The origin of the minuscule masses of the known neutrino flavors is an important open question in particle physics. The neutrino-family flavor mass sum is bound by several data-based analyses to less than about 0.12 eV/ c 2 . This sum is roughly 10 orders of magnitude smaller than the sum of the masses of the flavors of other fundamental fermion families. There are no explanations for the small value of this mass sum that are supported by observations. This paper provides an estimate of this sum using properties of the electroweak sector and the minimal Higgs sector with a derived permutational symmetry. The specific masses of the three generations of neutrino flavors can then be fit based on observations, but not fully determined, using properties of the homogeneous Higgs ghost Lagrangian.
KeywordsNeutrino MassesHiggs SectorQuantum Field TheoryElectroweak Sector
Peskin, M. and Schroeder, D. (1995) An Introduction to Quantum Field Theory. https://doi.org/10.1201/9780429503559
Giunti, C. and Kim, C.W. (2007) Fundamentals of Neutrino Physics and Astrophysics. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780198508717.001.0001
Dolinski, M.J., Poon, A.W.P. and Rodejohann, W. (2019) Neutrinoless Double-Beta Decay: Status and Prospects. Annual Review of Nuclear and Particle Science , 69, 219-251. https://doi.org/10.1146/annurev-nucl-101918-023407
Bahcall, J.N. and Davis, R. (1976) Solar Neutrinos: A Scientific Puzzle. Science , 191, 264-267. https://doi.org/10.1126/science.191.4224.264
Fukuda, Y., Hayakawa, T., Ichihara, E., Inoue, K., Ishihara, K., Ishino, H., et al. (1998) Evidence for Oscillation of Atmospheric Neutrinos. Physical Review Letters , 81, 1562-1567. https://doi.org/10.1103/physrevlett.81.1562
Ahmad, Q.R., Allen, R.C., Andersen, T.C., Anglin, J.D., Barton, J.C., Beier, E.W., et al. (2002) Direct Evidence for Neutrino Flavor Transformation from Neutral-Current Interactions in the Sudbury Neutrino Observatory. Physical Review Letters , 89, Article ID: 011301.
Kajita, T. (2016) Nobel Lecture: Discovery of Atmospheric Neutrino Oscillations. Reviews of Modern Physics , 88, Article ID: 030501. https://doi.org/10.1103/revmodphys.88.030501
McDonald, A.B. (2016) Nobel Lecture: The Sudbury Neutrino Observatory: Observation of Flavor Change for Solar Neutrinos. Reviews of Modern Physics , 88, Article ID: 030502. https://doi.org/10.1103/revmodphys.88.030502
Navas, S., Amsler, C., Gutsche, T., Hanhart, C., Hernández-Reye, J. J., Lourenco, C., et al. (2024) Sum of Neutrino Masses. https://pdg.lbl.gov/2024/reviews/rpp2024-rev-sum-neutrino-masses.pdf
Navas, S., Amsler, C., Gutsche, T., Hanhart, C., Hernández-Reye, J. J., Lourenco, C., et al. (2024) Neutrinos in Cosmology. https://pdg.lbl.gov/2024/reviews/rpp2024-rev-neutrinos-in-cosmology.pdf
Abbott, T.M.C., Aguena, M., Alarcon, A., Allam, S., Alves, O., Amon, A., et al. (2022) Dark Energy Survey Year 3 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing. arXiv: 2105.13549.
Navas, S., Amsler, C., Gutsche, T., Hanhart, C., Hernández-Reye, J. J., Lourenco, C., et al. (2024) Particle Properties. https://pdg.lbl.gov/2024/listings/particle_properties.html
Hernandez-Galeana, A. (2011) Predictions for Fermion Masses and Mixing from a Low Energy SU(3) Flavor Symmetry Model with a Light Sterile Neutrino. arXiv: 1111.7286. https://doi.org/10.48550/arXiv.1111.7286
Qiu, Y., Wang, J. and Yanagida, T.T. (2023) Predictions of mee and Neutrino Mass from a Consistent Froggatt-Nielsen Model. Physical Review D , 108, Article ID:115021. https://doi.org/10.1103/physrevd.108.115021
Minkowski, P. (1977) μ → e γ at a Rate of One Out of 10 9 Muon Decays? Physics Letters B , 67, 421-428. https://doi.org/10.1016/0370-2693(77)90435-x
Ma, E. and Popov, O. (2017) Pathways to Naturally Small Dirac Neutrino Masses. Physics Letters B , 764, 142-144. https://doi.org/10.1016/j.physletb.2016.11.027
Wang, W. and Han, Z. (2017) Naturally Small Dirac Neutrino Mass with Intermediate SU(2) L Multiplet Fields. Journal of High Energy Physics , 2017, Article No. 166. https://doi.org/10.1007/jhep04(2017)166
Mohapatra, R.N. (1988) Left-Right Symmetry and Finite One-Loop Dirac Neutrino Mass. Physics Letters B , 201, 517-524. https://doi.org/10.1016/0370-2693(88)90610-7
Yao, C. and Ding, G. (2017) Systematic Study of One-Loop Dirac Neutrino Masses and Viable Dark Matter Candidates. Physical Review D , 96, Article ID: 095004. https://doi.org/10.1103/physrevd.96.095004
Taylor, J.C. (1976) Gauge Theories of Weak Interactions, Cambridge University Press.
Holmes, R.B. (2025) Analysis and Reinterpretation of the Minimal Higgs Sector. Journal of Modern Physics , 16, 815-842. https://doi.org/10.4236/jmp.2025.166043
Holmes, R.B. (2025) Derivation and Fits of Fermion Masses from the Higgs Sector. Journal of Modern Physics , 16, 613-626. https://doi.org/10.4236/jmp.2025.164033
Holmes, R. (2021) A Quantum Field Theory with Permutational Symmetry. 2nd Edition, Lambert Academic Press. https://doi.org/10.5281/zenodo.5047237
Leighton, R.B. (1959) Principles of Modern Physics. McGraw Hill.
Halzen, F. and Martin, A. D. (1984) Quarks and Leptons: An Introductory Course in Modern Particle Physics. John Wiley & Sons.
Griffiths, D. (2008) Introduction to Elementary Particles. Wiley-VCH. https://doi.org/10.1002/9783527618460
Navas, S., Amsler, C., Gutsche, T., Hanhart, C., Hernández-Reye, J.J., Lourenco, C., et al. (2024) Mass and Width of the W Boson. https://pdg.lbl.gov/2025/reviews/rpp2024-rev-w-mass.pdf
Navas, S., Amsler, C., Gutsche, T., Hanhart, C., Hernández-Reye, J.J., Lourenco, C., et al. (2024) Electroweak Model and Constraints on New Physics. https://pdg.lbl.gov/2025/reviews/rpp2024-rev-standard-model.pdf
Aker, M., Beglarian, A., Behrens, J., Berlev, A., Besserer, U., Bieringer, B., et al. (2022) Direct Neutrino-Mass Measurement with Sub-Electronvolt Sensitivity. Nature Physics , 18, 160-166. https://doi.org/10.1038/s41567-021-01463-1
Elbers, W., Aviles, A., Noriega, H.E., Chebat, D., Menegas, A., Frenk, C.S., et al. (2025) Constraints on Neutrino Physics from DESI DR2 BAO and DR1 Full Shape. Physical Review D , 112, Article ID: 083513. https://doi.org/10.1103/w9pk-xsk7
Pompa, F., Capozzi, F., Mena, O. and Sorel, M. (2022) Absolute ν Mass Measurement with the DUNE Experiment. Physical Review Letters , 129, Article ID: 121802. https://doi.org/10.1103/physrevlett.129.121802
Holmes, R.B. (2020) Galactic Haloes from Self-Interacting Neutrinos. Journal of Modern Physics , 11, 854-885. https://doi.org/10.4236/jmp.2020.116053
Holmes, R.B. (2024) Method for Fitting and Deriving the CKM and PMNS Matrices from Underlying Wavefunctions. Journal of Modern Physics , 15, 2407-2421. https://doi.org/10.4236/jmp.2024.1513099
Thomson, M. (2013) Modern Particle Physics. Cambridge University Press. https://doi.org/10.1017/cbo9781139525367