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Nonmaximal symmetry breaking patterns in the supersymmetric su^(8)kU=1 theory

Ning Chen*, Jianan Tian†, and Bin Wang‡

  • *Contact author: chenning_symmetry@nankai.edu.cn
  • †Contact author: tianjianan@mail.nankai.edu.cn
  • ‡Contact author: wb@mail.nankai.edu.cn
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Phys. Rev. D 113, 055047 – Published 26 March, 2026

DOI: https://doi.org/10.1103/fs22-ynpr

Abstract

We study the nonmaximal symmetry breaking patterns of su(8)→g531/g351 allowed in a supersymmetric theory with the affine Lie algebra of su^(8)kU=1, which was recently proposed to explain the three-generational standard model quark/lepton mass hierarchies as well as the Cabbibo-Kobayashi-Maskawa mixing pattern. Three gauge couplings are found to achieve the unification below the Planck scales, according to the unification relations determined by the affine Lie algebra at a level of 1. We also prove that a separate nonmaximal symmetry breaking pattern of su(8)→g621 is unrealistic due to the additional massless vectorlike quarks in the spectrum.

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References (32)

  1. H. Georgi and S. L. Glashow, Unity of all elementary particle forces, Phys. Rev. Lett. 32, 438 (1974).
  2. H. Fritzsch and P. Minkowski, Unified interactions of leptons and hadrons, Ann. Phys. (N.Y.) 93, 193 (1975).
  3. N. Cabibbo, Unitary symmetry and leptonic decays, Phys. Rev. Lett. 10, 531 (1963).
  4. M. Kobayashi and T. Maskawa, CP violation in the renormalizable theory of weak interaction, Prog. Theor. Phys. 49, 652 (1973).
  5. N. Chen, Y.-n. Mao, and Z. Teng, The global B−L symmetry in the flavor-unified SU(N) theories, J. High Energy Phys. 04 (2024) 046.
  6. N. Chen, Y.-n. Mao, and Z. Teng, The standard model quark/lepton masses and the Cabibbo-Kobayashi-Maskawa mixing in an SU(8) theory, J. High Energy Phys. 12 (2024) 137.
  7. H. Georgi, Towards a grand unified theory of flavor, Nucl. Phys. B156, 126 (1979).
  8. S. M. Barr, Doubly lopsided mass matrices from unitary unification, Phys. Rev. D 78, 075001 (2008).
  9. R. D. Peccei and H. R. Quinn, CP conservation in the presence of instantons, Phys. Rev. Lett. 38, 1440 (1977).
  10. N. Chen, Z. Hou, Y.-n. Mao, and Z. Teng, The gauge coupling evolutions of an SU(8) theory with the maximally symmetry breaking pattern, J. High Energy Phys. 10 (2024) 149.
  11. L.-F. Li, Group theory of the spontaneously broken gauge symmetries, Phys. Rev. D 9, 1723 (1974).
  12. L. J. Hall, Grand unification of effective gauge theories, Nucl. Phys. B178, 75 (1981).
  13. S. Weinberg, Effective gauge theories, Phys. Lett. 91B, 51 (1980).
  14. P. Langacker and N. Polonsky, Uncertainties in coupling constant unification, Phys. Rev. D 47, 4028 (1993).
  15. P. H. Ginsparg, Gauge and gravitational couplings in four-dimensional string theories, Phys. Lett. B 197, 139 (1987).
  16. A. Font, L. E. Ibanez, and F. Quevedo, Higher level Kac-Moody string models and their phenomenological implications, Nucl. Phys. B345, 389 (1990).
  17. K. R. Dienes, String theory and the path to unification: A review of recent developments, Phys. Rep. 287, 447 (1997).
  18. N. Chen, Z. Hou, and Z. Teng, The unification in an su^(8)kU=1 affine Lie algebra, J. High Energy Phys. 04 (2025) 048.
  19. G. ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking, NATO Sci. Ser. B 59, 135 (1980).
  20. N. Chen, Z. Chen, Z. Hou, Z. Teng, and B. Wang, Further study of the maximally symmetry breaking patterns in an SU(8) theory, Phys. Rev. D 111, 115034 (2025).
  21. E. Witten, Dynamical breaking of supersymmetry, Nucl. Phys. B188, 513 (1981).
  22. C. T. Hill, Are there significant gravitational corrections to the unification scale?, Phys. Lett. B 135, 47 (1984).
  23. Q. Shafi and C. Wetterich, Modification of GUT predictions in the presence of spontaneous compactification, Phys. Rev. Lett. 52, 875 (1984).
  24. B. Wang, Non-maximal symmetry breaking patterns in the SU(8) theory, https://github.com/B-Wang-NKU/SU8_nonmaximal.git.
  25. P. Langacker, Grand unified theories and proton decay, Phys. Rep. 72, 185 (1981).
  26. P. Nath and P. Fileviez Perez, Proton stability in grand unified theories, in strings and in branes, Phys. Rep. 441, 191 (2007).
  27. A. Takenaka et al. (Super-Kamiokande Collaboration), Search for proton decay via p→e+π0 and p→μ+π0 with an enlarged fiducial volume in Super-Kamiokande I-IV, Phys. Rev. D 102, 112011 (2020).
  28. R. Acciarri et al. (DUNE Collaboration), Long-Baseline Neutrino Facility (LBNF) and Deep Underground Neutrino Experiment (DUNE): Conceptual Design Report, Volume 1: The LBNF and DUNE Projects, arXiv:1601.05471.
  29. M. E. Machacek and M. T. Vaughn, Two loop renormalization group equations in a general quantum field theory. (I). Wave function renormalization, Nucl. Phys. B222, 83 (1983).
  30. S. P. Martin and M. T. Vaughn, Two loop renormalization group equations for soft supersymmetry breaking couplings, Phys. Rev. D 50, 2282 (1994); Phys. Rev. D78, 039903(E) (2008).
  31. L. Sartore and I. Schienbein, pyr@te 3, Comput. Phys. Commun. 261, 107819 (2021).
  32. A. Ernst, A. Ringwald, and C. Tamarit, Axion predictions in SO(10)×U(1)PQ models, J. High Energy Phys. 02 (2018) 103.

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Phys. Rev. D 113, 055047– Published 26 March, 2026
  • Received 11 October 2025
  • Accepted 6 March 2026
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