arise as a natural consequence of the radiative mass generation mechanism at the electroweak scale. We present two benchmark models with different hypercharge assignments. The first model contains neutral fermions and charged scalars. We find that the model can predict a large signal of the tau EDM, dτ=O(10−19)e cm, and g−2, aτ=O(10−5), which are within the reach of future updates of their measurements. In contrast, the second model, containing a charged fermion and neutral scalars, yields a similar magnitude but different sign for g−2, and predicts a comparatively smaller EDM signal. Our models serve as well-motivated benchmarks for new physics scenarios in which radiative tau mass generation leads to sizable tau dipole moments.

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References (87)

  1. J. Schwinger, On quantum-electrodynamics and the magnetic moment of the electron, Phys. Rev. 73, 416 (1948).
  2. R. Aliberti et al., The anomalous magnetic moment of the muon in the standard model: An update, Phys. Rep. 1143, 1 (2025).
  3. X. Fan, T. G. Myers, B. A. D. Sukra, and G. Gabrielse, Measurement of the electron magnetic moment, Phys. Rev. Lett. 130, 071801 (2023).
  4. D. P. Aguillard et al. (Muon g-2 Collaboration), Measurement of the positive muon anomalous magnetic moment to 127 ppb, Phys. Rev. Lett. 135, 101802 (2025).
  5. P. Athron, K. Möhling, D. Stöckinger, and H. Stöckinger-Kim, The Muon magnetic moment and physics beyond the standard model, arXiv:2507.09289.
  6. V. Andreev et al. (ACME Collaboration), Improved limit on the electric dipole moment of the electron, Nature (London) 562, 355 (2018).
  7. T. S. Roussy et al., An improved bound on the electron’s electric dipole moment, Science 381, adg4084 (2023).
  8. Y. Nakai and M. Reece, Electric dipole moments in natural supersymmetry, J. High Energy Phys. 08 (2017) 031.
  9. C. Cesarotti, Q. Lu, Y. Nakai, A. Parikh, and M. Reece, Interpreting the electron EDM constraint, J. High Energy Phys. 05 (2019) 059.
  10. K. Ning and M. Ramsey-Musolf, Revisiting the electron EDM in the NMSSM, Phys. Lett. B 869, 139867 (2025).
  11. G. W. Bennett et al. (Muon (g-2) Collaboration), An improved limit on the Muon electric dipole moment, Phys. Rev. D 80, 052008 (2009).
  12. Y. Ema, T. Gao, and M. Pospelov, Improved indirect limits on Muon electric dipole moment, Phys. Rev. Lett. 128, 131803 (2022).
  13. M. Abe et al., A new approach for measuring the Muon anomalous magnetic moment and electric dipole moment, Prog. Theor. Exp. Phys. 2019, 053C02 (2019).
  14. A. Adelmann et al., Search for a Muon EDM using the frozen-spin technique, arXiv:2102.08838.
  15. M. Sakurai et al., muEDM: Towards a search for the Muon electric dipole moment at PSI using the frozen-spin technique, J. Phys. Soc. Jpn. Conf. Proc. 37, 020604 (2022).
  16. K. S. Khaw et al. (Muon EDM Initiative Collaboration), Search for the Muon electric dipole moment using frozen-spin technique at PSI, Proc. Sci., NuFact2021 (2022) 136 [arXiv:2201.08729].
  17. S. Eidelman and M. Passera, Theory of the tau lepton anomalous magnetic moment, Mod. Phys. Lett. A 22, 159 (2007).
  18. A. Keshavarzi, D. Nomura, and T. Teubner, g−2 of charged leptons, α(MZ2), and the hyperfine splitting of muonium, Phys. Rev. D 101, 014029 (2020).
  19. G. Aad et al. (ATLAS Collaboration), Observation of the γγ→ττ process in Pb+Pb collisions and constraints on the τ-lepton anomalous magnetic moment with the ATLAS detector, Phys. Rev. Lett. 131, 151802 (2023).
  20. A. Hayrapetyan et al. (CMS Collaboration), Observation of γγ→ττ in proton-proton collisions and limits on the anomalous electromagnetic moments of the τ lepton, Rep. Prog. Phys. 87, 107801 (2024).
  21. M. E. Pospelov and I. B. Khriplovich, Electric dipole moment of the W boson and the electron in the Kobayashi-Maskawa model, Sov. J. Nucl. Phys. 53, 638 (1991), arXiv:hep-ph/9310342.
  22. M. J. Booth, The electric dipole moment of the W and electron in the standard model, arXiv:hep-ph/9301293.
  23. M. Pospelov and A. Ritz, CKM benchmarks for electron electric dipole moment experiments, Phys. Rev. D 89, 056006 (2014).
  24. Y. Yamaguchi and N. Yamanaka, Large long-distance contributions to the electric dipole moments of charged leptons in the standard model, Phys. Rev. Lett. 125, 241802 (2020).
  25. Y. Yamaguchi and N. Yamanaka, Quark level and hadronic contributions to the electric dipole moment of charged leptons in the standard model, Phys. Rev. D 103, 013001 (2021).
  26. K. Inami et al. (Belle Collaboration), An improved search for the electric dipole moment of the τ lepton, J. High Energy Phys. 04 (2022) 110.
  27. Y. Ema, T. Gao, and M. Pospelov, Reevaluation of heavy-fermion-induced electron EDM at three loops, Phys. Lett. B 835, 137496 (2022).
  28. T. Abe et al. (Belle-II Collaboration), Belle II technical design report, arXiv:1011.0352.
  29. W. Altmannshofer et al. (Belle-II Collaboration), The Belle II physics book, Prog. Theor. Exp. Phys. 2019, 123C01 (2019).
  30. H. Aihara et al., The Belle II detector upgrades framework conceptual design report, arXiv:2406.19421.
  31. M. Ablikim et al. (BESIII Collaboration), Design and construction of the BESIII detector, Nucl. Instrum. Methods Phys. Res., Sect. A 614, 345 (2010).
  32. M. Ablikim et al. (BESIII Collaboration), Future physics programme of BESIII, Chin. Phys. C 44, 040001 (2020).
  33. W. Bernreuther, L. Chen, and O. Nachtmann, Probing the tau electric dipole moment at the BEPC-II collider, Phys. Rev. D 104, 115002 (2021).
  34. M. Dong et al. (CEPC Study Group), CEPC conceptual design report: Volume 2—Physics & detector, arXiv:1811.10545.
  35. H. Cheng et al. (CEPC Physics Study Group), The physics potential of the CEPC. Prepared for the US Snowmass community planning exercise (Snowmass 2021), in Snowmass 2021 (2022), arXiv:2205.08553.
  36. D. Bodrov (Belle Collaboration and Belle II Collaboration), Tau physics at Belle and Belle II, Int. J. Mod. Phys. A 39, 2442006 (2024).
  37. A. Crivellin, M. Hoferichter, and J. M. Roney, Toward testing the magnetic moment of the tau at one part per million, Phys. Rev. D 106, 093007 (2022).
  38. D. M. Asner et al. (US Belle II Group, Belle II/SuperKEKB e- Polarization Upgrade Working Group), Snowmass 2021 white paper on upgrading SuperKEKB with a Polarized electron beam: Discovery potential and proposed implementation, in Snowmass 2021 (2022), arXiv:2205.12847.
  39. K. S. Khaw, Y. Nakai, R. Sato, Y. Shigekami, and Z. Zhang, A large muon EDM from dark matter, J. High Energy Phys. 02 (2023) 234.
  40. B. De, Revisiting the scalar leptoquark (S1) model with the updated leptonic constraints, Eur. Phys. J. C 83, 1084 (2023).
  41. A. M. Sirunyan et al. (CMS Collaboration), Search for leptoquarks coupled to third-generation quarks in proton-proton collisions at s=13  TeV, Phys. Rev. Lett. 121, 241802 (2018).
  42. A. Tumasyan et al. (CMS Collaboration), Inclusive nonresonant multilepton probes of new phenomena at s=13  TeV, Phys. Rev. D 105, 112007 (2022).
  43. G. Aad et al. (ATLAS Collaboration), Search for pair production of third-generation scalar leptoquarks decaying into a top quark and a τ-lepton in pp collisions at s=13  TeV with the ATLAS detector, J. High Energy Phys. 06 (2021) 179.
  44. M. J. Baker, P. Cox, and R. R. Volkas, Has the origin of the third-family fermion masses been determined?, J. High Energy Phys. 04 (2021) 151.
  45. M. J. Baker, P. Cox, and R. R. Volkas, Radiative Muon mass models and (g−2)μ, J. High Energy Phys. 05 (2021) 174.
  46. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  47. A. Giarnetti, S. Marciano, D. Meloni, and M. Rettaroli, A roadmap for neutrino charge assignments in U(2)F flavor models: Implications for LFV processes and leptonic anomalous magnetic moments, arXiv:2505.20281.
  48. G. Aad et al. (ATLAS Collaboration), A detailed map of Higgs boson interactions by the ATLAS experiment ten years after the discovery, Nature (London) 607, 52 (2022).
  49. D. de Florian et al. (LHC Higgs Cross Section Working Group), Handbook of LHC Higgs Cross Sections: 4. Deciphering the nature of the Higgs sector, CERN Yellow Rep. Monogr. 2, 1 (2017).
  50. G. Aad et al. (ATLAS Collaboration), Search for charged Higgs bosons decaying via H±→τ±ν in fully hadronic final states using pp collision data at s=8  TeV with the ATLAS detector, J. High Energy Phys. 03 (2015) 088.
  51. V. Khachatryan et al. (CMS Collaboration), Search for a charged Higgs boson in pp collisions at s=8  TeV, J. High Energy Phys. 11 (2015) 018.
  52. M. Aaboud et al. (ATLAS Collaboration), Search for charged Higgs bosons decaying via H±→τ±ντ in the τ+jets and τ+lepton final states with 36  fb−1 of pp collision data recorded at s=13  TeV with the ATLAS experiment, J. High Energy Phys. 09 (2018) 139.
  53. G. Abbiendi et al. (ALEPH, DELPHI, L3, OPAL, and LEP Collaborations), Search for charged Higgs bosons: Combined results using LEP data, Eur. Phys. J. C 73, 2463 (2013).
  54. P. Achard et al. (L3 Collaboration), Search for heavy neutral and charged leptons in e+e− annihilation at LEP, Phys. Lett. B 517, 75 (2001).
  55. G. Aad et al. (ATLAS Collaboration), Search for the direct production of charginos, neutralinos and staus in final states with at least two hadronically decaying taus and missing transverse momentum in pp collisions at s=8  TeV with the ATLAS detector, J. High Energy Phys. 10 (2014) 096.
  56. G. Aad et al. (ATLAS Collaboration), Search for the electroweak production of supersymmetric particles in s=8  TeV pp collisions with the ATLAS detector, Phys. Rev. D 93, 052002 (2016).
  57. G. Aad et al. (ATLAS Collaboration), Search for direct stau production in events with two hadronic τ-leptons in s=13  TeV pp collisions with the ATLAS detector, Phys. Rev. D 101, 032009 (2020).
  58. V. Khachatryan et al. (CMS Collaboration), Search for electroweak production of charginos in final states with two τ leptons in pp collisions at s=8  TeV, J. High Energy Phys. 04 (2017) 018.
  59. A. M. Sirunyan et al. (CMS Collaboration), Search for direct pair production of supersymmetric partners to the τ lepton in proton-proton collisions at s=13  TeV, Eur. Phys. J. C 80, 189 (2020).
  60. A. Tumasyan et al. (CMS Collaboration), Search for direct pair production of supersymmetric partners of τ leptons in the final state with two hadronically decaying τ leptons and missing transverse momentum in proton-proton collisions at s=13  TeV, Phys. Rev. D 108, 012011 (2023).
  61. ATLAS Collaboration, Search for electroweak SUSY production in final states with two τ-leptons in s=13  TeV pp collisions with the ATLAS detector, J. High Energy Phys. 05 (2024) 150.
  62. S. Schael et al. (ALEPH, DELPHI, L3, OPAL, SLD Collaborations, LEP Electroweak Working Group, SLD Electroweak Group, and SLD Heavy Flavour Group), Precision electroweak measurements on the Z resonance, Phys. Rep. 427, 257 (2006).
  63. R. Aaij et al. (LHCb Collaboration), Measurement of Z→τ+τ− production in proton-proton collisions at s=8  TeV, J. High Energy Phys. 09 (2018) 159.
  64. J. de Blas, M. Ciuchini, E. Franco, S. Mishima, M. Pierini, L. Reina, and L. Silvestrini, Electroweak precision observables and Higgs-boson signal strengths in the standard model and beyond: Present and future, J. High Energy Phys. 12 (2016) 135.
  65. W. Bernreuther, L. Chen, and O. Nachtmann, Electric dipole moment of the tau lepton revisited, Phys. Rev. D 103, 096011 (2021).
  66. X.-G. He, C.-W. Liu, J.-P. Ma, C. Yang, and Z.-Y. Zou, Precise measurement of CP violating τ EDM through e+e−→ γ*, ψ(2s)→ τ+τ−, J. High Energy Phys. 04 (2025) 001.
  67. Z.-L. Huang, X.-Y. Du, X.-G. He, C.-W. Liu, and Z.-Y. Zou, Generating sizable real and imaginary τ electric dipole moment, arXiv:2510.23348.
  68. D. Y. Shao, H. Xiang, F. Xu, B. Yan, and C. Zhang, Linearly polarized photon fusion as a precision probe of the tau lepton dipole moments at lepton colliders, arXiv:2506.15245.
  69. M. Achasov et al., STCF conceptual design report (Volume 1): Physics & detector, Front. Phys. (Beijing) 19, 14701 (2024).
  70. X. Sun, Y. Wu, and X. Zhou, Search for the electric dipole moment of the tau lepton at the super tau-charm facility, Chin. Phys. 49, 113001 (2025).
  71. D. Shao, B. Yan, S.-R. Yuan, and C. Zhang, Spin asymmetry and dipole moments in τ-pair production with ultraperipheral heavy ion collisions, Sci. China Phys. Mech. Astron. 67, 281062 (2024).
  72. M. Hoferichter and G. Levati, Light new physics and the τ lepton dipole moments: Prospects at Belle II, arXiv:2510.13966.
  73. M. Hoferichter and G. Levati, Light new physics and the τ lepton dipole moments, arXiv:2511.03786.
  74. A. Heister et al. (ALEPH Collaboration), Search for anomalous weak dipole moments of the tau lepton, Eur. Phys. J. C 30, 291 (2003).
  75. W. Lohmann, Electromagnetic and weak moments of the tau-lepton, Nucl. Phys. B, Proc. Suppl. 144, 122 (2005).
  76. M. Arroyo-Ureña and E. Díaz, Dipole moments of charged leptons in the THDM-III with textures, J. Phys. G 43, 045002 (2016).
  77. M. A. Arroyo-Ureña, G. Hernández-Tomé, and G. Tavares-Velasco, Anomalous magnetic and weak magnetic dipole moments of the τ lepton in the simplest little Higgs model, Eur. Phys. J. C 77, 227 (2017).
  78. M. A. Arroyo-Ureña, G. Tavares-Velasco, and G. Hernández-Tomé, Weak dipole moments of the tau lepton in models with an extended scalar sector, Phys. Rev. D 97, 013006 (2018).
  79. P.-C. Lu, Z.-G. Si, and H. Zhang, Probing the electromagnetic dipole moment of the τ lepton in the e+e−→γ*/Z→τ+τ− reaction, Phys. Rev. D 112, 075039 (2025).
  80. J. Gogniat, M. Hoferichter, and Y. Ulrich, Towards testing (g−2)τ in e+e−→ τ+τ−: Radiative corrections and projections for Belle II, J. High Energy Phys. 07 (2025) 172.
  81. M. E. Peskin and T. Takeuchi, Estimation of oblique electroweak corrections, Phys. Rev. D 46, 381 (1992).
  82. W. Grimus, L. Lavoura, O. M. Ogreid, and P. Osland, A precision constraint on multi-Higgs-doublet models, J. Phys. G 35, 075001 (2008).
  83. W. Grimus, L. Lavoura, O. M. Ogreid, and P. Osland, The oblique parameters in multi-Higgs-doublet models, Nucl. Phys. B801, 81 (2008).
  84. F. Albergaria, D. Jurčiukonis, and L. Lavoura, The oblique parameters from arbitrary new fermions, J. High Energy Phys. 05 (2024) 190.
  85. A. Sirlin, Radiative corrections in the SU(2)L× U(1) theory: A simple renormalization framework, Phys. Rev. D 22, 971 (1980).
  86. W. F. L. Hollik, Radiative corrections in the standard model and their role for precision tests of the electroweak theory, Fortschr. Phys. 38, 165 (1990).
  87. G. Passarino and M. J. G. Veltman, One loop corrections for e+e− annihilation into μ+μ− in the Weinberg model, Nucl. Phys. B160, 151 (1979).

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