- Open Access
Froggatt-Nielsen-like mechanism in the framework of modular symmetry for neutrino mass, mixing, and leptogenesis
Phys. Rev. D 113, 015015 – Published 14 January, 2026
DOI: https://doi.org/10.1103/585g-vv4y
Abstract
We study a neutrino mass model with Froggatt-Nielsen (FN) like modular symmetry. The FN mechanism requires an additional gauge symmetry, , which is spontaneously broken at high energies. But in this work, we do not need an extra symmetry as modular weights play the role of the FN charges of the additional symmetry. We have constructed a neutrino mass model using FN-like modular symmetry in the group. This model can accommodate neutrino oscillation parameters and also address other phenomena beyond the Standard Model, such as neutrinoless double beta decay and the baryon asymmetry of the Universe.
Physics Subject Headings (PhySH)
Article Text
References (65)
- F. Feruglio, Are Neutrino Masses Modular Forms? (2019), pp. 227–266.
- D. Meloni and M. Parriciatu, A simplest modular model for leptons, J. High Energy Phys. 09 (2023) 043.
- H. Okada and Y. Orikasa, Modular symmetric radiative seesaw model, Phys. Rev. D 100, 115037 (2019).
- M. Kashav and S. Verma, Broken scaling neutrino mass matrix and leptogenesis based on modular invariance, J. High Energy Phys. 09 (2021) 100.
- T. Nomura and H. Okada, A modular symmetric model of dark matter and neutrino, Phys. Lett. B 797, 134799 (2019).
- M. K. Behera, S. Singirala, S. Mishra, and R. Mohanta, A modular symmetric scotogenic model for neutrino mass and dark matter, J. Phys. G 49, 035002 (2022).
- G. Altarelli and F. Feruglio, Tri-bimaximal neutrino mixing, A(4) and the modular symmetry, Nucl. Phys. B741, 215 (2006).
- G. Pathak and M. K. Das, Matter-antimatter asymmetry in minimal inverse seesaw framework with modular symmetry, arXiv:2505.03000.
- G. Pathak, P. Das, and M. K. Das, Neutrino mass genesis in scoto-inverse seesaw with modular , Eur. Phys. J. C 85, 569 (2025).
- T. Kobayashi, Y. Shimizu, K. Takagi, M. Tanimoto, and T. H. Tatsuishi, lepton flavor model and modulus stabilization from modular symmetry, Phys. Rev. D 100, 115045 (2019); 101, 039904(E) (2020).
- J. T. Penedo and S. T. Petcov, Lepton masses and mixing from modular symmetry, Nucl. Phys. B939, 292 (2019).
- X. Zhang and S. Zhou, Inverse seesaw model with a modular S 4 symmetry: Lepton flavor mixing and warm dark matter, J. Cosmol. Astropart. Phys. 09 (2021) 043.
- X. Wang and S. Zhou, The minimal seesaw model with a modular symmetry, J. High Energy Phys. 05 (2020) 017.
- P. P. Novichkov, J. T. Penedo, S. T. Petcov, and A. V. Titov, Modular symmetry for flavour model building, J. High Energy Phys. 04 (2019) 174.
- G.-J. Ding, S. F. King, and X.-G. Liu, Neutrino mass and mixing with modular symmetry, Phys. Rev. D 100, 115005 (2019).
- X.-G. Liu and G.-J. Ding, Neutrino masses and mixing from double covering of finite modular groups, J. High Energy Phys. 08 (2019) 134.
- P. Mishra, M. K. Behera, and R. Mohanta, Neutrino phenomenology, W-mass anomaly, and muon (g-2) in a minimal type-III seesaw model using a T’ modular symmetry, Phys. Rev. D 107, 115004 (2023).
- P. P. Novichkov, J. T. Penedo, and S. T. Petcov, Double cover of modular for flavour model building, Nucl. Phys. B963, 115301 (2021).
- X.-G. Liu, C.-Y. Yao, and G.-J. Ding, Modular invariant quark and lepton models in double covering of modular group, Phys. Rev. D 103, 056013 (2021).
- X. Wang, B. Yu, and S. Zhou, Double covering of the modular group and lepton flavor mixing in the minimal seesaw model, Phys. Rev. D 103, 076005 (2021).
- C.-Y. Yao, X.-G. Liu, and G.-J. Ding, Fermion masses and mixing from the double cover and metaplectic cover of the modular group, Phys. Rev. D 103, 095013 (2021).
- M. K. Behera and R. Mohanta, Inverse seesaw in modular symmetry, J. Phys. G 49, 045001 (2022).
- C. D. Froggatt and H. B. Nielsen, Hierarchy of quark masses, Cabibbo angles and violation, Nucl. Phys. B147, 277 (1979).
- M. Ibe, S. Shirai, and K. Watanabe, Comprehensive Bayesian exploration of Froggatt-Nielsen mechanism, J. High Energy Phys. 03 (2025) 150.
- H. Kamikado, T. Shindou, and E. Takasugi, Froggatt-Nielsen hierarchy and the neutrino mass matrix, arXiv:0805.1338.
- Y.-C. Qiu, J.-W. Wang, and T. T. Yanagida, Predictions of and neutrino mass from a consistent Froggatt-Nielsen model, Phys. Rev. D 108, 115021 (2023).
- C. Cornella, D. Curtin, G. Krnjaic, and M. Mellors, Testing the Froggatt-Nielsen mechanism with lepton violation, Phys. Rev. D 112, 115010 (2025).
- V. Brdar, A. J. Helmboldt, S. Iwamoto, and K. Schmitz, Type-I seesaw as the common origin of neutrino mass, baryon asymmetry, and the electroweak scale, Phys. Rev. D 100, 075029 (2019).
- M. K. Behera, P. Ittisamai, C. Pongkitivanichkul, and P. Uttayarat, Exploring type-I seesaw under S 3 modular symmetry, EPJ Web Conf. 312, 02010 (2024).
- P. Minkowski, at a rate of one out of 109 muon decays?, Phys. Lett. 67B, 421 (1977).
- J. Schechter and J. W. Valle, Neutrino masses in theories, Phys. Rev. D 22, 2227 (1980).
- R. N. Mohapatra and G. Senjanović, Neutrino mass and spontaneous parity nonconservation, Phys. Rev. Lett. 44, 912 (1980).
- S. J. D. King and S. F. King, Fermion mass hierarchies from modular symmetry, J. High Energy Phys. 09 (2020) 043.
- H. Kuranaga, H. Ohki, and S. Uemura, Modular origin of mass hierarchy: Froggatt-Nielsen like mechanism, J. High Energy Phys. 07 (2021) 068.
- B. J. P. Jones, The physics of neutrinoless double beta decay: A primer, in Theoretical Advanced Study Institute in Elementary Particle Physics: The Obscure Universe: Neutrinos and Other Dark Matters (2021), arXiv:2108.09364.
- M. J. Dolinski, A. W. P. Poon, and W. Rodejohann, Neutrinoless double-beta decay: Status and prospects, Annu. Rev. Nucl. Part. Sci. 69, 219 (2019).
- S. M. Bilenky and C. Giunti, Neutrinoless double-beta decay: A brief review, Mod. Phys. Lett. A 27, 1230015 (2012).
- J. J. Gomez-Cadenas, J. Martin-Albo, M. Sorel, P. Ferrario, F. Monrabal, J. Munoz-Vidal, P. Novella, and A. Poves, Sense and sensitivity of double beta decay experiments, J. Cosmol. Astropart. Phys. 06 (2011) 007.
- A. D. Sakharov, Violation of invariance, C asymmetry, and baryon asymmetry of the universe, Pis’ma Zh. Eksp. Teor. Fiz. 5, 32 (1967).
- G.-J. Ding, F. R. Joaquim, and J.-N. Lu, Texture-zero patterns of lepton mass matrices from modular symmetry, J. High Energy Phys. 03 (2023) 141.
- K. Hochmuth, S. Petcov, and W. Rodejohann, , Phys. Lett. B 654, 177 (2007).
- 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.
- S. Antusch and V. Maurer, Running quark and lepton parameters at various scales, J. High Energy Phys. 11 (2013) 115.
- N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
- S. Abe et al. (KamLAND-Zen Collaboration), Search for the Majorana nature of neutrinos in the inverted mass ordering region with KamLAND-Zen, Phys. Rev. Lett. 130, 051801 (2023).
- J. B. Albert et al. (nEXO Collaboration), Sensitivity and discovery potential of nEXO to neutrinoless double beta decay, Phys. Rev. C 97, 065503 (2018).
- S. Marciano, D. Meloni, and M. Parriciatu, Minimal seesaw and leptogenesis with the smallest modular finite group, J. High Energy Phys. 05 (2024) 020.
- S. Davidson, E. Nardi, and Y. Nir, Leptogenesis, Phys. Rep. 466, 105 (2008).
- W. Buchmuller, P. Di Bari, and M. Plumacher, Leptogenesis for pedestrians, Ann. Phys. (Amsterdam) 315, 305 (2005).
- W. Buchmuller, R. D. Peccei, and T. Yanagida, Leptogenesis as the origin of matter, Annu. Rev. Nucl. Part. Sci. 55, 311 (2005).
- A. Pilaftsis, violation and baryogenesis due to heavy Majorana neutrinos, Phys. Rev. D 56, 5431 (1997).
- 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).
- M. Plumacher, Baryogenesis and lepton number violation, Z. Phys. C 74, 549 (1997).
- R. Barbieri, P. Creminelli, A. Strumia, and N. Tetradis, Baryogenesis through leptogenesis, Nucl. Phys. B575, 61 (2000).
- P. Fileviez Perez, C. Murgui, and A. D. Plascencia, Baryogenesis via leptogenesis: Spontaneous B and L violation, Phys. Rev. D 104, 055007 (2021).
- A. Granelli, K. Moffat, Y. F. Perez-Gonzalez, H. Schulz, and J. Turner, ulysses: Universal leptogenesis equation solver, Comput. Phys. Commun. 262, 107813 (2021).
- A. Granelli, C. Leslie, Y. F. Perez-Gonzalez, H. Schulz, B. Shuve, J. Turner, and R. Walker, ulysses, universal LeptogeneSiS equation solver: Version 2, Comput. Phys. Commun. 291, 108834 (2023).
- T. Asaka and T. Yoshida, Resonant leptogenesis at TeV-scale and neutrinoless double beta decay, J. High Energy Phys. 09 (2019) 089.
- S. Iso, N. Okada, and Y. Orikasa, Resonant leptogenesis in the minimal B-L extended standard model at TeV, Phys. Rev. D 83, 093011 (2011).
- A. Granelli, K. Moffat, and S. T. Petcov, Flavoured resonant leptogenesis at sub-TeV scales, Nucl. Phys. B973, 115597 (2021).
- P. Das, M. K. Das, and N. Khan, Phenomenological study of neutrino mass, dark matter and baryogenesis within the framework of minimal extended seesaw, J. High Energy Phys. 03 (2020) 018.
- I. Chakraborty and H. Roy, Type-I thermal leptogenesis in -symmetric three Higgs doublet model, Eur. Phys. J. C 80, 1038 (2020).
- W. Buchmuller, P. Di Bari, and M. Plumacher, Some aspects of thermal leptogenesis, New J. Phys. 6, 105 (2004).
- S. Blanchet, P. Di Bari, D. A. Jones, and L. Marzola, Leptogenesis with heavy neutrino flavours: From density matrix to Boltzmann equations, J. Cosmol. Astropart. Phys. 01 (2013) 041.
- W. Elbers et al. (DESI Collaboration), Constraints on neutrino physics from DESI DR2 BAO and DR1 full shape, Phys. Rev. D 112, 083513 (2025).