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Dark-portal leptogenesis in a nonholomorphic modular scoto-seesaw model

Salah Nasri1,*, Labh Singh2,†, Tapender2,‡, and Surender Verma2,§

  • *Contact author: snasri@uaeu.ac.ae
  • †Contact author: sainilabh5@gmail.com
  • ‡Contact author: tapenderphy@gmail.com
  • §Contact author: s_7verma@hpcu.ac.in

Phys. Rev. D 113, 115008 – Published 3 June, 2026

DOI: https://doi.org/10.1103/vbtk-561v

Abstract

This work explores the neutrino phenomenology of the scoto-seesaw model under nonholomorphic A4 modular flavor symmetry providing a nonsupersymmetry framework for realization of the modular symmetry. To prevent mixing between the beyond-standard-model fields associated with the tree- and loop-level neutrino mass contributions, we assign even and odd modular weights to these sectors, respectively. The physical allowed ranges of oscillation parameters are used to identify the viable region of modulus parameter τ in its fundamental domain. With the complex modulus τ serving as the unique source of CP violation (all other parameters are real), the framework realizes successful low-scale leptogenesis through CP-violating decays of the lightest righthanded neutrino into Standark model leptons and the Higgs boson. The requisite CP asymmetry arises from one-loop diagrams involving dark-sector states, obviating the need for degenerate mass spectra and thereby circumventing the usual resonant leptogenesis mechanism. The observation of a long-lived charged particle (η±) in collider experiments would offer compelling evidence for the inert scalar sector of the model and provide a crucial experimental hint as to the dark-sector-assisted generation of neutrino masses and leptogenesis.

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References (100)

  1. Super-Kamiokande Collaboration, Evidence for oscillation of atmospheric neutrinos, Phys. Rev. Lett. 81, 1562 (1998).
  2. SNO Collaboration, Direct evidence for neutrino flavor transformation from neutral current interactions in the Sudbury Neutrino Observatory, Phys. Rev. Lett. 89, 011301 (2002).
  3. Daya Bay Collaboration, Observation of electron-antineutrino disappearance at Daya Bay, Phys. Rev. Lett. 108, 171803 (2012).
  4. Double Chooz Collaboration, Indication for the disappearance of reactor electron antineutrinos in the Double Chooz experiment, Phys. Rev. Lett. 108, 131801 (2012).
  5. KamLAND Collaboration, First results from KamLAND: Evidence for reactor anti-neutrino disappearance, Phys. Rev. Lett. 90, 021802 (2003).
  6. SNO Collaboration, Measurement of the rate of νe+d→p+p+e− interactions produced by B8 solar neutrinos at the Sudbury Neutrino Observatory, Phys. Rev. Lett. 87, 071301 (2001).
  7. S. Weinberg, Baryon and Lepton Nonconserving Processes, Phys. Rev. Lett. 43, 1566 (1979).
  8. 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).
  9. P.-H. Gu, Weinberg dimension-5 operator by vector-like lepton doublets, arXiv:2006.08616.
  10. 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.
  11. Y. Liao, Unique neutrino mass operator at any mass dimension, Phys. Lett. B 694, 346 (2011).
  12. M. Chala and A. Titov, Neutrino masses in the Standard Model effective field theory, Phys. Rev. D 104, 035002 (2021).
  13. X. Li and S. Zhou, One-loop matching of the type-III seesaw model onto the Standard Model Effective Field Theory, J. High Energy Phys. 05 (2024) 169.
  14. Y. Du, X.-X. Li, and J.-H. Yu, Neutrino seesaw models at one-loop matching: discrimination by effective operators, J. High Energy Phys. 09 (2022) 207.
  15. E. Ma, Verifiable radiative seesaw mechanism of neutrino mass and dark matter, Phys. Rev. D 73, 077301 (2006).
  16. Tapender, L. Singh, and S. Verma, Dark matter and collider phenomenology in radiative Type-III seesaw model with two inert doublets, Phys. Dark Universe 50, 102085 (2025).
  17. Tapender, S. Verma, and S. Kumar, On lepton flavor violation and dark matter in Scotogenic model with trimaximal mixing, Eur. Phys. J. Plus 140, 43 (2025).
  18. Tapender, S. Kumar, and S. Verma, Neutrino phenomenology in a model with generalized CP symmetry within type-I seesaw framework, Phys. Rev. D 109, 015004 (2024).
  19. L. Singh, Tapender, M. Kashav, and S. Verma, Trimaximal mixing and extended magic symmetry in a model of neutrino mass matrix, Europhys. Lett. 142, 64002 (2023).
  20. M. Kashav and S. Verma, Broken scaling neutrino mass matrix and leptogenesis based on A4 modular invariance, J. High Energy Phys. 09 (2021) 100.
  21. Priya, L. Singh, B. C. Chauhan, and S. Verma, Type-III Seesaw in Non-Holomorphic Modular Symmetry and Leptogenesis, J. High Energy Phys. 01 (2026) 036.
  22. L. Singh, M. Kashav, and S. Verma, Minimal type-I Dirac seesaw and leptogenesis under A4 modular invariance, Nucl. Phys. B1007, 116666 (2024).
  23. L. Singh, D. Mahanta, and S. Verma, Low scale leptogenesis in singlet-triplet scotogenic model, J. Cosmol. Astropart. Phys. 02 (2024) 041.
  24. L. Singh, R. Srivastava, S. Verma, and S. Yadav, Type-III scotogenic model: Inflation, dark matter, and collider phenomenology, Phys. Rev. D 112, 095014 (2025).
  25. M. Kashav and S. Verma, A4 flavor model for deviation in μ−τ reflection symmetry with type-I+II seesaw extensions, Int. J. Theor. Phys. 62, 267 (2023).
  26. S. Verma, M. Kashav, and S. Bhardwaj, Highly predictive and testable A4 flavor model within type-I and II seesaw framework and associated phenomenology, Nucl. Phys. B946, 114704 (2019).
  27. J. N. Ng, Neutrino mass models in extra dimensions, J. Korean Phys. Soc. 45, S341 (2004).
  28. N. Arkani-Hamed, S. Dimopoulos, G. R. Dvali, and J. March-Russell, Neutrino masses from large extra dimensions, Phys. Rev. D 65, 024032 (2001).
  29. M. Neubert, Neutrino physics with small extra dimensions, Int. J. Mod. Phys. A 16S1B, 704 (2001).
  30. T. Asaka, Y. Heo, T. H. Tatsuishi, and T. Yoshida, Modular A4 invariance and leptogenesis, J. High Energy Phys. 01 (2020) 144.
  31. G.-J. Ding, S. F. King, J.-N. Lu, and B.-Y. Qu, Leptogenesis in SO(10) models with A4 modular symmetry, J. High Energy Phys. 10 (2022) 071.
  32. M. K. Behera and R. Mohanta, Linear seesaw in A5’ modular symmetry with leptogenesis, Front. Phys. 10, 854595 (2022).
  33. G. Pathak and M. K. Das, Matter-antimatter asymmetry in minimal inverse seesaw framework with A4 modular symmetry, J. Phys. G 53, 025004 (2026).
  34. M. Kashav and S. Verma, On minimal realization of topological Lorentz structures with one-loop seesaw extensions in A4 modular symmetry, J. Cosmol. Astropart. Phys. 03 (2023) 010.
  35. P. Mishra, M. K. Behera, P. Panda, and R. Mohanta, Type III seesaw under A4 modular symmetry with leptogenesis, Eur. Phys. J. C 82, 1115 (2022).
  36. S. Marciano, D. Meloni, and M. Parriciatu, Minimal seesaw and leptogenesis with the smallest modular finite group, J. High Energy Phys. 05 (2024) 020.
  37. M. K. Behera, S. Mishra, S. Singirala, and R. Mohanta, Implications of A4 modular symmetry on neutrino mass, mixing and leptogenesis with linear seesaw, Phys. Dark Universe 36, 101027 (2022).
  38. R. Mohanta, M. K. Behera, S. Singirala, and S. Mishra, Implications of A4 modular symmetry on neutrino mass, mixing and leptogenesis with linear seesaw, Proc. Sci. FPCP2023 (2023) 063.
  39. Abhishek and V. S. Mummidi, Resonant leptogenesis in inverse see-saw framework with modular S4 symmetry, Eur. Phys. J. C 86, 116 (2026).
  40. H. B. Nogueira, J. S. F. Neto, R. N. d. C. Filho, and J. R. d. S. Leite, Neutrino mass generation via the inverse seesaw mechanism in a U(1)B−L gauge extension, arXiv:2507.03795.
  41. S. K. Kang and C. S. Kim, Extended double seesaw model for neutrino mass spectrum and low scale leptogenesis, Phys. Lett. B 646, 248 (2007).
  42. A. E. Cárcamo Hernández, Y. H. Velásquez, S. Kovalenko, N. A. Pérez-Julve, and I. Schmidt, Models of radiative linear seesaw with electrically charged mediators, Prog. Theor. Exp. Phys. 2024, 103B02 (2024).
  43. A. G. Dias, C. A. de S. Pires, and P. S. R. da Silva, How the inverse see-saw mechanism can reveal itself natural, canonical and independent of the right-handed neutrino mass, Phys. Rev. D 84, 053011 (2011).
  44. E. Ma, Inverse seesaw neutrino mass from lepton triplets in the U(1)(sigma) model, Mod. Phys. Lett. A 24, 2491 (2009).
  45. A. Batra, P. Bharadwaj, S. Mandal, R. Srivastava, and J. W. F. Valle, Phenomenology of the simplest linear seesaw mechanism, J. High Energy Phys. 07 (2023) 221.
  46. A. Das, T. Nomura, H. Okada, and S. Roy, Generation of a radiative neutrino mass in the linear seesaw framework, charged lepton flavor violation, and dark matter, Phys. Rev. D 96, 075001 (2017).
  47. B.-Y. Qu and G.-J. Ding, Non-holomorphic modular flavor symmetry, J. High Energy Phys. 08 (2024) 136.
  48. T. Nomura and H. Okada, Type-II seesaw of a non-holomorphic modular A4 symmetry, Phys. Lett. B 868, 139763 (2025).
  49. T. Nomura, H. Okada, and O. Popov, Non-holomorphic modular A4 symmetric scotogenic model, Phys. Lett. B 860, 139171 (2025).
  50. T. Nomura and H. Okada, Zee model in a non-holomorphic modular A4 symmetry, Phys. Lett. B 867, 139618 (2025).
  51. T. Nomura, H. Okada, and X.-Y. Wang, A radiative neutrino mass model with leptoquarks under non-holomorphic modular A4 symmetry, J. High Energy Phys. 09 (2025) 163.
  52. T. Nomura and H. Okada, Neutrino mass model at a three-loop level from a non-holomorphic modular A4 symmetry, Chin. Phys. C 50, 023108 (2026).
  53. T. Nomura and H. Okada, A new type of lepton seesaw model in a modular A4 symmetry, arXiv:2503.19251.
  54. S. K. Kang and H. Okada, Neutrino masses and mixing in an axion model, Eur. Phys. J. C 85, 917 (2025).
  55. G.-J. Ding, J.-N. Lu, S. T. Petcov, and B.-Y. Qu, Non-holomorphic modular S4 lepton flavour models, J. High Energy Phys. 01 (2025) 191.
  56. C.-C. Li, J.-N. Lu, and G.-J. Ding, Non-holomorphic modular A5 symmetry for lepton masses and mixing, J. High Energy Phys. 12 (2024) 189.
  57. H. Okada and Y. Orikasa, A radiative seesaw in a non-holomorphic modular S3 flavor symmetry, arXiv:2501.15748.
  58. T. Kobayashi, H. Okada, and Y. Orikasa, Zee-Babu model in a non-holomorphic modular A4 symmetry and modular stabilization, arXiv:2502.12662.
  59. M. A. Loualidi, M. Miskaoui, and S. Nasri, Nonholomorphic A4 modular invariance for fermion masses and mixing in SU(5) GUT, Phys. Rev. D 112, 015008 (2025).
  60. X. Zhang and Y. Reyimuaji, Inverse seesaw model in non-holomorphic modular A4 flavor symmetry, Phys. Rev. D 112, 075050 (2025).
  61. T. Nomura and H. Okada, Lepton seesaw model in a modular A4 symmetry, J. Subatomic Part. Cosmol. 5, 100364 (2026).
  62. M. Abbas, Lepton masses and mixing in nonholomorphic modular A4 symmetry, Prog. High Energy Phys. 2025, 7 (2025).
  63. C.-C. Li and G.-J. Ding, Lepton models from non-holomorphic A5′ modular flavor symmetry, J. High Energy Phys. 01 (2026) 032.
  64. M. Dey, The seesaw evaded modular Dirac framework, Phys. Lett. B 875, 140374 (2026).
  65. S. K. Nanda, M. Ricky Devi, and S. Patra, Non-Holomorphic A4 modular symmetry in type-I seesaw: Implications for neutrino masses and leptogenesis, arXiv:2509.22108.
  66. B. Kumar and M. K. Das, Leptogenesis, 0νββ and lepton flavor violation in modular left-right asymmetric model with polyharmonic Maaß forms, J. High Energy Phys. 09 (2025) 071.
  67. B.-Y. Qu, J.-N. Lu, and G.-J. Ding, Non-holomorphic modular flavor symmetry and odd weight polyharmonic Maaß form, J. High Energy Phys. 11 (2025) 140.
  68. M. Fukugita and T. Yanagida, Baryogenesis without grand unification, Phys. Lett. B 174, 45 (1986).
  69. S. Davidson, E. Nardi, and Y. Nir, Leptogenesis, Phys. Rep. 466, 105 (2008).
  70. W. Buchmuller, R. D. Peccei, and T. Yanagida, Leptogenesis as the origin of matter, Annu. Rev. Nucl. Part. Sci. 55, 311 (2005).
  71. C. S. Fong, E. Nardi, and A. Riotto, Leptogenesis in the Universe, Adv. High Energy Phys. 2012, 158303 (2012).
  72. A. Pilaftsis, The little review on leptogenesis, J. Phys. Conf. Ser. 171, 012017 (2009).
  73. J. Kubo and D. Suematsu, Neutrino masses and CDM in a non-supersymmetric model, Phys. Lett. B 643, 336 (2006).
  74. N. Rojas, R. Srivastava, and J. W. F. Valle, Simplest scoto-seesaw mechanism, Phys. Lett. B 789, 132 (2019).
  75. 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).
  76. NOvA Collaboration, Improved measurement of neutrino oscillation parameters by the NOvA experiment, Phys. Rev. D 106, 032004 (2022).
  77. T2K Collaboration, Measurements of neutrino oscillation parameters from the T2K experiment using 3.6×1021 protons on target, Eur. Phys. J. C 83, 782 (2023).
  78. KamLAND-Zen Collaboration, Search for Majorana neutrinos with the complete KamLAND-Zen dataset, Phys. Rev. Lett. 135, 262501 (2025).
  79. LEGEND Collaboration, First results on the search for lepton number violating neutrinoless double beta decay with the LEGEND-200 experiment, Phys. Rev. Lett. 136, 022701 (2026).
  80. nEXO Collaboration, nEXO: Neutrinoless double beta decay search beyond 1028  year half-life sensitivity, J. Phys. G 49, 015104 (2022).
  81. 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.
  82. Particle Data Group Collaboration, Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  83. MEG Collaboration, Final results of the MEG experiment, Nuovo Cimento Soc. Ital. Fis. 39C, 325 (2017).
  84. T. Toma and A. Vicente, Lepton flavor violation in the scotogenic model, J. High Energy Phys. 01 (2014) 160.
  85. SINDRUM II Collaboration, A search for muon to electron conversion in muonic gold, Eur. Phys. J. C 47, 337 (2006).
  86. MEG II Collaboration, The design of the MEG II experiment, Eur. Phys. J. C 78, 380 (2018).
  87. A. Blondel et al., Research proposal for an experiment to search for the decay μ→eee, arXiv:1301.6113.
  88. COMET Collaboration, COMET Phase-I technical design report, Prog. Theor. Exp. Phys. 2020, 033C01 (2020).
  89. Mu2e Collaboration, Mu2e technical design report, arXiv:1501.05241.
  90. Y. Kuno, PRISM/PRIME, Nucl. Phys. B, Proc. Suppl. 149, 376 (2005).
  91. S. Davidson and A. Ibarra, A lower bound on the right-handed neutrino mass from leptogenesis, Phys. Lett. B 535, 25 (2002).
  92. E. Nardi, Y. Nir, E. Roulet, and J. Racker, The importance of flavor in leptogenesis, J. High Energy Phys. 01 (2006) 164.
  93. A. Abada, S. Davidson, F.-X. Josse-Michaux, M. Losada, and A. Riotto, Flavor issues in leptogenesis, J. Cosmol. Astropart. Phys. 04 (2006) 004.
  94. A. Abada, S. Davidson, A. Ibarra, F. X. Josse-Michaux, M. Losada, and A. Riotto, Flavour matters in leptogenesis, J. High Energy Phys. 09 (2006) 010.
  95. K. Moffat, S. Pascoli, S. T. Petcov, H. Schulz, and J. Turner, Three-flavored nonresonant leptogenesis at intermediate scales, Phys. Rev. D 98, 015036 (2018).
  96. D. M. Barreiros, H. B. Câmara, R. G. Felipe, and F. R. Joaquim, Scalar-singlet assisted leptogenesis with CP violation from the vacuum, J. High Energy Phys. 01 (2023) 010.
  97. D. Borah, D. Mahanta, and I. Saha, Gravitational wave signatures of dark sector portal leptogenesis, arXiv:2504.14671.
  98. S. Mandal, R. Srivastava, and J. W. F. Valle, The simplest scoto-seesaw model: WIMP dark matter phenomenology and Higgs vacuum stability, Phys. Lett. B 819, 136458 (2021).
  99. ATLAS Collaboration, Search for long-lived charged particles using large specific ionisation loss and time of flight in 140  fb−1 of pp collisions at s=13  TeV with the ATLAS detector, J. High Energy Phys. 07 (2025) 140.
  100. S.-Y. Guo and M.-Y. Zhao, Probing the scotogenic Dirac model with FIMP dark matter and ΔNeff, Chin. Phys. C 50, 033102 (2026).

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