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

Rolling down the leptonic BSM landscape using machine learning techniques

Alfredo Aranda1,2,3,*, Raymundo Ramos4,†, and Alexander J. Stuart1,2,‡

  • *Contact author: fefo@ucol.mx
  • †Contact author: raramos@kias.re.kr
  • ‡Contact author: astuart@ucol.mx

Phys. Rev. D 114, 075037 – Published 28 October, 2026

DOI: https://doi.org/10.1103/g5l2-bzs4

Abstract

In this work, we adapt and apply techniques from machine learning to the exploration of physics beyond the Standard Model in the leptonic sector. Namely, we employ initialization and optimization, as they are applied in machine learning, to minimize a loss function that describes textures or conditions which we want in the neutrino mass matrix. The model free parameters are explored during the optimization, and after training for a number of optimization steps, we obtain matrices that approximately follow the desired forms, as well as their corresponding optimized parameters. We also discuss extensions and additional applications of the ideas presented here in conjunction with other methods based on artificial intelligence.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (54)

  1. Particle Data Group, Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  2. A. K. Mann and H. Primakoff, Neutrino oscillations and the number of neutrino types, Phys. Rev. D 15, 655 (1977).
  3. L. Wolfenstein, Oscillations among three neutrino types and CP violation, Phys. Rev. D 18, 958 (1978).
  4. P. F. Harrison, D. H. Perkins, and W. G. Scott, Tri-bimaximal mixing and the neutrino oscillation data, Phys. Lett. B 530, 167 (2002).
  5. P. F. Harrison and W. G. Scott, Symmetries and generalizations of tri—bimaximal neutrino mixing, Phys. Lett. B 535, 163 (2002).
  6. Z.-z. Xing, Nearly tri bimaximal neutrino mixing and CP violation, Phys. Lett. B 533, 85 (2002).
  7. X. G. He and A. Zee, Some simple mixing and mass matrices for neutrinos, Phys. Lett. B 560, 87 (2003).
  8. Z.-z. Xing, H. Zhang, and S. Zhou, Nearly tri-bimaximal neutrino mixing and CP violation from mu-tau symmetry breaking, Phys. Lett. B 641, 189 (2006).
  9. Daya Bay Collaboration, Observation of electron-antineutrino disappearance at Daya Bay, Phys. Rev. Lett. 108, 171803 (2012).
  10. RENO Collaboration, Observation of reactor electron antineutrino disappearance in the RENO experiment, Phys. Rev. Lett. 108, 191802 (2012).
  11. Double Chooz Collaboration, Improved measurements of the neutrino mixing angle θ13 with the Double Chooz detector, J. High Energy Phys. 10 (2014) 086.
  12. K. T. Matchev, K. Matcheva, P. Ramond, and S. Verner, Seeking truth and beauty in flavor physics with machine learning, in 37th Conference on Neural Information Processing Systems (Neural Information Processing Systems Foundation, Inc. (NeurIPS), 2023).
  13. K. T. Matchev, K. Matcheva, P. Ramond, and S. Verner, Exploring the truth and beauty of theory landscapes with machine learning, Phys. Lett. B 856, 138941 (2024).
  14. S. Nishimura, C. Miyao, and H. Otsuka, Exploring the flavor structure of quarks and leptons with reinforcement learning, J. High Energy Phys. 12 (2020) 021.
  15. S. Nishimura, C. Miyao, and H. Otsuka, Reinforcement learning-based statistical search strategy for an axion model from flavor, J. High Energy Phys. 10 (2025) 043.
  16. S. Nishimura, H. Otsuka, and H. Uchiyama, Exploring the flavor structure of leptons via diffusion models, Phys. Rev. D 113, 055030 (2026).
  17. S. Nishimura, H. Otsuka, and H. Uchiyama, Diffusion-model approach to flavor models: A case study for S4′ modular flavor model, Prog. Theor. Exp. Phys. 2026, 053B08 (2026).
  18. A. Giarnetti and D. Meloni, Reinforcement learning techniques for the flavor problem in particle physics, Symmetry 18, 131 (2026).
  19. Particle Data Group, Review of particle physics, Phys. Rev. D 98, 030001 (2018).
  20. C. Jarlskog, Commutator of the quark mass matrices in the standard electroweak model and a measure of maximal CP nonconservation, Phys. Rev. Lett. 55, 1039 (1985).
  21. D.-d. Wu, The pephasing invariants and CP, Phys. Rev. D 33, 860 (1986).
  22. KATRIN Collaboration, Direct neutrino-mass measurement based on 259 days of KATRIN data, Science 388, adq9592 (2025).
  23. 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.
  24. NuFIT Collaboration, nufit v6.1, http://www.nu-fit.org/ (2025).
  25. T. Fukuyama and H. Nishiura, Mass matrix of Majorana neutrinos, arXiv:hep-ph/9702253.
  26. E. Ma and M. Raidal, Neutrino mass, muon anomalous magnetic moment, and lepton flavor nonconservation, Phys. Rev. Lett. 87, 011802 (2001).
  27. K. R. S. Balaji, W. Grimus, and T. Schwetz, The solar LMA neutrino oscillation solution in the Zee model, Phys. Lett. B 508, 301 (2001).
  28. C. S. Lam, A 2-3 symmetry in neutrino oscillations, Phys. Lett. B 507, 214 (2001).
  29. P. F. Harrison and W. G. Scott, μ−τ reflection symmetry in lepton mixing and neutrino oscillations, Phys. Lett. B 547, 219 (2002).
  30. Z.-z. Xing and Z.-h. Zhao, A review of μ−τ flavor symmetry in neutrino physics, Rep. Prog. Phys. 79, 076201 (2016).
  31. D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, arXiv:1412.6980.
  32. H. Fritzsch, Z.-z. Xing, and S. Zhou, Two-zero textures of the Majorana neutrino mass matrix and current experimental tests, J. High Energy Phys. 09 (2011) 083.
  33. D. Meloni, A. Meroni, and E. Peinado, Two-zero Majorana textures in the light of the Planck results, Phys. Rev. D 89, 053009 (2014).
  34. T. P. Nguyen, Texture zeros of neutrino mass matrix with seesaw mechanism and leptogenesis, Mod. Phys. Lett. A 29, 1450038 (2014).
  35. R. H. Benavides, D. V. Forero, L. Muñoz, J. M. Muñoz, A. Rico, and A. Tapia, Five texture zeros in the lepton sector and neutrino oscillations at DUNE, Phys. Rev. D 107, 036008 (2023).
  36. 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.
  37. M. R. Devi, Retrieving texture zeros in 3+1 active-sterile neutrino framework under the action of A4 modular-invariants, arXiv:2303.04900.
  38. A. Rico, R. H. Benavides, D. V. Forero, L. Muñoz, and A. Tapia, Five texture zeros in the lepton sector that reproduce the observable neutrino masses and mixings: A mapping between the standard parameterization and our parameterization, Proc. Sci. ICRC2023 (2023) 1047.
  39. Z.-h. Zhao, Combinations of the μ−τ reflection symmetry and texture zeros in the Dirac neutrino mass matrix of the seesaw model, Eur. Phys. J. Plus 138, 1055 (2023).
  40. S. Kumar and R. R. Gautam, Neutrino mass matrices with generalized CP symmetries and texture zeros, Nucl. Phys. B1001, 116520 (2024).
  41. S. Zhou, Texture zeros for lepton flavor mixing, Int. J. Mod. Phys. A 39, 2441014 (2024).
  42. T. Nomura, H. Okada, and H. Otsuka, Texture zeros realization in a three-loop radiative neutrino mass model from modular A4 symmetry, Nucl. Phys. B1004, 116579 (2024).
  43. A. Carrillo-Monteverde, S. Gómez-Ávila, and L. López-Lozano, 2-zeros texture and the universal texture constraint in the leptonic sector, Int. J. Mod. Phys. A 39, 2450052 (2024).
  44. L. Singh, M. Kashav, and S. Verma, Implications of dark-θ12 solution on two-zero texture inverse neutrino mass matrix, Springer Proc. Phys. 304, 675 (2024).
  45. I. A. Mazumder and R. Dutta, Bottom-up approach to texture zeros in the neutrino mass matrix, Int. J. Mod. Phys. A 41, 2650010 (2026).
  46. T. Kobayashi, H. Otsuka, and M. Tanimoto, Yukawa textures from non-invertible symmetries, J. High Energy Phys. 12 (2024) 117.
  47. T. Kobayashi, Y. Nishioka, H. Otsuka, and M. Tanimoto, More about quark Yukawa textures from selection rules without group actions, J. High Energy Phys. 05 (2025) 177.
  48. T. Kobayashi, H. Otsuka, M. Tanimoto, and H. Uchida, Lepton mass textures from non-invertible multiplication rules, J. High Energy Phys. 08 (2025) 189.
  49. L. Calibbi, X. Gao, and M. Yuan, Hunting for neutrino texture zeros with muon and tau flavor violation, J. High Energy Phys. 05 (2026) 188.
  50. A. Biswas, S. Jangid, and S. C. Park, Investigating two-zero texture in the light of gauged type-II seesaw, Phys. Lett. B 868, 139786 (2025).
  51. J. Gogoi and M. K. Das, A study of texture zeros using A4 discrete symmetry group, J. Subatomic Part. Cosmol. 3, 100071 (2025).
  52. Z. Jiang, B.-Y. Qu, and G.-J. Ding, Texture-zeros in minimal seesaw from noninvertible symmetry fusion rules, Phys. Rev. D 112, 115029 (2025).
  53. D. Borah, P. Das, and D. Dutta, Neutrino texture-zeros after JUNO’s first results: Implications for long-baseline neutrino experiments, arXiv:2512.13587.
  54. Priya, R. Kumar, L. Singh, and S. Verma, Implications of the first JUNO results for Dirac neutrino texture zeros, arXiv:2604.19122.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation