• [1]

    Z. Cao, F.A. Aharonian, Q. An et al., Nature 594, 33-36 (2021)

  • [2]

    M. Amenomori, Y. W. Bao, X. J. Bi et al., Phys. Rev. Lett. 123(5), 051101 (2019), arXiv:1906.05521[astro-ph.HE

  • [3]

    M. Amenomori et al. (Tibet ASgamma), Phys. Rev. Lett. 126(14), 141101 (2021), arXiv:2104.05181[astro-ph.HE

  • [4]

    A. U. Abeysekara et al. (HAWC), Astrophys. J. 881, 134 (2019), arXiv:1905.12518[astro-ph.HE

  • [5]

    A. U. Abeysekara et al. (HAWC), Phys. Rev. Lett. 124(2), 021102 (2020), arXiv:1909.08609[astro-ph.HE

  • [6]

    D. D. Dzhappuev et al. (Carpet-3), arXiv: 2105.07242 [astro-ph.HE]

  • [7]

    Hillas, Anthony M. Annual review of astronomy and astrophysics 22(1), 425-444 (1984)

  • [8]

    R. Aloisio, Coccia, E. Vissani, F. (eds) Multiple Messengers and Challenges in Astroparticle Physics (Springer, 2018)

  • [9]

    L. Maccione, S. Liberati, and G. Sigl, Phys. Rev. Lett. 105, 021101 (2010), arXiv:1003.5468[astro-ph.HE

  • [10]

    S. Liberati, Class. Quant. Grav. 30, 133001 (2013), arXiv:1304.5795[gr-qc

  • [11]

    V. Vasileiou, A. Jacholkowska, F. Piron et al., Phys. Rev. D 87(12), 122001 (2013), arXiv:1305.3463[astro-ph.HE

  • [12]

    N. E. Mavromatos, Int. J. Mod. Phys. A 25, 5409-5485 (2010), arXiv:1010.5354[hep-th

  • [13]

    L. Shao and B. Q. Ma, Mod. Phys. Lett. A 25, 3251-3266 (2010), arXiv:1007.2269[hep-ph

  • [14]

    G. Amelino-Camelia, J. Ellis, N. E. Mavromatos et al., Int. J. Mod. Phys. A 12, 607-624 (1997), arXiv:hep-th/9605211[hep-th

  • [15]

    G. Amelino-Camelia, J. Ellis, N. E. Mavromatos et al., Nature 393, 763-765 (1998)

  • [16]

    D. Mattingly, Living Rev. Rel. 8, 5 (2005), arXiv:gr-qc/0502097[gr-qc

  • [17]

    T. Jacobson, S. Liberati, and D. Mattingly, Annals Phys. 321, 150-196 (2006), arXiv:astro-ph/0505267[astro-ph

  • [18]

    G. Amelino-Camelia, Living Rev. Rel. 16, 5 (2013), arXiv:0806.0339[gr-qc

  • [19]

    S. Liberati and L. Maccione, Ann. Rev. Nucl. Part. Sci. 59, 245-267 (2009), arXiv:0906.0681[astro-ph.HE

  • [20]

    L. Chen, Z. Xiong, C. Li et al., Chin. Phys. C 45, 105105 (2021), arXiv:2105.07927[astro-ph.HE

  • [21]

    H. Li and B. Q. Ma, JHEAp 32, 1-5 (2021), arXiv:2105.06647[hep-ph

  • [22]

    C. Li and B. Q. Ma, Phys. Rev. D 104(6), 063012 (2021), arXiv:2105.07967[astro-ph.HE

  • [23]

    P. Satunin, Eur. Phys. J. C 81, 750 (2021), arXiv:2106.06393[hep-ph

  • [24]

    Z. Cao et al. (LHAASO), arXiv: 2106.12350 [astro-ph.HE]

  • [25]

    H. Martínez-Huerta and A. Pérez-Lorenzana, Phys. Rev. D 95(6), 063001 (2017), arXiv:1610.00047[astro-ph.HE

  • [26]

    K. Astapov, D. Kirpichnikov, and P. Satunin, JCAP 04, 054 (2019), arXiv:1903.08464[hep-ph

  • [27]

    P. Satunin, Eur. Phys. J. C 79(12), 1011 (2019), arXiv:1906.08221[astro-ph.HE

  • [28]

    A. Albert et al. (HAWC), Phys. Rev. Lett. 124(13), 131101 (2020), arXiv:1911.08070[astro-ph.HE

  • [29]

    J. J. Wei and X. F. Wu, arXiv: 2111.02029 [astro-ph.HE]

  • [30]

    R. J. Gould and G. P. Schreder, Phys. Rev. 155, 1408-1411 (1967)

  • [31]

    I. V. Moskalenko, T. A. Porter, and A. W. Strong, Astrophys. J. Lett. 640, L155-L158 (2006), arXiv:astro-ph/0511149[astro-ph

  • [32]

    A. De Angelis, G. Galanti, and M. Roncadelli, Monthly Notices of the Royal Astronomical Society 432, 3245 (2013)

  • [33]

    R. Guedes Lang, H. Martínez-Huerta, and V. de Souza, Astrophys. J. 853(1), 23 (2018), arXiv:1701.04865[astro-ph.HE

  • [34]

    H. Martínez-Huerta and A. Pérez-Lorenzana, J. Phys. Conf. Ser. 761(1), 012035 (2016), arXiv:1609.07185[astro-ph.HE