- 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

Neutrino mass and leptogenesis in the non-SUSY modular A5′ inverse seesaw model

Xianshuo Zhang* and Yakefu Reyimuaji†

  • *Contact author: zxianshuo@yeah.net
  • †Contact author: yreyi@hotmail.com
PDF

Phys. Rev. D 114, 015021 – Published 17 July, 2026

DOI: https://doi.org/10.1103/q63q-456k

Abstract

A nonsupersymmetric inverse seesaw model of neutrino mass based on the A5′ modular symmetry is presented. This framework provides a combined explanation for neutrino masses, mixing, and the cosmic baryon asymmetry through leptogenesis. Three concrete realizations are constructed, and their phenomenological predictions are analyzed. The results are not only compatible with the measured neutrino oscillation parameters within the current experimental 3σ ranges, but also provide predictions for the neutrino mass ordering, Dirac and Majorana CP-violating phases, and the effective Majorana mass in neutrinoless double beta decay. The model further realizes TeV-scale leptogenesis consistent with the observed baryon asymmetry, rendering the scenario testable in both low-energy neutrino experiments and high-energy collider searches.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (81)

  1. G. Aad et al. (ATLAS Collaboration), Observation of a new particle in the search for the standard model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716, 1 (2012).
  2. S. Chatrchyan et al. (CMS Collaboration), Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716, 30 (2012).
  3. T. Kajita, Nobel lecture: Discovery of atmospheric neutrino oscillations, Rev. Mod. Phys. 88, 030501 (2016).
  4. A. B. McDonald, Nobel Lecture: The Sudbury Neutrino Observatory: Observation of flavor change for solar neutrinos, Rev. Mod. Phys. 88, 030502 (2016).
  5. R. N. Mohapatra, Mechanism for understanding small neutrino mass in superstring theories, Phys. Rev. Lett. 56, 561 (1986).
  6. R. N. Mohapatra and J. W. F. Valle, Neutrino mass and baryon number nonconservation in superstring models, Phys. Rev. D 34, 1642 (1986).
  7. F. Deppisch and J. W. F. Valle, Enhanced lepton flavor violation in the supersymmetric inverse seesaw model, Phys. Rev. D 72, 036001 (2005).
  8. P. S. B. Dev and R. N. Mohapatra, TeV scale inverse Seesaw in SO(10) and leptonic non-unitarity effects, Phys. Rev. D 81, 013001 (2010).
  9. S. Centelles Chuliá, R. Srivastava, and A. Vicente, The inverse seesaw family: Dirac and Majorana, J. High Energy Phys. 03 (2021) 248.
  10. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  11. S. Navas et al. (Particle Data Group Collaboration), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  12. A. D. Sakharov, Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe, Pis’ma Zh. Eksp. Teor. Fiz. 5, 32 (1967).
  13. M. Fukugita and T. Yanagida, Baryogenesis without grand unification, Phys. Lett. B 174, 45 (1986).
  14. A. Pilaftsis, CP violation and baryogenesis due to heavy Majorana neutrinos, Phys. Rev. D 56, 5431 (1997).
  15. A. Pilaftsis and T. E. J. Underwood, Resonant leptogenesis, Nucl. Phys. B692, 303 (2004).
  16. F. Feruglio, Are neutrino masses modular forms?, in From My Vast Repertoire … (World Scientific, Singapore, 2019), pp. 227–266.
  17. F. Feruglio and A. Romanino, Lepton flavor symmetries, Rev. Mod. Phys. 93, 015007 (2021).
  18. G.-J. Ding and S. F. King, Neutrino mass and mixing with modular symmetry, Rep. Prog. Phys. 87, 084201 (2024).
  19. B.-Y. Qu and G.-J. Ding, Non-holomorphic modular flavor symmetry, J. High Energy Phys. 08 (2024) 136.
  20. 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.
  21. B. Kumar and M. K. Das, Study of neutrino phenomenology and 0νββ decay using polyharmonic Maass forms, Int. J. Mod. Phys. A 40, 2550090 (2025).
  22. T. Nomura and H. Okada, Type-II seesaw of a non-holomorphic modular A4 symmetry, Phys. Lett. B 868, 139763 (2025).
  23. T. Nomura and H. Okada, Zee model in a non-holomorphic modular A4 symmetry, Phys. Lett. B 867, 139618 (2025).
  24. T. Kobayashi, H. Okada, and Y. Orikasa, Zee-Babu model in a non-holomorphic modular A4 symmetry and modular stabilization, Prog. Theor. Exp. Phys. 2026, 033B07 (2026).
  25. 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).
  26. 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.
  27. 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.
  28. 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).
  29. X. Zhang and Y. Reyimuaji, Inverse seesaw model in nonholomorphic modular A4 flavor symmetry, Phys. Rev. D 112, 075050 (2025).
  30. 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.
  31. B. Kumar and M. K. Das, Neutrino phenomenology and dark matter in a left-right asymmetric model with non-holomorphic modular A4 group, Phys. Lett. B 872, 140064 (2026).
  32. S. K. Nanda, M. R. Devi, and S. Patra, Non-holomorphic A4 modular symmetry in type-I Seesaw: Implications for neutrino masses and leptogenesis, arXiv:2509.22108.
  33. S. Jangid and H. Okada, A radiative seesaw model in a non-invertible selection rule with the assistance of a non-holomorphic modular A4 symmetry, Prog. Theor. Exp. Phys. 2026, 053B05 (2026).
  34. X.-Y. Gao and C.-C. Li, Minimal lepton models with non-holomorphic modular A4 symmetry, Chin. Phys. C 50, 053109 (2026).
  35. H. Okada and Y. Orikasa, A radiative Seesaw in a non-holomorphic modular S3 flavor symmetry arXiv:2501.15748.
  36. 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.
  37. 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.
  38. C.-C. Li and G.-J. Ding, Lepton models from non-holomorphic A5′ modular flavor symmetry, J. High Energy Phys. 01 (2026) 032.
  39. S. Nasri, L. Singh, Tapender, and S. Verma, Dark-portal leptogenesis in a non-holomorphic modular scoto-Seesaw model, Phys. Rev. D 113, 115008 (2026).
  40. A. Herrero-Brocal and A. Vicente, The Majoron coupling to charged leptons, J. High Energy Phys. 01 (2024) 078.
  41. A. Vicente, Neutrino mass models: A short review with emphasis on the Majoron, in NuPhys2026: Prospect in Neutrino Physics (2026), arXiv:2604.15995.
  42. R. Bayes et al. (TWIST Collaboration), Search for two body muon decay signals, Phys. Rev. D 91, 052020 (2015).
  43. R. Abramishvili et al. (COMET Collaboration), COMET phase-I technical design report, Prog. Theor. Exp. Phys. 2020, 033C01 (2020).
  44. T. Xing, C. Wu, H. Miao, H. Li, W. Li, Y. Yuan, and Y. Zhang, Search for Majoron at the COMET Experiment*, Chin. Phys. C 47, 013108 (2023).
  45. I. M. Ávila et al., Dark matter as the source of neutrino mass: Theory overview and experimental prospects, Phys. Rep. 1173, 1 (2026).
  46. Z. Wang, Y. Reyimuaji, and N. Yalikun, Z4 symmetric inverse Seesaw model for neutrino masses and FIMP dark matter, Phys. Rev. D 112, 055041 (2025).
  47. P. P. Novichkov, J. T. Penedo, S. T. Petcov, and A. V. Titov, Generalised CP symmetry in modular-invariant models of flavour, J. High Energy Phys. 07 (2019) 165.
  48. P. P. Novichkov, J. T. Penedo, S. T. Petcov, and A. V. Titov, Modular S4 models of lepton masses and mixing, J. High Energy Phys. 04 (2019) 005.
  49. I. Esteban, M. C. 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.
  50. 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.
  51. Z.-z. Xing, H. Zhang, and S. Zhou, Updated values of running quark and lepton masses, Phys. Rev. D 77, 113016 (2008).
  52. A. Baur, FlavorPy (2024), URL https://doi.org/10.5281/zenodo.11060597.
  53. M. Aker et al. (Katrin Collaboration), Direct neutrino-mass measurement based on 259 days of KATRIN data, Science 388, adq9592 (2025).
  54. S. Abe et al. (KamLAND-Zen Collaboration), Search for Majorana neutrinos with the complete KamLAND-Zen dataset, Phys. Rev. Lett. 135, 262501 (2025).
  55. S. Vagnozzi, E. Giusarma, O. Mena, K. Freese, M. Gerbino, S. Ho, and M. Lattanzi, Unveiling ν secrets with cosmological data: Neutrino masses and mass hierarchy, Phys. Rev. D 96, 123503 (2017).
  56. A. G. Adame et al. (DESI Collaboration), DESI 2024 VI: Cosmological constraints from the measurements of baryon acoustic oscillations, J. Cosmol. Astropart. Phys. 02 (2025) 021.
  57. D. Chebat et al., Cosmological neutrino mass: A frequentist overview in light of DESI, J. Cosmol. Astropart. Phys. 01 (2026) 041.
  58. N. Abgrall et al. (LEGEND Collaboration), The Large Enriched Germanium experiment for neutrinoless ββ decay: LEGEND-1000 preconceptual design report, arXiv:2107.11462.
  59. G. Adhikari et al. (nEXO Collaboration), nEXO: Neutrinoless double beta decay search beyond 1028  year half-life sensitivity, J. Phys. G 49, 015104 (2022).
  60. P. Stöcker et al. (GAMBIT Cosmology Workgroup Collaboration), Strengthening the bound on the mass of the lightest neutrino with terrestrial and cosmological experiments, Phys. Rev. D 103, 123508 (2021).
  61. C. S. Lorenz, L. Funcke, E. Calabrese, and S. Hannestad, Time-varying neutrino mass from a supercooled phase transition: Current cosmological constraints and impact on the Ωm−σ8 plane, Phys. Rev. D 99, 023501 (2019).
  62. S. Antusch and O. Fischer, Non-unitarity of the leptonic mixing matrix: Present bounds and future sensitivities, J. High Energy Phys. 10 (2014) 094.
  63. M. Blennow, P. Coloma, E. Fernandez-Martinez, J. Hernandez-Garcia, and J. Lopez-Pavon, Non-unitarity, sterile neutrinos, and non-standard neutrino interactions, J. High Energy Phys. 04 (2017) 153.
  64. E. Fernandez-Martinez, J. Hernandez-Garcia, and J. Lopez-Pavon, Global constraints on heavy neutrino mixing, J. High Energy Phys. 08 (2016) 033.
  65. D. Aristizabal Sierra, M. Losada, and E. Nardi, Lepton flavor equilibration and leptogenesis, J. Cosmol. Astropart. Phys. 12 (2009) 015.
  66. S. Blanchet, P. S. B. Dev, and R. N. Mohapatra, Leptogenesis with TeV scale inverse Seesaw in SO(10), Phys. Rev. D 82, 115025 (2010).
  67. L. Covi, E. Roulet, and F. Vissani, CP violating decays in leptogenesis scenarios, Phys. Lett. B 384, 169 (1996).
  68. W. Buchmuller and M. Plumacher, CP asymmetry in Majorana neutrino decays, Phys. Lett. B 431, 354 (1998).
  69. S. Blanchet, T. Hambye, and F.-X. Josse-Michaux, Reconciling leptogenesis with observable μ→eγ rates, J. High Energy Phys. 04 (2010) 023.
  70. I. Chakraborty, H. Roy, and T. Srivastava, Resonant leptogenesis in (2, 2) inverse See-saw realisation, Nucl. Phys. B979, 115780 (2022).
  71. Y. Shao and Z.-h. Zhao, Linear seesaw leptogenesis before and after electroweak symmetry breaking, Phys. Rev. D 112, 115033 (2025).
  72. W. Buchmuller, P. Di Bari, and M. Plumacher, Leptogenesis for pedestrians, Ann. Phys. (Amsterdam) 315, 305 (2005).
  73. K. Agashe, P. Du, M. Ekhterachian, C S. Fong, S. Hong, and L. Vecchi, Natural Seesaw and leptogenesis from hybrid of high-scale type I and TeV-scale inverse, J. High Energy Phys. 04 (2019) 029.
  74. B. Abi et al. (DUNE Collaboration), Deep Underground Neutrino Experiment (DUNE), Far detector technical design report, Volume II: DUNE physics, arXiv:2002.03005.
  75. K. Abe et al. (Hyper-Kamiokande Collaboration), Hyper-Kamiokande design report, arXiv:1805.04163.
  76. F. An et al. (JUNO Collaboration), Neutrino physics with JUNO, J. Phys. G 43, 030401 (2016).
  77. M. Aker et al. (KATRIN Collaboration), KATRIN: Status and prospects for the neutrino mass and beyond, J. Phys. G 49, 100501 (2022).
  78. A. A. Esfahani et al. (Project 8 Collaboration), The project 8 neutrino mass experiment, in Snowmass 2021 (2022), arXiv:2203.07349.
  79. F. Feruglio, Universal predictions of modular invariant flavor models near the self-dual point, Phys. Rev. Lett. 130, 101801 (2023).
  80. A. Granelli, D. Meloni, M. Parriciatu, J. T. Penedo, and S. T. Petcov, Modular-symmetry-protected seesaw, J. High Energy Phys. 12 (2025) 035.
  81. C.-Y. Yao, X.-G. Liu, and G.-J. Ding, Fermion masses and mixing from the double cover and metaplectic cover of the A5 modular group, Phys. Rev. D 103, 095013 (2021).

Outline

Information

Phys. Rev. D 114, 015021– Published 17 July, 2026
  • Received 25 March 2026
  • Accepted 24 June 2026
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