• [1]

    V. P. Gonçalves and M. V. T. Machado, Mod. Phys. Lett. A 19, 2525 (2004); A. J. Baltz et al. Phys. Rept. 458, 1 (2008).

  • [2]

    K. Akiba et al. [LHC Forward Physics Working Group], J. Phys. G 43, 110201 (2016)

  • [3]

    G. Baur, K. Hencken, D. Trautmann, S. Sadovsky and Y. Kharlov, Phys. Rep. 364, 359 (2002)

  • [4]

    Z. L. Ma and J. Q. Zhu, Phys. Rev. D 97, 054030 (2018)

  • [5]

    Z. L. Ma, Z. Lu and L. Zhang, Nucl. Phys. B974, 115645 (2022)

  • [6]

    V. P. Gonçalves and M. V. T. Machado, Eur. Phys. J. C 40, 519 (2005); Phys. Rev. D 77, 014037 (2008).

  • [7]

    A. Manohar, P. Nason, G. P. Salam and G. Zanderighi, Phys. Rev. Lett. 117, 242002 (2016)

  • [8]

    S. R. Klein, J. Nystrand and R. Vogt, Phys. Rev. C 66, 044906 (2002)

  • [9]

    C. A. Salgado, et al., J. Phys. G 39, 015010 (2012)

  • [10]

    E. Fermi, Z. Phys. 29, 315 (1924)

  • [11]

    C. F. von Weizsacker, Z. Phys. 88, 612 (1934)

  • [12]

    E. J. Williams, Phys. Rev. 45, 729 (1934)

  • [13]

    J. Q. Zhu, Z. L. Ma, C. Y. Shi and Y. D. Li, Nucl. Phys. B900, 431 (2015)

  • [14]

    Y. P. Fu and Y. D. Li, Chin. Phys. C 36, 721 (2012)

  • [15]

    J. Q. Zhu, Z. L. Ma, C. Y. Shi and Y. D. Li, Phys. Rev. C 92, 054907 (2015)

  • [16]

    G. M. Yu, Y. C. Yu, Y. D. Li and J. S. Wang, Nucl. Phys. B917, 234 (2017)

  • [17]

    M. Drees and D. Zeppenfeld, Phys. Rev. D 39, 2536 (1989)

  • [18]

    Y. P. Fu and Y. D. Li, Phys. Rev. C 84, 044906 (2011)

  • [19]

    Y. P. Fu and Y. D. Li, Nucl. Phys. A865, 76 (2011)

  • [20]

    G. M. Yu and Y. D. Li, Phys. Rev. C 91, 044908 (2015)

  • [21]

    G. M. Yu, Y. B. Cai, Y. D. Li and J. S. Wang, Phys. Rev. C 95, 014905 (2017)

  • [22]

    B. A. Kniehl, Phys. Lett. B 254, 267 (1991)

  • [23]

    M. Drees, J. R. Ellis and D. Zeppenfeld, Phys. Lett. B 223, 454 (1989)

  • [24]

    S. Frixione, M. L. Mangano, P. Nason and G. Ridolfi, Phys. Lett. B 319, 339 (1993)

  • [25]

    J. Nystrand, Nucl. Phys. A787, 29 (2005)

  • [26]

    B. A. Kniehl and L. Zwirner, Nucl. Phys. B621, 337 (2002)

  • [27]

    Y. Yang, S. Cai, Y. Cai and W. Xiang, Nucl. Phys. A990, 17 (2019)

  • [28]

    J. Wu, Y. Cai and W. Xiang, Phys. Rev. C 104, 015204 (2021)

  • [29]

    G. Baur, K. Hencken and D. Trautmann, J. Phys. G 24, 1657 (1998)

  • [30]

    J. C. Collins and D. E. Soper, Nucl. Phys. B 194, 445 (1982)

  • [31]

    P. L. Cho and A. K. Leibovich, Phys. Rev. D 53, 150 (1996); 53, 6203 (1996).

  • [32]

    G. T. Bodwin, K. T. Chao, H. S. Chung, U. R. Kim, J. Lee and Y. Q. Ma, Phys. Rev. D 93, 034041 (2016)

  • [33]

    G. T. Bodwin, H. S. Chung, U. R. Kim and J. Lee, Phys. Rev. D 92, 074042 (2015)

  • [34]

    G. T. Bodwin, H. S. Chung, U. R. Kim and J. Lee, Phys. Rev. Lett. 113, 022001 (2014)

  • [35]

    P. Faccioli, V. Knünz, C. Lourenco, J. Seixas and H. K. Wöhri, Phys. Lett. B 736, 98 (2014)

  • [36]

    V. P. Gonçalves and R. Palota da Silva, Phys. Rev. D 101, 034025 (2020)

  • [37]

    Y. P. Xie and V. P. Gonçalves, Eur. Phys. J. C 81, 645 (2021)

  • [38]

    L. Jenkovszky, V. Libov and M. V. T. Machado, Phys. Lett. B 824, 136836 (2022)

  • [39]

    F. Kopp and M. V. T. Machado, Phys. Rev. D 98, 014010 (2018)

  • [40]

    S. R. Klein and Y. P. Xie, Phys. Rev. C 100, 024620 (2019)

  • [41]

    S. R. Klein and J. Nystrand, Phys. Rev. Lett. 92, 142003 (2004); Phys. Rev. C 60, 014903 (1999).

  • [42]

    A. J. Baltz, S. R. Klein and J. Nystrand, Phys. Rev. Lett. 89, 012301 (2002)

  • [43]

    S. R. Klein, J. Nystrand, J. Seger, Y. Gorbunov and J. Butterworth, Comput. Phys. Commun. 212, 258 (2017)

  • [44]

    M. B. Gay Ducati, M. T. Griep and M. V. T. Machado, Phys. Rev. D 88, 017504 (2013)

  • [45]

    S. Fleming and T. Mehen, Phys. Rev. D 57, 1846 (1998)

  • [46]

    X. Wu, X. Li, Z. Tang, K. Wang and W. Zha, [arXiv: 2410.06676 [hep-ph]].

  • [47]

    G. T. Bodwin, E. Braaten and G. P. Lepage, Phys. Rev. D 51, 1125 (1995)

  • [48]

    K. J. Eskola, P. Paakkinen, H. Paukkunen and C. A. Salgado, Eur. Phys. J. C 77, 163 (2017)

  • [49]

    V. M. Budnev, I. F. Ginzburg, G. V. Meledin and V. G. Serbo, Phys. Rep. 15, 181 (1975)

  • [50]

    A. D. Martin and M. G. Ryskin, Eur. Phys. J. C 74, 3040 (2014)

  • [51]

    M. Dyndal, A. Glazov, M. Luszczak and R. Sadykov, Phys. Rev. D 99, 114008 (2019)

  • [52]

    M. Klasen, B. A. Kniehl, L. N. Mihaila and M. Steinhauser, Phys. Rev. D 68, 034017 (2003); 77, 117501 (2008).

  • [53]

    M. Gluck, E. Reya and I. Schienbein, Phys. Rev. D 60, 054019 (1999)

  • [54]

    Z. B. Kang, J. W. Qiu and G. Sterman, Phys. Rev. Lett. 108, 102002 (2012)

  • [55]

    G. C. Nayak, J. W. Qiu and G. F. Sterman, Phys. Rev. D 72, 114012 (2005)

  • [56]

    Z. L. Ma, Z. Lu, J. Q. Zhu and L. Zhang, Phys. Rev. D 104, 074023 (2021)

  • [57]

    J. F. Owens, Rev. Mod. Phys. 59, 465 (1987)

  • [58]

    E. Braaten and Y. Q. Chen, Phys. Rev. D 55, 2693 (1997)

  • [59]

    G. T. Bodwin, U. R. Kim and J. Lee, JHEP 11, 020 (2012) [erratum: JHEP 07, 170 (2023)].

  • [60]

    E. Braaten and T. C. Yuan, Phys. Rev. D 50, 3176 (1994)

  • [61]

    Y. Q. Ma, J. W. Qiu and H. Zhang, Phys. Rev. D 89, 094029 (2014); 89, 094030 (2014).

  • [62]

    J. P. Ma, Phys. Rev. D 53, 1185 (1996)

  • [63]

    J. D. Jackson, Classical Electrodynamics, Third edition (New York: Wiley, 1998).

  • [64]

    M. Drees, R. M. Godbole, M. Nowakowski and S. D. Rindani, Phys. Rev. D 50, 2335 (1994)

  • [65]

    S. J. Brodsky, T. Kinoshita and H. Terazawa, Phys. Rev. D 4, 1532 (1971)

  • [66]

    W. Zha, J. D. Brandenburg, Z. Tang and Z. Xu, Phys. Lett. B 800, 135089 (2020)

  • [67]

    P. Lu, Z. Tang, X. Wu and W. Zha, [arXiv: 2502.09063 [hep-ph]].

  • [68]

    M. Aaboud et al. [ATLAS], Phys. Lett. B 777, 303 (2018)

  • [69]

    D. d'Enterria and G. G. da Silveira, Phys. Rev. Lett. 111, 080405 (2013)

  • [70]

    G. Aad et al. [ATLAS], Phys. Rev. Lett. 123, 052001 (2019)

  • [71]

    A. M. Sirunyan et al. [CMS], Phys. Lett. B 797, 134826 (2019)

  • [72]

    C. Bierlich, et al., SciPost Phys. Codeb. 2022, 8 (2022)

  • [73]

    K. A. Olive et al. [Particle Data Group], Chin. Phys. C 38, 090001 (2014)

  • [74]

    Z. L. Ma, J. Q. Zhu, C. Y. Shi and Y. D. Li, Chin. Phys. Lett. 32, 121202 (2015)

  • [75]

    S. Bailey, T. Cridge, L. A. Harland-Lang, A. D. Martin and R. S. Thorne, Eur. Phys. J. C 81, 341 (2021)

  • [76]

    B. A. Kniehl and G. Kramer, Eur. Phys. J. C 6, 493 (1999)

  • [77]

    V. Khachatryan et al. [CMS], Phys. Rev. Lett. 114, 191802 (2015)

  • [78]

    V. Khachatryan et al. (CMS Collaboration), Phys. Lett. B 749, 14 (2015)

  • [79]

    M. Butenschoen and B. A. Kniehl, Phys. Rev. Lett. 106, 022003 (2011); 104, 072001 (2010); Phys. Rev. D 84, 051501(R) (2011).

  • [80]

    R. Sharma and I. Vitev, Phys. Rev. C 87, 044905 (2013)

  • [81]

    Y. Feng, B. Gong, L. P. Wan and J. X. Wang, Chin. Phys. C 39, 123102 (2015)