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  • Open Access

Constraints on birefringence-free photon theory within standard model extensions

Zhi Xiao*

Hanlin Song†

Bo-Qiang Ma‡

  • *Contact author: spacecraft@pku.edu.cn
  • †Contact author: hsongphy@gmail.com
  • ‡Contact author: mabq@pku.edu.cn
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Phys. Rev. D 113, 035036 – Published 26 February, 2026

DOI: https://doi.org/10.1103/ld2j-wk8z

Abstract

Constraints on the birefringence-free subset of Lorentz-violating (LV) operators are derived using 14 gamma-ray burst photons in the GeV band. These constraints target the isotropic c(I)00(d) coefficients for dimensions d=6, 8, 10 within the framework of the Standard-Model extension. Employing theory-agnostic Bayesian parameter estimation methods, our analysis indicates a preference for subluminal LV effects. Focusing on this case, we further refine the parameter constraints, yielding results that are mutually consistent. Within the 95% posterior credible interval, our constraints yield the bounds, |c(I)00(6)|≤7.75×10−20  GeV−2, |c(I)00(8)|≤4.92×10−24  GeV−4, and |c(I)00(10)|≤3.46×10−28  GeV−6, which improve upon the most stringent credible-interval bounds reported in the literature by at least five orders of magnitude.

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References (106)

  1. V. A. Kostelecký and M. Mewes, Phys. Rev. D 66, 056005 (2002).
  2. D. Colladay and V. A. Kostelecký, Phys. Rev. D 55, 6760 (1997).
  3. D. Colladay and V. A. Kostelecký, Phys. Rev. D 58, 116002 (1998).
  4. V. A. Kostelecký and S. Samuel, Phys. Rev. D 39, 683 (1989).
  5. V. A. Kostelecký and S. Samuel, Phys. Rev. D 40, 1886 (1989).
  6. G. Amelino-Camelia, J. R. Ellis, N. E. Mavromatos, and D. V. Nanopoulos, Int. J. Mod. Phys. A 12, 607 (1997).
  7. G. Amelino-Camelia, J. R. Ellis, N. E. Mavromatos, D. V. Nanopoulos, and S. Sarkar, Nature (London) 393, 763 (1998).
  8. J. R. Ellis, N. E. Mavromatos, and D. V. Nanopoulos, Gen. Relativ. Gravit. 31, 1257 (1999).
  9. J. R. Ellis, N. E. Mavromatos, and D. V. Nanopoulos, Gen. Relativ. Gravit. 32, 127 (2000).
  10. J. R. Ellis, N. E. Mavromatos, and D. V. Nanopoulos, Phys. Lett. B 665, 412 (2008).
  11. T. Li, N. E. Mavromatos, D. V. Nanopoulos, and D. Xie, Phys. Lett. B 679, 407 (2009).
  12. C. Li and B.-Q. Ma, Phys. Lett. B 819, 136443 (2021).
  13. C. Li and B.-Q. Ma, Results Phys. 26, 104380 (2021).
  14. C. Li and B.-Q. Ma, J. High Energy Phys. 05 (2024) 266.
  15. C. Li, Phys. Lett. B 869, 139823 (2025).
  16. C. Li and B.-Q. Ma, J. High Energy Phys. 10 (2025) 216.
  17. R. Gambini and J. Pullin, Phys. Rev. D 59, 124021 (1999).
  18. J. Alfaro, H. A. Morales-Tecotl, and L. F. Urrutia, Phys. Rev. Lett. 84, 2318 (2000).
  19. H. Li and B.-Q. Ma, Phys. Lett. B 836, 137613 (2023).
  20. G. Amelino-Camelia, Nature (London) 418, 34 (2002).
  21. G. Amelino-Camelia, Int. J. Mod. Phys. D 11, 1643 (2002).
  22. G. Amelino-Camelia, Int. J. Mod. Phys. D 11, 35 (2002).
  23. G. Amelino-Camelia, Symmetry 2, 230 (2010).
  24. D. Anselmi, J. High Energy Phys. 02 (2008) 051.
  25. P. Horava, Phys. Rev. D 79, 084008 (2009).
  26. A. Wang, Int. J. Mod. Phys. D 26, 1730014 (2017).
  27. U. Jacob and T. Piran, J. Cosmol. Astropart. Phys. 01 (2008) 031.
  28. J. R. Ellis, N. E. Mavromatos, D. V. Nanopoulos, A. S. Sakharov, and E. K. G. Sarkisyan, Astropart. Phys. 25, 402 (2006); 29, 158(E) (2008).
  29. L. Shao, Z. Xiao, and B.-Q. Ma, Astropart. Phys. 33, 312 (2010).
  30. S. Zhang and B.-Q. Ma, Astropart. Phys. 61, 108 (2015).
  31. H. Xu and B.-Q. Ma, Astropart. Phys. 82, 72 (2016).
  32. H. Xu and B.-Q. Ma, Phys. Lett. B 760, 602 (2016).
  33. Y. Huang, H. Li, and B.-Q. Ma, Phys. Rev. D 99, 123018 (2019).
  34. J. Zhu and B.-Q. Ma, Phys. Lett. B 820, 136518 (2021).
  35. J. Zhu and B.-Q. Ma, Phys. Lett. B 820, 136546 (2021).
  36. J. Zhu and B.-Q. Ma, J. Phys. G 50, 06LT01 (2023).
  37. H. Song and B.-Q. Ma, Phys. Lett. B 856, 138951 (2024).
  38. H. Song and B.-Q. Ma, Phys. Dark Universe 47, 101808 (2025).
  39. H. Song and B.-Q. Ma, Astrophys. J. 983, 9 (2025).
  40. H. Song and B.-Q. Ma, Phys. Rev. D 111, 103015 (2025).
  41. H. Song and B.-Q. Ma, Phys. Lett. B 870, 139959 (2025).
  42. M. Ackermann et al. (Fermi GBM/LAT Collaboration), Nature (London) 462, 331 (2009).
  43. V. Vasileiou, A. Jacholkowska, F. Piron, J. Bolmont, C. Couturier, J. Granot, F. W. Stecker, J. Cohen-Tanugi, and F. Longo, Phys. Rev. D 87, 122001 (2013).
  44. J.-J. Wei, B.-B. Zhang, L. Shao, X.-F. Wu, and P. Mészáros, Astrophys. J. Lett. 834, L13 (2017).
  45. J. Ellis, R. Konoplich, N. E. Mavromatos, L. Nguyen, A. S. Sakharov, and E. K. Sarkisyan-Grinbaum, Phys. Rev. D 99, 083009 (2019).
  46. V. A. Acciari et al. (MAGIC Collaboration), Phys. Rev. Lett. 125, 021301 (2020).
  47. J.-N. Wei, Z.-K. Liu, J.-J. Wei, B.-B. Zhang, and X.-F. Wu, Universe 8, 519 (2022).
  48. Z. Cao et al. (LHAASO Collaboration), Phys. Rev. Lett. 133, 071501 (2024).
  49. M. Guerrero, A. Campoy-Ordaz, R. Potting, and M. Gaug, Phys. Rev. D 112, 104002 (2025).
  50. A. Addazi et al., Prog. Part. Nucl. Phys. 125, 103948 (2022).
  51. P. He and B.-Q. Ma, Universe 8, 323 (2022).
  52. R. Alves Batista et al., Classical Quantum Gravity 42, 032001 (2025).
  53. C. Li and B.-Q. Ma, Symmetry 17, 974 (2025).
  54. L. Caloni, S. Giardiello, M. Lembo, M. Gerbino, G. Gubitosi, M. Lattanzi, and L. Pagano, J. Cosmol. Astropart. Phys. 03 (2023) 018.
  55. B. Feng, M. Li, J.-Q. Xia, X. Chen, and X. Zhang, Phys. Rev. Lett. 96, 221302 (2006).
  56. V. A. Kostelecký and M. Mewes, Phys. Rev. Lett. 99, 011601 (2007).
  57. L. Pogosian, M. Shimon, M. Mewes, and B. Keating, Phys. Rev. D 100, 023507 (2019).
  58. L. Shao and B.-Q. Ma, Phys. Rev. D 83, 127702 (2011).
  59. S. M. Carroll and G. B. Field, Phys. Rev. Lett. 79, 2394 (1997).
  60. V. A. Kostelecký and M. Mewes, Phys. Rev. Lett. 97, 140401 (2006).
  61. V. A. Kostelecký and M. Mewes, Phys. Rev. Lett. 110, 201601 (2013).
  62. F. Kislat and H. Krawczynski, Phys. Rev. D 95, 083013 (2017).
  63. A. S. Friedman, D. Leon, K. D. Crowley, D. Johnson, G. Teply, D. Tytler, B. G. Keating, and G. M. Cole, Phys. Rev. D 99, 035045 (2019).
  64. T. Jacobson, S. Liberati, and D. Mattingly, Phys. Rev. D 67, 124011 (2003).
  65. V. A. Kostelecký and A. G. M. Pickering, Phys. Rev. Lett. 91, 031801 (2003).
  66. V. A. Kostelecký and M. Mewes, Phys. Rev. D 80, 015020 (2009).
  67. J.-J. Wei, X.-F. Wu, B.-B. Zhang, L. Shao, P. Mészáros, and V. A. Kostelecký, Astrophys. J. 842, 115 (2017).
  68. Z. Xiao and B.-Q. Ma, Phys. Rev. D 80, 116005 (2009).
  69. Y. Itin, J. Phys. A 42, 475402 (2009).
  70. S. M. Carroll, G. B. Field, and R. Jackiw, Phys. Rev. D 41, 1231 (1990).
  71. D. J. Schwarz, J. Goswami, and A. Basu, Phys. Rev. D 103, L081306 (2021).
  72. Y. Itin, Phys. Rev. D 72, 087502 (2005).
  73. Y. N. Obukhov, T. Fukui, and G. F. Rubilar, Phys. Rev. D 62, 044050 (2000).
  74. R. Penrose and W. Rindler, Spinors and Space-Time. Vol. 1: Two-Spinor Calculus and Relativistic Fields (Cambridge University Press, Cambridge, England, 1984).
  75. U. Seljak and M. Zaldarriaga, Phys. Rev. Lett. 78, 2054 (1997).
  76. M. Zaldarriaga and U. Seljak, Phys. Rev. D 55, 1830 (1997).
  77. M. Mewes, Phys. Rev. D 99, 104062 (2019).
  78. C. Mills and S. Fairhurst, Phys. Rev. D 103, 024042 (2021).
  79. M. Schreck, Phys. Rev. D 92, 125032 (2015).
  80. Q. Exirifard, Phys. Lett. B 699, 1 (2011).
  81. Z. Xiao and H. Wang, Phys. Rev. D 111, 095014 (2025).
  82. P. A. Bolokhov, S. Groot Nibbelink, and M. Pospelov, Phys. Rev. D 72, 015013 (2005).
  83. A. Kostelecký and M. Mewes, Phys. Rev. D 88, 096006 (2013).
  84. V. A. Kostelecký and Z. Li, Phys. Rev. D 99, 056016 (2019).
  85. V. A. Kostelecký and M. Mewes, Astrophys. J. Lett. 689, L1 (2008).
  86. A. A. Abdo et al. (Fermi-LAT Collaboration), Phys. Rev. Lett. 103, 251101 (2009).
  87. C. Meegan et al., Astrophys. J. 702, 791 (2009).
  88. H. Tajima, J. Bregeon, J. Chiang, and G. Thayer, GRB Coordinates Network 8246, 1 (2008).
  89. M. Ohno and V. Pelassa, GRB Coordinates Network 9334, 1 (2009).
  90. F. de Palma, J. Bregeon, and H. Tajima, GRB Coordinates Network 9867, 1 (2009), https://gcn.nasa.gov/circulars/9867.
  91. T. Uehara, H. Takahashi, and J. McEnery, GRB Coordinates Network 9934, 1 (2009).
  92. H. Takahashi, M. Ohno, and N. Omodei, GRB Coordinates Network 10594, 1 (2010).
  93. S. Zhu, J. Racusin, J. Chiang, and G. Vianello, GRB Coordinates Network 14508, 1 (2013).
  94. D. Kocevski, F. Longo, G. Vianello, V. Connaughton, J. McEnery, and E. Sonbas, GRB Coordinates Network 16420, 1 (2014).
  95. F. Longo, E. Bissaldi, G. Vianello, E. Moretti, N. Omodei, J. Bregeon, F. Dirirsa, M. Yassine, D. Kocevski, J. Racusin, J. McEnery, and M. Ohno, GRB Coordinates Network 19413, 1 (2016).
  96. Y. Liu and B.-Q. Ma, Eur. Phys. J. C 78, 825 (2018).
  97. N. Aghanim et al. (Planck Collaboration), Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  98. Y. Pan, J. Qi, S. Cao, T. Liu, Y. Liu, S. Geng, Y. Lian, and Z.-H. Zhu, Astrophys. J. 890, 169 (2020).
  99. V. Vardanyan, V. Takhistov, M. Ata, and K. Murase, Phys. Rev. D 108, 123023 (2023).
  100. G. Ashton et al., Astrophys. J. Suppl. Ser. 241, 27 (2019).
  101. I. M. Romero-Shaw et al., Mon. Not. R. Astron. Soc. 499, 3295 (2020).
  102. F. W. Stecker and S. L. Glashow, Astropart. Phys. 16, 97 (2001).
  103. F. R. Klinkhamer and M. Schreck, Phys. Rev. D 78, 085026 (2008).
  104. T. Tanimori et al. (CANGAROO Collaboration), Astrophys. J. Lett. 492, L33 (1998).
  105. V. A. Kostelecký and N. Russell, Rev. Mod. Phys. 83, 11 (2011).
  106. B. Altschul, Phys. Rev. Lett. 98, 041603 (2007).

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Phys. Rev. D 113, 035036– Published 26 February, 2026
  • Received 8 September 2025
  • Accepted 2 February 2026
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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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