- 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

Z4 scotogenic model with a Higgs portal

Noel Jonathan Jobu* and Kenji Nishiwaki†

  • *Contact author: nj702@snu.edu.in
  • †Contact author: kenji.nishiwaki@snu.edu.in
PDF

Phys. Rev. D 112, 115009 – Published 3 December, 2025

DOI: https://doi.org/10.1103/xwv3-239s

Abstract

We propose a new scotogenic type model based on a global Z4 symmetry involving dark matter candidates. After the symmetry breaking as Z4 to Z2 via the singlet scalar vacuum expectation value (VEV), the lightest Majorana fermion works as a viable thermal freeze-out dark matter (DM) candidate, and the mass terms for active neutrinos are generated as a finite quantum correction at the one-loop level. A key point of realizing our scotogenic structure is to introduce two types of Majorana fermions (heavy right-handed neutrinos) and inert Higgs doublets with opposite Z4 parities. Since a large VEV for the singlet scalar is not so harmful in an appropriate realization of the Higgs mechanism for the SM gauge symmetry, we can naturally realize a TeV-scale fermionic DM candidate, where constraints via direct detection experiments are less than those for sub-TeV DM. Our scenario involves the Higgs-portal DM interactions, which help the realization of the correct DM relic abundance. Relying on the structure of the model, it is possible to find a natural partner for coannihilation. Our scenario can be investigated via the measurement of the Higgs trilinear self-coupling at the Large Hadron Collider. The simplest way to evade the domain-wall problem, by adding a tiny soft Z2 breaking term, works, keeping a sufficient longevity of the decaying DM lifetime.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (263)

  1. Y. Fukuda et al. (Super-Kamiokande Collaboration), Evidence for oscillation of atmospheric neutrinos, Phys. Rev. Lett. 81, 1562 (1998).
  2. Q. R. Ahmad et al. (SNO Collaboration), Direct evidence for neutrino flavor transformation from neutral current interactions in the Sudbury Neutrino Observatory, Phys. Rev. Lett. 89, 011301 (2002).
  3. C. Giganti, S. Lavignac, and M. Zito, Neutrino oscillations: The rise of the PMNS paradigm, Prog. Part. Nucl. Phys. 98, 1 (2018).
  4. B. Pontecorvo, Mesonium and anti-mesonium, Sov. Phys. JETP 6, 429 (1957).
  5. B. Pontecorvo, Inverse beta processes and nonconservation of lepton charge, Zh. Eksp. Teor. Fiz. 34, 247 (1957).
  6. Z. Maki, M. Nakagawa, and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28, 870 (1962).
  7. B. Abi et al. (DUNE Collaboration), Long-baseline neutrino oscillation physics potential of the DUNE experiment, Eur. Phys. J. C 80, 978 (2020).
  8. K. Abe et al. (Hyper-Kamiokande Collaboration), Physics potentials with the second Hyper-Kamiokande detector in Korea, Prog. Theor. Exp. Phys. 2018, 063C01 (2018).
  9. Z.-z. Xing, Flavor structures of charged fermions and massive neutrinos, Phys. Rep. 854, 1 (2020).
  10. P. Minkowski, μ→eγ at a rate of one out of 109 Muon decays?, Phys. Lett. B 67B, 421 (1977).
  11. T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, Conf. Proc. C 7902131, 95 (1979).
  12. M. Gell-Mann, P. Ramond, and R. Slansky, Complex spinors and unified theories, Conf. Proc. C 790927, 315 (1979).
  13. S. L. Glashow, The future of elementary particle physics, NATO Sci. Ser. B 61, 687 (1980).
  14. R. N. Mohapatra and G. Senjanovic, Neutrino mass and spontaneous parity nonconservation, Phys. Rev. Lett. 44, 912 (1980).
  15. P. Ramond, The family group in grand unified theories, in International Symposium on Fundamentals of Quantum Theory and Quantum Field Theory (World Scientific, 1979).
  16. J. Schechter and J. W. F. Valle, Neutrino masses in SU(2)×U(1) theories, Phys. Rev. D 22, 2227 (1980).
  17. G. Lazarides, Q. Shafi, and C. Wetterich, Proton lifetime and fermion masses in an SO(10) model, Nucl. Phys. B181, 287 (1981).
  18. R. N. Mohapatra and G. Senjanovic, Neutrino masses and mixings in gauge models with spontaneous parity violation, Phys. Rev. D 23, 165 (1981).
  19. C. Wetterich, Neutrino masses and the scale of B-L violation, Nucl. Phys. B187, 343 (1981).
  20. J. Schechter and J. W. F. Valle, Neutrino decay and spontaneous violation of lepton number, Phys. Rev. D 25, 774 (1982).
  21. R. Foot, H. Lew, X. G. He, and G. C. Joshi, Seesaw neutrino masses induced by a triplet of leptons, Z. Phys. C 44, 441 (1989).
  22. R. N. Mohapatra and J. W. F. Valle, Neutrino mass and baryon number nonconservation in superstring models, Phys. Rev. D 34, 1642 (1986).
  23. D. Wyler and L. Wolfenstein, Massless neutrinos in left-right symmetric models, Nucl. Phys. B218, 205 (1983).
  24. E. K. Akhmedov, M. Lindner, E. Schnapka, and J. W. F. Valle, Left-right symmetry breaking in NJL approach, Phys. Lett. B 368, 270 (1996).
  25. E. K. Akhmedov, M. Lindner, E. Schnapka, and J. W. F. Valle, Dynamical left-right symmetry breaking, Phys. Rev. D 53, 2752 (1996).
  26. M. Fukugita and T. Yanagida, Baryogenesis without grand unification, Phys. Lett. B 174, 45 (1986).
  27. S. Weinberg, Baryon and lepton nonconserving processes, Phys. Rev. Lett. 43, 1566 (1979).
  28. F. Bonnet, M. Hirsch, T. Ota, and W. Winter, Systematic study of the d=5 Weinberg operator at one-loop order, J. High Energy Phys. 07 (2012) 153.
  29. A. Zee, A theory of lepton number violation, neutrino majorana mass, and oscillation, Phys. Lett. 93B, 389 (1980); 95B, 461(E) (1980).
  30. T. P. Cheng and L.-F. Li, Neutrino masses, mixings and oscillations in SU(2)×U(1) models of electroweak interactions, Phys. Rev. D 22, 2860 (1980).
  31. A. Zee, Quantum numbers of Majorana neutrino nasses, Nucl. Phys. B264, 99 (1986).
  32. K. S. Babu, Model of ‘Calculable’ Majorana neutrino masses, Phys. Lett. B 203, 132 (1988).
  33. E. Ma, Pathways to naturally small neutrino masses, Phys. Rev. Lett. 81, 1171 (1998).
  34. L. M. Krauss, S. Nasri, and M. Trodden, A model for neutrino masses and dark matter, Phys. Rev. D 67, 085002 (2003).
  35. Y. Cai, J. Herrero-García, M. A. Schmidt, A. Vicente, and R. R. Volkas, From the trees to the forest: A review of radiative neutrino mass models, Front. Phys. 5, 63 (2017).
  36. E. Ma, Verifiable radiative seesaw mechanism of neutrino mass and dark matter, Phys. Rev. D 73, 077301 (2006).
  37. E. Ma and D. Suematsu, Fermion triplet dark matter and radiative neutrino mass, Mod. Phys. Lett. A 24, 583 (2009).
  38. Y. Farzan, A minimal model linking two great mysteries: Neutrino mass and dark matter, Phys. Rev. D 80, 073009 (2009).
  39. C.-H. Chen, C.-Q. Geng, and D. V. Zhuridov, Neutrino masses, leptogenesis and decaying dark matter, J. Cosmol. Astropart. Phys. 10 (2009) 001.
  40. Y. Farzan, S. Pascoli, and M. A. Schmidt, AMEND: A model explaining neutrino masses and dark matter testable at the LHC and MEG, J. High Energy Phys. 10 (2010) 111.
  41. M. Aoki, S. Kanemura, and K. Yagyu, Doubly-charged scalar bosons from the doublet, Phys. Lett. B 702, 355 (2011); 706, 495(E) (2012).
  42. M. K. Parida, Radiative seesaw in SO(10) with dark matter, Phys. Lett. B 704, 206 (2011).
  43. Y. Cai, X.-G. He, M. Ramsey-Musolf, and L.-H. Tsai, RνMDM and lepton flavor violation, J. High Energy Phys. 12 (2011) 054.
  44. W. Chao, Dark matter, LFV and neutrino magnetic moment in the radiative seesaw model with fermion triplet, Int. J. Mod. Phys. A 30, 1550007 (2015).
  45. Y. Farzan and E. Ma, Dirac neutrino mass generation from dark matter, Phys. Rev. D 86, 033007 (2012).
  46. H. Okada and T. Toma, Fermionic dark matter in radiative inverse seesaw model with U(1)B−L, Phys. Rev. D 86, 033011 (2012).
  47. D. Hehn and A. Ibarra, A radiative model with a naturally mild neutrino mass hierarchy, Phys. Lett. B 718, 988 (2013).
  48. Y. Kajiyama, H. Okada, and K. Yagyu, Two loop radiative seesaw model with inert triplet scalar field, Nucl. Phys. B874, 198 (2013).
  49. M. Hirsch, R. A. Lineros, S. Morisi, J. Palacio, N. Rojas, and J. W. F. Valle, WIMP dark matter as radiative neutrino mass messenger, J. High Energy Phys. 10 (2013) 149.
  50. E. Ma, Unified framework for matter, dark matter, and radiative neutrino mass, Phys. Rev. D 88, 117702 (2013).
  51. V. Brdar, I. Picek, and B. Radovcic, Radiative neutrino mass with scotogenic scalar triplet, Phys. Lett. B 728, 198 (2014).
  52. S. S. C. Law and K. L. McDonald, A class of inert N-tuplet models with radiative neutrino mass and dark matter, J. High Energy Phys. 09 (2013) 092.
  53. H. Okada, T. Toma, and K. Yagyu, Inert extension of the Zee-Babu model, Phys. Rev. D 90, 095005 (2014).
  54. S. Patra, N. Sahoo, and N. Sahu, Dipolar dark matter in light of the 3.5 keV x-ray line, neutrino mass, and LUX data, Phys. Rev. D 91, 115013 (2015).
  55. S. Fraser, E. Ma, and O. Popov, Scotogenic inverse seesaw model of neutrino mass, Phys. Lett. B 737, 280 (2014).
  56. H. Okada and Y. Orikasa, Classically conformal radiative neutrino model with gauged B− L symmetry, Phys. Lett. B 760, 558 (2016).
  57. S. Baek, H. Okada, and K. Yagyu, Flavour dependent gauged radiative neutrino mass model, J. High Energy Phys. 04 (2015) 049.
  58. T. A. Chowdhury and S. Nasri, Lepton flavor violation in the inert scalar model with higher representations, J. High Energy Phys. 12 (2015) 040.
  59. M. A. Díaz, N. Rojas, S. Urrutia-Quiroga, and J. W. F. Valle, Heavy Higgs boson production at colliders in the singlet-triplet scotogenic dark matter model, J. High Energy Phys. 08 (2017) 017.
  60. P. M. Ferreira, W. Grimus, D. Jurciukonis, and L. Lavoura, Scotogenic model for co-bimaximal mixing, J. High Energy Phys. 07 (2016) 010.
  61. A. Ahriche, K. L. McDonald, and S. Nasri, The scale-invariant scotogenic model, J. High Energy Phys. 06 (2016) 182.
  62. F. von der Pahlen, G. Palacio, D. Restrepo, and O. Zapata, Radiative Type III seesaw model and its collider phenomenology, Phys. Rev. D 94, 033005 (2016).
  63. W.-B. Lu and P.-H. Gu, Mixed inert scalar triplet dark matter, radiative neutrino masses and leptogenesis, Nucl. Phys. B924, 279 (2017).
  64. A. Merle, M. Platscher, N. Rojas, J. W. F. Valle, and A. Vicente, Consistency of WIMP dark matter as radiative neutrino mass messenger, J. High Energy Phys. 07 (2016) 013.
  65. P. Rocha-Moran and A. Vicente, Lepton flavor violation in the singlet-triplet scotogenic model, J. High Energy Phys. 07 (2016) 078.
  66. T. Nomura, H. Okada, and Y. Orikasa, Radiative neutrino model with SU(2)L triplet fields, Phys. Rev. D 94, 115018 (2016).
  67. K. Cheung, T. Nomura, and H. Okada, Three-loop neutrino mass model with a colored triplet scalar, Phys. Rev. D 95, 015026 (2017).
  68. T. A. Chowdhury and S. Nasri, The sommerfeld enhancement in the scotogenic model with large electroweak scalar multiplets, J. Cosmol. Astropart. Phys. 01 (2017) 041.
  69. K. Cheung, T. Nomura, and H. Okada, A three-loop neutrino model with leptoquark triplet scalars, Phys. Lett. B 768, 359 (2017).
  70. S. Lee, T. Nomura, and H. Okada, Radiatively induced neutrino mass model with flavor dependent gauge symmetry, Nucl. Phys. B931, 179 (2018).
  71. E. C. F. S. Fortes, A. C. B. Machado, J. Montaño, and V. Pleitez, Lepton masses and mixing in a scotogenic model, Phys. Lett. B 803, 135289 (2020).
  72. Y.-L. Tang, Some phenomenologies of a simple scotogenic inverse seesaw model, Phys. Rev. D 97, 035020 (2018).
  73. C. Guo, S.-Y. Guo, and Y. Liao, Dark matter and LHC phenomenology of a scale invariant scotogenic model, Chin. Phys. C 43, 103102 (2019).
  74. N. Rojas, R. Srivastava, and J. W. F. Valle, Simplest scoto-seesaw mechanism, Phys. Lett. B 789, 132 (2019).
  75. A. Aranda, C. Bonilla, and E. Peinado, Dynamical generation of neutrino mass scales, Phys. Lett. B 792, 40 (2019).
  76. Z.-L. Han and W. Wang, Predictive scotogenic model with flavor dependent symmetry, Eur. Phys. J. C 79, 522 (2019).
  77. D. Suematsu, Low scale leptogenesis in a hybrid model of the scotogenic type I and III seesaw models, Phys. Rev. D 100, 055008 (2019).
  78. S. Pramanick, Scotogenic S3 symmetric generation of realistic neutrino mixing, Phys. Rev. D 100, 035009 (2019).
  79. D. Restrepo and A. Rivera, Phenomenological consistency of the singlet-triplet scotogenic model, J. High Energy Phys. 04 (2020) 134.
  80. S. Mandal, N. Rojas, R. Srivastava, and J. W. F. Valle, Dark matter as the origin of neutrino mass in the inverse seesaw mechanism, Phys. Lett. B 821, 136609 (2021).
  81. I. M. Ávila, V. De Romeri, L. Duarte, and J. W. F. Valle, Phenomenology of scotogenic scalar dark matter, Eur. Phys. J. C 80, 908 (2020).
  82. P. Escribano, M. Reig, and A. Vicente, Generalizing the scotogenic model, J. High Energy Phys. 07 (2020) 097.
  83. T. Nomura, H. Okada, and Y. Uesaka, A two-loop induced neutrino mass model, dark matter, and LFV processes ℓi→ℓjγ, and μe→ee in a hidden local U(1) symmetry, Nucl. Phys. B962, 115236 (2021).
  84. A. Beniwal, J. Herrero-García, N. Leerdam, M. White, and A. G. Williams, The scotosinglet model: A scalar singlet extension of the scotogenic model, J. High Energy Phys. 21 (2020) 136.
  85. V. De Romeri, M. Puerta, and A. Vicente, Dark matter in a charged variant of the scotogenic model, Eur. Phys. J. C 82, 623 (2022).
  86. B. De, D. Das, M. Mitra, and N. Sahoo, Magnetic moments of leptons, charged lepton flavor violations and dark matter phenomenology of a minimal radiative Dirac neutrino mass model, J. High Energy Phys. 08 (2022) 202.
  87. D. W. Kang, J. Kim, and H. Okada, Muon g−2 in U(1)μ−τ symmetric gauged radiative neutrino mass model, Phys. Lett. B 822, 136666 (2021).
  88. M. Sarazin, J. Bernigaud, and B. Herrmann, Dark matter and lepton flavour phenomenology in a singlet-doublet scotogenic model, J. High Energy Phys. 12 (2021) 116.
  89. K. I. Nagao, T. Nomura, and H. Okada, A model explaining the new CDF II W boson mass linking to muon g−2 and dark matter, Eur. Phys. J. Plus 138, 365 (2023).
  90. A. Ahriche, A scotogenic model with two inert doublets, J. High Energy Phys. 02 (2023) 028.
  91. R. Cepedello, P. Escribano, and A. Vicente, Neutrino masses, flavor anomalies, and muon g-2 from dark loops, Phys. Rev. D 107, 035034 (2023).
  92. E. J. Chun, A. Roy, S. Mandal, and M. Mitra, Fermionic dark matter in dynamical scotogenic model, J. High Energy Phys. 08 (2023) 130.
  93. P. Escribano, V. M. Lozano, and A. Vicente, Scotogenic explanation for the 95 GeV excesses, Phys. Rev. D 108, 115001 (2023).
  94. D. Borah, S. Mahapatra, P. K. Paul, and N. Sahu, Scotogenic U(1)Lμ−Lτ origin of (g−2)μ, W-mass anomaly and 95 GeV excess, Phys. Rev. D 109, 055021 (2024).
  95. B. Garbrecht and E. Wang, A scotogenic model as a prototype for leptogenesis with one single gauge singlet, Phys. Rev. D 110, 116019 (2024).
  96. T. Nomura and O. Popov, Extended scotogenic model of neutrino mass and proton decay, Phys. Rev. D 110, 075035 (2024).
  97. K. M. Cárdenas, G. Mohlabeng, and A. C. Vincent, Global fit to loopy dark matter and neutrino masses, Phys. Rev. D 111, 055024 (2025).
  98. L. Singh, R. Srivastava, S. Verma, and S. Yadav, Type-III scotogenic model: Inflation, dark matter and collider phenomenology, arXiv:2501.13171.
  99. A. E. Cárcamo Hernández, J. E. Puentes, R. Pasechnik, and D. Salinas-Arizmendi, Strongly coupled inert scalar sector with radiative neutrino masses, J. High Energy Phys. 10 (2025) 061.
  100. P. Escribano, V. M. Lozano, S. Norero, and A. Vicente, Exploring dimuon higgs decay in an extended scotogenic model, J. High Energy Phys. 09 (2025) 136.
  101. A. AbuSiam and A. Ahriche, The scotogenic model with two inert doublets: Parameters space and electroweak precision tests, Int. J. Mod. Phys. A 40, 2550157 (2025).
  102. E. Ma, Dark scalar doublets and neutrino tribimaximal mixing from A(4) symmetry, Phys. Lett. B 671, 366 (2009).
  103. A. Adulpravitchai, M. Lindner, A. Merle, and R. N. Mohapatra, Radiative transmission of lepton flavor hierarchies, Phys. Lett. B 680, 476 (2009).
  104. E. Ma, A. Natale, and A. Rashed, Scotogenic A4 neutrino model for nonzero θ13 and large δCP, Int. J. Mod. Phys. A 27, 1250134 (2012).
  105. S. Bhattacharya, E. Ma, A. Natale, and A. Rashed, Radiative scaling neutrino mass with A4 symmetry, Phys. Rev. D 87, 097301 (2013).
  106. Y. Kajiyama, H. Okada, and T. Toma, Multicomponent dark matter particles in a two-loop neutrino model, Phys. Rev. D 88, 015029 (2013).
  107. E. Ma, Neutrino mixing and geometric CP violation with Delta(27) symmetry, Phys. Lett. B 723, 161 (2013).
  108. E. Ma and A. Natale, Scotogenic Z2 or U(1)D model of neutrino mass with Δ(27) symmetry, Phys. Lett. B 734, 403 (2014).
  109. H. Okada, N. Okada, and Y. Orikasa, Radiative seesaw mechanism in a minimal 3-3-1 model, Phys. Rev. D 93, 073006 (2016).
  110. S. Baek, H. Okada, and Y. Orikasa, A two loop radiative neutrino model, Nucl. Phys. B941, 744 (2019).
  111. A. Ahriche, A. Jueid, and S. Nasri, A natural scotogenic model for neutrino mass & dark matter, Phys. Lett. B 814, 136077 (2021).
  112. S.-L. Chen, A. Dutta Banik, and Z.-K. Liu, Common origin of radiative neutrino mass, dark matter and leptogenesis in scotogenic Georgi-Machacek model, Nucl. Phys. B966, 115394 (2021).
  113. F. J. de Anda, O. Medina, J. W. F. Valle, and C. A. Vaquera-Araujo, Scotogenic Majorana neutrino masses in a predictive orbifold theory of flavor, Phys. Rev. D 105, 055030 (2022).
  114. S. Chuliá Centelles, R. Cepedello, and O. Medina, Absolute neutrino mass scale and dark matter stability from flavour symmetry, J. High Energy Phys. 10 (2022) 080.
  115. D. M. Barreiros, H. B. Camara, and F. R. Joaquim, Flavour and dark matter in a scoto/type-II seesaw model, J. High Energy Phys. 08 (2022) 030.
  116. C. Bonilla, J. Herms, O. Medina, and E. Peinado, Discrete dark matter mechanism as the source of neutrino mass scales, J. High Energy Phys. 06 (2023) 078.
  117. R. Kumar, P. Mishra, M. K. Behera, R. Mohanta, and R. Srivastava, Predictions from scoto-seesaw with A4 modular symmetry, Phys. Lett. B 853, 138635 (2024).
  118. J. Ganguly, J. Gluza, B. Karmakar, and S. Mahapatra, Phenomenology of the flavor symmetric scoto-seesaw model with dark matter and TM1 mixing, Phys. Rev. D 110, 035012 (2024).
  119. S. Arora and B. C. Chauhan, Dark matter and Muon (g−2) from a discrete Z4 symmetric model, Lett. High Energy Phys. 2024, 512 (2024).
  120. R. Kumar, N. Nath, and R. Srivastava, Cutting the scotogenic loop: Adding flavor to dark matter, J. High Energy Phys. 12 (2024) 036.
  121. J. Kim, S.-S. Kim, H. M. Lee, and R. Padhan, Small neutrino masses from a decoupled singlet scalar field, Phys. Lett. B 861, 139243 (2025).
  122. L. M. G. de la Vega, P. J. Fitzpatrick, R. Martinez-Ramirez, and E. Peinado, Dark matter for Majorana neutrinos in a Z4 symmetry, Phys. Rev. D 110, 115024 (2024).
  123. A. E. Cárcamo Hernández, D. Salinas-Arizmendi, J. Vignatti, and A. Zerwekh, Phenomenology of an extended 1+2 Higgs doublet model with S3 family symmetry, Eur. Phys. J. C 84, 1135 (2024).
  124. D. M. Luong and P. Van Dong, Scotoseesaw mechanism from a Z3 symmetry of matter, Eur. Phys. J. C 85, 473 (2025).
  125. J. Kubo and D. Suematsu, Neutrino masses and CDM in a non-supersymmetric model, Phys. Lett. B 643, 336 (2006).
  126. W.-F. Chang and C.-F. Wong, A model for neutrino masses and dark matter with the discrete gauge symmetry, Phys. Rev. D 85, 013018 (2012).
  127. Y. Kajiyama, H. Okada, and K. Yagyu, T7 flavor model in three loop seesaw and Higgs phenomenology, J. High Energy Phys. 10 (2013) 196.
  128. E. Ma, I. Picek, and B. Radovčić, New scotogenic model of neutrino mass with U(1)D gauge interaction, Phys. Lett. B 726, 744 (2013).
  129. D. Aristizabal Sierra, M. Dhen, C. S. Fong, and A. Vicente, Dynamical flavor origin of ZN symmetries, Phys. Rev. D 91, 096004 (2015).
  130. H. Hatanaka, K. Nishiwaki, H. Okada, and Y. Orikasa, A three-loop neutrino model with global U(1) symmetry, Nucl. Phys. B894, 268 (2015).
  131. K. Nishiwaki, H. Okada, and Y. Orikasa, Three loop neutrino model with isolated k±±, Phys. Rev. D 92, 093013 (2015).
  132. H. Okada and Y. Orikasa, Radiative neutrino model with an inert triplet scalar, Phys. Rev. D 94, 055002 (2016).
  133. S. Kanemura, K. Nishiwaki, H. Okada, Y. Orikasa, S. C. Park, and R. Watanabe, LHC 750 GeV diphoton excess in a radiative seesaw model, Prog. Theor. Exp. Phys. 2016, 123B04 (2016).
  134. J.-H. Yu, Hidden gauged U(1) model: Unifying scotogenic neutrino and flavor dark matter, Phys. Rev. D 93, 113007 (2016).
  135. T. Nomura and H. Okada, A four-loop radiative seesaw model, Phys. Lett. B 770, 307 (2017).
  136. W. Wang, R. Wang, Z.-L. Han, and J.-Z. Han, The B−L scotogenic models for dirac neutrino masses, Eur. Phys. J. C 77, 889 (2017).
  137. T. Nomura and H. Okada, Radiative neutrino mass in an alternative U(1)B−L gauge symmetry, Nucl. Phys. B941, 586 (2019).
  138. T. Nomura and H. Okada, A model with isospin doublet U(1)D gauge symmetry, Int. J. Mod. Phys. A 33, 1850089 (2018).
  139. E. Ma, D. Restrepo, and O. Zapata, Anomalous leptonic U(1) symmetry: Syndetic origin of the QCD axion, weak-scale dark matter, and radiative neutrino mass, Mod. Phys. Lett. A 33, 1850024 (2018).
  140. T. Nomura and H. Okada, Neutrino mass in flavor dependent gauged lepton model, Phys. Rev. D 97, 055044 (2018).
  141. C. Hagedorn, J. Herrero-García, E. Molinaro, and M. A. Schmidt, Phenomenology of the generalized scotogenic model with fermionic dark matter, J. High Energy Phys. 11 (2018) 103.
  142. Z.-L. Han and W. Wang, Z′ portal dark matter in B−L scotogenic dirac model, Eur. Phys. J. C 78, 839 (2018).
  143. J. Calle, D. Restrepo, C. E. Yaguna, and O. Zapata, Minimal radiative Dirac neutrino mass models, Phys. Rev. D 99, 075008 (2019).
  144. C. D. R. Carvajal and O. Zapata, One-loop Dirac neutrino mass and mixed axion-WIMP dark matter, Phys. Rev. D 99, 075009 (2019).
  145. S. Centelles Chuliá, R. Cepedello, E. Peinado, and R. Srivastava, Scotogenic dark symmetry as a residual subgroup of standard model symmetries, Chin. Phys. C 44, 083110 (2020).
  146. E. Ma, Scotogenic U(1)χ Dirac neutrinos, Phys. Lett. B 793, 411 (2019).
  147. S. K. Kang, O. Popov, R. Srivastava, J. W. F. Valle, and C. A. Vaquera-Araujo, Scotogenic dark matter stability from gauged matter parity, Phys. Lett. B 798, 135013 (2019).
  148. T. Nomura and H. Okada, A modular A4 symmetric model of dark matter and neutrino, Phys. Lett. B 797, 134799 (2019).
  149. S. Jana, P. K. Vishnu, and S. Saad, Minimal dirac neutrino mass models from U(1)R gauge symmetry and left–right asymmetry at colliders, Eur. Phys. J. C 79, 916 (2019).
  150. E. Ma, Scotogenic cobimaximal Dirac neutrino mixing from Δ(27) and U(1)χ, Eur. Phys. J. C 79, 903 (2019).
  151. T. Nomura and H. Okada, A two loop induced neutrino mass model with modular A4 symmetry, Nucl. Phys. B966, 115372 (2021).
  152. J. Fuentes-Martín, M. Reig, and A. Vicente, Strong CP problem with low-energy emergent QCD: The 4321 case, Phys. Rev. D 100, 115028 (2019).
  153. H. Okada and Y. Orikasa, Modular S3 symmetric radiative seesaw model, Phys. Rev. D 100, 115037 (2019).
  154. C. Bonilla, L. M. G. de la Vega, J. M. Lamprea, R. A. Lineros, and E. Peinado, Fermion dark matter and radiative neutrino masses from spontaneous lepton number breaking, New J. Phys. 22, 033009 (2020).
  155. Z.-L. Han, R. Ding, S.-J. Lin, and B. Zhu, Gauged U(1)Lμ−Lτ scotogenic model in light of RK(*) anomaly and AMS-02 positron excess, Eur. Phys. J. C 79, 1007 (2019).
  156. T. Nomura, H. Okada, and O. Popov, A modular A4 symmetric scotogenic model, Phys. Lett. B 803, 135294 (2020).
  157. J. Leite, O. Popov, R. Srivastava, and J. W. F. Valle, A theory for scotogenic dark matter stabilised by residual gauge symmetry, Phys. Lett. B 802, 135254 (2020).
  158. S. Jana, P. K. Vishnu, and S. Saad, Minimal realizations of Dirac neutrino mass from generic one-loop and two-loop topologies at d=5, J. Cosmol. Astropart. Phys. 04 (2020) 018.
  159. W. Wang and Z.-L. Han, U(1)B−3Lα extended scotogenic models and single-zero textures of neutrino mass matrices, Phys. Rev. D 101, 115040 (2020).
  160. L. M. G. de la Vega, N. Nath, and E. Peinado, Dirac neutrinos from Peccei-Quinn symmetry: Two examples, Nucl. Phys. B957, 115099 (2020).
  161. H. Okada and Y. Shoji, A radiative seesaw model with three Higgs doublets in modular A4 symmetry, Nucl. Phys. B961, 115216 (2020).
  162. J. Kim, T. Nomura, and H. Okada, A radiative seesaw model linking to XENON1T anomaly, Phys. Lett. B 811, 135862 (2020).
  163. C.-F. Wong, Anomaly-free chiral U(1)D and its scotogenic implication, Phys. Dark Universe 32, 100818 (2021).
  164. M. K. Behera, S. Singirala, S. Mishra, and R. Mohanta, A modular A4 symmetric scotogenic model for neutrino mass and dark matter, J. Phys. G 49, 035002 (2022).
  165. N. Bernal, J. Calle, and D. Restrepo, Anomaly-free Abelian gauge symmetries with Dirac scotogenic models, Phys. Rev. D 103, 095032 (2021).
  166. H. Okada, Y. Orikasa, and Y. Shoji, Radiative dark matter and neutrino masses from an alternative U(1) B-L gauge symmetry, J. Cosmol. Astropart. Phys. 07 (2021) 006.
  167. T. Nomura and H. Okada, Radiative neutrino mass model in dark non-Abelian gauge symmetry, Phys. Rev. D 105, 075010 (2022).
  168. P. Escribano and A. Vicente, An ultraviolet completion for the scotogenic model, Phys. Lett. B 823, 136717 (2021).
  169. A. Dasgupta, T. Nomura, H. Okada, O. Popov, and M. Tanimoto, Dirac radiative neutrino mass with modular symmetry and leptogenesis, arXiv:2111.06898.
  170. M. Berbig, Freeze-In of radiative keV-scale neutrino dark matter from a new U(1)B−L, J. High Energy Phys. 09 (2022) 101.
  171. D. Portillo-Sánchez, P. Escribano, and A. Vicente, Ultraviolet extensions of the scotogenic model, J. High Energy Phys. 08 (2023) 023.
  172. T. de Boer, M. Klasen, and S. Zeinstra, Anomaly-free dark matter models with one-loop neutrino masses and a gauged U(1) symmetry, J. High Energy Phys. 01 (2024) 013.
  173. T. Nomura and H. Okada, Scotogenic models with a general lepton flavor dependent U(1) gauge symmetry, Phys. Lett. B 848, 138393 (2024).
  174. J. Leite, S. Sadhukhan, and J. W. F. Valle, Dynamical scoto-seesaw mechanism with gauged B-L symmetry, Phys. Rev. D 109, 035023 (2024).
  175. T. Nomura and H. Okada, Radiative inverse seesaw model with hidden U(1) gauge symmetry enhancing lepton g−2, arXiv:2403.14193.
  176. D. Van Loi, N. T. Duy, C. H. Nam, and P. Van Dong, Scoto-seesaw model implied by flavor-dependent Abelian gauge charge, Eur. Phys. J. C 85, 109 (2025).
  177. T. Nomura, H. Okada, and O. Popov, Non-holomorphic modular A4 symmetric scotogenic model, Phys. Lett. B 860, 139171 (2025).
  178. S. Centelles Chuliá, R. Srivastava, and S. Yadav, Comprehensive phenomenology of the dirac scotogenic model: Novel low-mass dark matter, J. High Energy Phys. 04 (2025) 038.
  179. Y. Garnica, A. Morales, and C. A. Vaquera-Araujo, Scotogenic dark matter from gauged B−L, Phys. Lett. B 868, 139790 (2025).
  180. G. Pathak, P. Das, and M. K. Das, Neutrino mass genesis in scoto-inverse seesaw with modular A4, Eur. Phys. J. C 85, 569 (2025).
  181. K. Agudelo, D. Restrepo, A. Rivera, and D. Suarez, Multicomponent secluded WIMP dark matter and Dirac neutrino masses with an extra Abelian gauge symmetry, Phys. Rev. D 111, 095018 (2025).
  182. K. S. Babu and S. Saad, Ultraviolet completion of a two-loop neutrino mass model, J. High Energy Phys. 03 (2025) 132.
  183. S. Gola, Dark matter from axions and small neutrino masses, Phys. Rev. D 112, 035006 (2025).
  184. A. Batra, H. B. Câmara, F. R. Joaquim, N. Nath, R. Srivastava, and J. W. F. Valle, Axion framework with color-mediated Dirac neutrino masses, Phys. Lett. B 868, 139629 (2025).
  185. Z. A. Borboruah, L. Malhotra, U. Patel, S. Patra, and S. U. Sankar, Left-right symmetric neutrino mass model without scalar bi-doublet, arXiv:2504.08267.
  186. I. Doršner, M. Matković, and S. Saad, Nonrenormalizable SU(5) GUTs: Leptoquark-induced neutrino masses, Phys. Rev. D 111, 115039 (2025).
  187. R. Kumar, N. Nath, R. Srivastava, and S. Yadav, Dirac scoto inverse-seesaw from A4 flavor symmetry, J. High Energy Phys. 10 (2025) 088.
  188. T. Nomura and H. Okada, Neutrino mass model at a three-loop level from a non-holomorphic modular A4 symmetry, arXiv:2506.02639.
  189. E. Ma, MonoHiggsology, arXiv:2507.04563.
  190. J. Leite, J. Perez-Soler, and A. Vicente, Scotogenic mechanism from an extended SU(2)1×SU(2)2×U(1)Y electroweak symmetry, J. High Energy Phys. 10 (2025) 129.
  191. M. Reig, D. Restrepo, J. W. F. Valle, and O. Zapata, Bound-state dark matter and Dirac neutrino masses, Phys. Rev. D 97, 115032 (2018).
  192. M. Reig, D. Restrepo, J. W. F. Valle, and O. Zapata, Bound-state dark matter with Majorana neutrinos, Phys. Lett. B 790, 303 (2019).
  193. D. Aristizabal Sierra, M. Hirsch, and S. G. Kovalenko, Leptoquarks: Neutrino masses and accelerator phenomenology, Phys. Rev. D 77, 055011 (2008).
  194. P. Fileviez Perez and M. B. Wise, On the origin of neutrino masses, Phys. Rev. D 80, 053006 (2009).
  195. M. Kohda, H. Sugiyama, and K. Tsumura, Lepton number violation at the LHC with leptoquark and diquark, Phys. Lett. B 718, 1436 (2013).
  196. C. Cordova, S. Hong, S. Koren, and K. Ohmori, Neutrino masses from generalized symmetry breaking, Phys. Rev. X 14, 031033 (2024).
  197. T. Kobayashi, H. Okada, and H. Otsuka, Radiative neutrino mass models from non-invertible selection rules, arXiv:2505.14878.
  198. T. Nomura and O. Popov, No-group scotogenic model, arXiv:2507.10299.
  199. M. Suzuki, L.-X. Xu, and H. Y. Zhang, Spurion analysis for non-invertible selection rules from near-group fusions, arXiv:2508.14970.
  200. A. Darricau, H. Lee, J. Orloff, and A. M. Teixeira, Flavour and precision probes of a class of scotogenic models, arXiv:2506.23383.
  201. G. Cacciapaglia and M. Rosenlyst, Loop-generated neutrino masses in composite Higgs models, J. High Energy Phys. 09 (2021) 167.
  202. LZ Collaboration, J. Aalbers et al., First dark matter search results from the LUX-ZEPLIN (LZ) experiment, Phys. Rev. Lett. 131, 041002 (2023).
  203. J. Aalbers et al. (LZ Collaboration), Dark matter search results from 4.2  tonne−years of exposure of the LUX-ZEPLIN (LZ) experiment, Phys. Rev. Lett. 135, 011802 (2025).
  204. M. Freytsis and Z. Ligeti, On dark matter models with uniquely spin-dependent detection possibilities, Phys. Rev. D 83, 115009 (2011).
  205. S. Ipek, D. McKeen, and A. E. Nelson, A renormalizable model for the galactic center gamma ray excess from dark matter annihilation, Phys. Rev. D 90, 055021 (2014).
  206. G. Arcadi, M. Lindner, F. S. Queiroz, W. Rodejohann, and S. Vogl, Pseudoscalar mediators: A WIMP model at the neutrino floor, J. Cosmol. Astropart. Phys. 03 (2018) 042.
  207. N. F. Bell, G. Busoni, and I. W. Sanderson, Loop effects in direct detection, J. Cosmol. Astropart. Phys. 08 (2018) 017; 01 (2019) E01(E).
  208. T. Abe, M. Fujiwara, and J. Hisano, Loop corrections to dark matter direct detection in a pseudoscalar mediator dark matter model, J. High Energy Phys. 02 (2019) 028.
  209. T. Abe, M. Fujiwara, J. Hisano, and Y. Shoji, Maximum value of the spin-independent cross section in the 2HDM+a, J. High Energy Phys. 01 (2020) 114.
  210. V. Barger, M. McCaskey, and G. Shaughnessy, Complex scalar dark matter vis-‘a-vis CoGeNT, DAMA/LIBRA and XENON100, Phys. Rev. D 82, 035019 (2010).
  211. D. Barducci, A. Bharucha, N. Desai, M. Frigerio, B. Fuks, A. Goudelis, S. Kulkarni, G. Polesello, and D. Sengupta, Monojet searches for momentum-dependent dark matter interactions, J. High Energy Phys. 01 (2017) 078.
  212. C. Gross, O. Lebedev, and T. Toma, Cancellation mechanism for dark-matter–Nucleon interaction, Phys. Rev. Lett. 119, 191801 (2017).
  213. R. Balkin, M. Ruhdorfer, E. Salvioni, and A. Weiler, Charged composite scalar dark matter, J. High Energy Phys. 11 (2017) 094.
  214. K. Ishiwata and T. Toma, Probing pseudo Nambu-Goldstone boson dark matter at loop level, J. High Energy Phys. 12 (2018) 089.
  215. Y. Abe, T. Toma, K. Tsumura, and N. Yamatsu, Pseudo-Nambu-Goldstone dark matter model inspired by grand unification, Phys. Rev. D 104, 035011 (2021).
  216. N. Okada, D. Raut, Q. Shafi, and A. Thapa, Pseudo-Goldstone dark matter in SO(10), Phys. Rev. D 104, 095002 (2021).
  217. C.-W. Chiang, K. Tsumura, Y. Uchida, and N. Yamatsu, Pseudo-Nambu-Goldstone dark matter in SU(7) grand unification, Phys. Rev. D 109, 055040 (2024).
  218. S. Bhattacharya, D. Mahanta, N. Mondal, and D. Pradhan, Two-component dark matter and low scale thermal Leptogenesis, J. Cosmol. Astropart. Phys. 09 (2025) 032.
  219. Z. Wang, Y. Reyimuaji, and N. Yalikun, A Z4 symmetric inverse seesaw model for neutrino masses and FIMP dark matter, Phys. Rev. D 112, 055041 (2025).
  220. J. Ellis, TikZ-Feynman: Feynman diagrams with TikZ, Comput. Phys. Commun. 210, 103 (2017).
  221. J. A. Casas and A. Ibarra, Oscillating neutrinos and μ→e,γ, Nucl. Phys. B618, 171 (2001).
  222. I. Cordero-Carrión, M. Hirsch, and A. Vicente, General parametrization of Majorana neutrino mass models, Phys. Rev. D 101, 075032 (2020).
  223. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  224. 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.
  225. M. Thomson, Modern Particle Physics. (Cambridge University Press, New York, 2013).
  226. K. Afanaciev et al. (MEG II Collaboration), A search for μ+→e+γ with the first dataset of the MEG II experiment, Eur. Phys. J. C 84, 216 (2024); 84, 1042(E) (2024).
  227. B. Aubert et al. (BABAR Collaboration), Searches for lepton flavor violation in the decays τ±→e±γ and τ±→μ±γ, Phys. Rev. Lett. 104, 021802 (2010).
  228. W. Grimus, L. Lavoura, O. M. Ogreid, and P. Osland, A precision constraint on multi-Higgs-doublet models, J. Phys. G 35, 075001 (2008).
  229. P. D. Group, R. Workman, V. Burkert, V. Crede, E. Klempt, U. Thoma, L. Tiator, K. Agashe, G. Aielli, B. Allanach et al., Review of particle physics, Prog. Theor. Exp. Phys. 2022, 083C01 (2022).
  230. K. Kannike, Vacuum stability of a general scalar potential of a few fields, Eur. Phys. J. C 76, 324 (2016); 78, 355(E) (2018)].
  231. V. Keus, S. F. King, and S. Moretti, Three-Higgs-doublet models: Symmetries, potentials and Higgs boson masses, J. High Energy Phys. 01 (2014) 052.
  232. J. Edsjo and P. Gondolo, Neutralino relic density including coannihilations, Phys. Rev. D 56, 1879 (1997).
  233. M. Srednicki, R. Watkins, and K. A. Olive, Calculations of relic densities in the early universe, Nucl. Phys. B310, 693 (1988).
  234. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  235. F. Tanedo, Defense against the dark arts, Notes on Dark Matter and Particle Physics (2011).
  236. L. Husdal, On effective degrees of freedom in the early universe, Galaxies 4, 78 (2016).
  237. J. Kopp, L. Michaels, and J. Smirnov, Loopy constraints on leptophilic dark matter and internal bremsstrahlung, J. Cosmol. Astropart. Phys. 04 (2014) 022.
  238. Y. Bai and J. Berger, Lepton portal dark matter, J. High Energy Phys. 08 (2014) 153.
  239. G. Arcadi, A. Djouadi, and M. Kado, The Higgs-portal for dark matter: Effective field theories versus concrete realizations, Eur. Phys. J. C 81, 653 (2021).
  240. G. Van Rossum and F. L. Drake, python 3 Reference Manual (CreateSpace, Scotts Valley, CA, 2009).
  241. G. Van Rossum, The python Library Reference, release 3.8.2 (python Software Foundation, 2020).
  242. C. R. Harris et al., Array programming with numpy, Nature (London) 585, 357 (2020).
  243. T. pandas development team, pandas-dev/pandas: Pandas, Feb., 2020.https://doi.org/10.5281/zenodo.3509134.
  244. P. Virtanen et al. (SciPy 1.0 Contributors), scipy 1.0: Fundamental algorithms for scientific computing in python, Nat. Methods 17, 261 (2020).
  245. J. D. Hunter, Matplotlib: A 2d graphics environment, Comput. Sci. Eng. 9, 90 (2007).
  246. P. Gondolo and G. Gelmini, Cosmic abundances of stable particles: Improved analysis, Nucl. Phys. B360, 145 (1991).
  247. G. Aad et al. (ATLAS Collaboration), Constraints on the Higgs boson self-coupling from single- and double-Higgs production with the ATLAS detector using pp collisions at s=13  TeV, Phys. Lett. B 843, 137745 (2023).
  248. P. Stylianou and G. Weiglein, Constraints on the trilinear and quartic Higgs couplings from triple Higgs production at the LHC and beyond, Eur. Phys. J. C 84, 366 (2024).
  249. M. Cepeda et al., Report from Working Group 2: Higgs physics at the HL-LHC and HE-LHC, CERN Yellow Rep. Monogr. 7, 221 (2019).
  250. Y. B. Zeldovich, I. Y. Kobzarev, and L. B. Okun, Cosmological consequences of the spontaneous breakdown of discrete symmetry, Zh. Eksp. Teor. Fiz. 67, 3 (1974).
  251. A. Ghoshal, N. Okada, and A. Paul, eV Hubble scale inflation with a radiative plateau: Very light inflaton, reheating, and dark matter in B-L extensions, Phys. Rev. D 106, 095021 (2022).
  252. A. Caputo, M. Geller, and G. Rossi, New source for light dark matter isocurvature in low scale inflation, Phys. Rev. D 110, 055027 (2024).
  253. M. Czerny, T. Higaki, and F. Takahashi, Multi-natural inflation in supergravity, J. High Energy Phys. 05 (2014) 144.
  254. A. Vilenkin and A. E. Everett, Cosmic strings and domain walls in models with Goldstone and PseudoGoldstone bosons, Phys. Rev. Lett. 48, 1867 (1982).
  255. J. Preskill, S. P. Trivedi, F. Wilczek, and M. B. Wise, Cosmology and broken discrete symmetry, Nucl. Phys. B363, 207 (1991).
  256. D. I. Dunsky, A. Ghoshal, H. Murayama, Y. Sakakihara, and G. White, GUTs, hybrid topological defects, and gravitational waves, Phys. Rev. D 106, 075030 (2022).
  257. R. Maji, Q. Shafi, and A. Tiwari, Topological structures, dark matter and gravitational waves in E6, J. High Energy Phys. 08 (2024) 060.
  258. S. E. Larsson, S. Sarkar, and P. L. White, Evading the cosmological domain wall problem, Phys. Rev. D 55, 5129 (1997).
  259. K. Saikawa, A review of gravitational waves from cosmic domain walls, Universe 3, 40 (2017).
  260. T. Hiramatsu, M. Kawasaki, and K. Saikawa, Gravitational waves from collapsing domain walls, J. Cosmol. Astropart. Phys. 05 (2010) 032.
  261. G. B. Gelmini, M. Gleiser, and E. W. Kolb, Cosmology of biased discrete symmetry breaking, Phys. Rev. D 39, 1558 (1989).
  262. Y. Wu, K.-P. Xie, and Y.-L. Zhou, Collapsing domain walls beyond Z2, Phys. Rev. D 105, 095013 (2022).
  263. Y. Wu, K.-P. Xie, and Y.-L. Zhou, Classification of Abelian domain walls, Phys. Rev. D 106, 075019 (2022).

Outline

Information

Phys. Rev. D 112, 115009– Published 3 December, 2025
  • Received 3 September 2025
  • Accepted 27 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