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Magnetic monopoles and exotic states in SU(4)c×SU(2)L×SU(2)R

Thomas W. Kephart1,* and Qaisar Shafi2

  • *Contact author: tom.kephart@gmail.com
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Phys. Rev. D 112, 075013 – Published 6 October, 2025

DOI: https://doi.org/10.1103/y7cd-ds58

Abstract

In the Pati-Salam gauge symmetry SU(4)c×SU(2)L×SU(2)R (4-2-2, for short), the observed quarks and leptons of each family reside in the bi-fundamental representations (4,2,1) and (4¯,1,2). There exist, however, the fundamental representations (4,1,1), (1,2,1), and (1,1,2) and their Hermitian conjugates, which show the presence, in principle, of yet to be discovered color triplets that carry electric charge ±e/6, and color singlet particles with charges of ±e/2. These standard model charges are in full accord with the fact that the 4-2-2 model predicts the presence of a topologically stable, finite energy magnetic monopole that carries two quanta of Dirac magnetic charge, i.e., 4π/e, as well as color magnetic charge that is screened beyond the quark confinement scale. The 4-2-2 model, therefore, predicts the existence of exotic baryons, mesons, and leptons that carry fractional (±e/2) electric charges. Since their origin lies in the fundamental representations of 4-2-2, these exotic particles may turn out to be relatively light, in the TeV mass range or so. The 4-2-2 magnetic monopole mass depends on the 4-2-2 symmetry breaking scale, which is approximately 100 TeV.

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References (49)

  1. J. C. Pati and A. Salam, Lepton number as the fourth color, Phys. Rev. D 10, 275 (1974); 11, 703(E) (1975).
  2. P. A. M. Dirac, Quantised singularities in the electromagnetic field, Proc. R. Soc. A 133, 60 (1931).
  3. G. Lazarides, M. Magg, and Q. Shafi, Phase transitions and magnetic monopoles in SO(10), Phys. Lett. B 97, 87 (1980).
  4. G. ’t Hooft, Magnetic monopoles in unified gauge theories, Nucl. Phys. B79, 276 (1974).
  5. A. M. Polyakov, Particle spectrum in quantum field theory, JETP Lett. 20, 194 (1974) [Particle spectrum in quantum field theory, Pis’ma Zh. Eksp. Teor. Fiz. 20, 430 (1974)].
  6. D. Raut, Q. Shafi, and A. Thapa, Monopoles, exotic states, and muon g−2 in TeV scale trinification, Eur. Phys. J. C 82, 803 (2022).
  7. R. Slansky, Group theory for unified model building, Phys. Rep. 79, 1 (1981).
  8. T. W. Kephart and Q. Shafi, Family unification, exotic states and magnetic monopoles, Phys. Lett. B 520, 313 (2001).
  9. T. W. Kephart, C.-A. Lee, and Q. Shafi, Family unification, exotic states and light magnetic monopoles, J. High Energy Phys. 01 (2007) 088.
  10. T. W. Kephart, G. K. Leontaris, and Q. Shafi, Magnetic monopoles and free fractionally charged states at accelerators and in cosmic rays, J. High Energy Phys. 10 (2017) 176.
  11. M. J. Dolan, T. P. Dutka, and R. R. Volkas, Lowering the scale of Pati-Salam breaking through seesaw mixing, J. High Energy Phys. 05 (2021) 199.
  12. T. W. Kephart and T. J. Weiler, Magnetic monopoles as the highest energy cosmic ray primaries, Astropart. Phys. 4, 271 (1996).
  13. P. H. Frampton and T. W. Kephart, The Amaterasu cosmic ray as a magnetic monopole and implications for extensions of the standard model, Phys. Lett. B 855, 138777 (2024).
  14. R. N. Mohapatra and J. C. Pati, Left-right gauge symmetry and an Isoconjugate model of CP violation, Phys. Rev. D 11, 566 (1975).
  15. R. N. Mohapatra and J. C. Pati, A natural left-right symmetry, Phys. Rev. D 11, 2558 (1975).
  16. G. Senjanovic and R. N. Mohapatra, Exact left-right symmetry and spontaneous violation of parity, Phys. Rev. D 12, 1502 (1975).
  17. R. Maji and Q. Shafi, C-parity, magnetic monopoles and higher frequency gravitational waves, Phys. Rev. D 111, 075027 (2025).
  18. G. Lazarides and Q. Shafi, Monopoles, strings, and necklaces in SO(10) and E6, J. High Energy Phys. 10 (2019) 193.
  19. G. Lazarides, Q. Shafi, and A. Tiwari, Composite topological structures in SO(10), J. High Energy Phys. 05 (2019) 119.
  20. G. Lazarides and Q. Shafi, Triply charged monopole and magnetic quarks, Phys. Lett. B 818, 136363 (2021).
  21. T. W. B. Kibble, Some implications of a cosmological phase transition, Phys. Rep. 67, 183 (1980).
  22. E. W. Kolb, The Early Universe (Taylor and Francis, London, 2019), Vol. 69.
  23. R. Maji and Q. Shafi, Monopoles, strings and gravitational waves in non-minimal inflation, J. Cosmol. Astropart. Phys. 03 (2023) 007.
  24. G. Lazarides, R. Maji, and Q. Shafi, Quantum tunneling in the early Universe: Stable magnetic monopoles from metastable cosmic strings, J. Cosmol. Astropart. Phys. 05 (2024) 128.
  25. A. Moursy and Q. Shafi, Primordial monopoles, black holes and gravitational waves, J. Cosmol. Astropart. Phys. 08 (2024) 064.
  26. S. D. Wick, T. W. Kephart, T. J. Weiler, and P. L. Biermann, Signatures for a cosmic flux of magnetic monopoles, Astropart. Phys. 18, 663 (2003).
  27. K. Greisen, End to the cosmic ray spectrum?, Phys. Rev. Lett. 16, 748 (1966).
  28. G. T. Zatsepin and V. A. Kuzmin, Upper limit of the spectrum of cosmic rays, JETP Lett. 4, 78 (1966) [Upper limit of the spectrum of cosmic rays, Pis’ma Zh. Eksp. Teor. Fiz. 4, 114 (1966)].
  29. T. W. Kephart and M. J. Padgett, Trans-GZK magnetic monopoles from the local void (to be published).
  30. I. Ahmed, S. Swalheen, M. U. Rehman, and R. Tariq, Magnetic monopole phenomenology at future hadron colliders, J. Phys. G 51, 125006 (2024).
  31. M. Nagano and A. A. Watson, Observations and implications of the ultrahigh-energy cosmic rays, Rev. Mod. Phys. 72, 689 (2000).
  32. B. R. Dawson, M. Fukushima, and P. Sokolsky, Past, present and future of UHECR observations, Prog. Theor. Exp. Phys. 2017, 12A101 (2017).
  33. R. Abbasi et al. (IceCube Collaboration), Search for relativistic magnetic monopoles with eight years of IceCube data, Phys. Rev. Lett. 128, 051101 (2022).
  34. M. G. Aartsen et al., Searches for relativistic magnetic monopoles in IceCube, Eur. Phys. J. C 76, 133 (2016).
  35. A. Albert et al., Search for relativistic magnetic monopoles with five years of the antares detector data, J. High Energy Phys. 07 (2017) 054.
  36. G. S. LaRue, W. M. Fairbank, and A. F. Hebard, Evidence for the existence of fractional charge on matter, Phys. Rev. Lett. 38, 1011 (1977).
  37. H. Goldberg, T. W. Kephart, and M. T. Vaughn, Fractionally charged color singlet fermions in a grand unified theory, Phys. Rev. Lett. 47, 1429 (1981).
  38. P. H. Frampton and T. W. Kephart, Fractionally charged particles as evidence for supersymmetry, Phys. Rev. Lett. 49, 1310 (1982).
  39. B. Acharya et al. (MoEDAL Collaboration), MoEDAL search in the CMS beam pipe for magnetic monopoles produced via the Schwinger effect, Phys. Rev. Lett. 133, 071803 (2024).
  40. G. Aad et al.Search for magnetic monopole pair production in ultraperipheral Pb+Pb collisions at sNN=5.36  TeV with the ATLAS detector at the LHC, Phys. Rev. Lett. 134, 061803 (2025).
  41. G. Aad et al. (ATLAS Collaboration), Search for magnetic monopoles and stable particles with high electric charges in s=13  TeV  pp collisions with the ATLAS detector, J. High Energy Phys. 11 (2023) 112.
  42. C.-E. Wulz (ATLAS Collaboration and CMS Collaboration), Searches for anomalous ionizing particles, SIMPs, and monopoles at the LHC, Proc. Sci. LHCP2021 (2021) 009.
  43. M. J. Frank, A. Antoshkin, D. Coveyou, E. C. Dukes, R. Ehrlich, and L. Panda (NOvA Collaboration), Latest magnetic monopole search results from NOvA, Proc. Sci. EPS-HEP2023 (2024) 441.
  44. L. Panda and S. Swain, Search for fast magnetic monopoles with NOvA far detector, Springer Proc. Phys. 304, 1058 (2024).
  45. M. A. Acero et al. (NOvA Collaboration), Search for slow magnetic monopoles with the NOvA detector on the surface, Phys. Rev. D 103, 012007 (2021).
  46. E. Sheridan and T. W. Kephart, A survey of family unification models with bifundamental matter, Nucl. Phys. B987, 116108 (2023).
  47. CMS Collaboration, Search for fractionally charged particles in proton-proton collisions at s=13 tev, Phys. Rev. Lett. 134, 131802 (2025).
  48. C. Arnaboldi et al. (CUORE Collaboration), CUORE: A cryogenic underground observatory for rare events, Nucl. Instrum. Methods Phys. Res., Sect. A 518, 775 (2004).
  49. D. Q. Adams et al. (CUORE Collaboration), Search for fractionally charged particles with cuore, Phys. Rev. Lett. 133, 241801 (2024).

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Phys. Rev. D 112, 075013– Published 6 October, 2025
  • Received 27 March 2025
  • Accepted 16 July 2025
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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.

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