• [1]

    D. J. Gross and F. Wilczek, Phys. Rev. Lett. 30, 1343 (1973)

  • [2]

    H. D. Politzer, Phys. Rev. Lett. 30, 1346 (1973)

  • [3]

    C. G. Callan Jr, Phys. Rev. D 2, 1541 (1970)

  • [4]

    K. Symanzik, Commun.Math. Phys. 18, 227 (1970)

  • [5]

    V. Vanyashin and M. Terent'ev, Sov. Phys. JETP 21, 375 (1965)

  • [6]

    I. Khriplovich, GREEN'S FUNCTIONS IN THEORIES WITH NON-ABELIAN GAUGE GROUP, Tech. Rep. (Inst. of Nuclear Physics, Novosibirsk, USSR, 1969)

  • [7]

    H. Fritzsch, M. Gell-Mann, and H. Leutwyler, Phys. Lett. B 47, 365 (1973)

  • [8]

    D. J. Gross and F. Wilczek, Phys. Rev. D 8, 3633 (1973)

  • [9]

    H. D. Politzer, Phys. Rep. 14, 129 (1974)

  • [10]

    M. Gell-Mann, The eightfold way: A theory of strong interaction symmetry, The Eightfold Way (CRC Press, 2018), p. 11

  • [11]

    S. Okubo, Prog. Theor. Phys. 27, 949 (1962)

  • [12]

    M. Gell-Mann, Symmetries of baryons and mesons, The eightfold way (CRC Press, 2018), p. 216

  • [13]

    H. X. Chen, W. Chen, X. Liu et al., Phys. Rep. 639, 1 (2016)

  • [14]

    Y. R. Liu, H. X. Chen, W. Chen et al., Prog. Part. and Nucl. Phys. 107, 237 (2019)

  • [15]

    H. X. Chen, W. Chen, X. Liu et al., Rep. Prog. Phys. 80, 076201 (2017)

  • [16]

    Y. Dong, A. Faessler, and V. E. Lyubovitskij, Prog. Part. and Nucl. Phys. 94, 282 (2017)

  • [17]

    R. F. Lebed, R. E. Mitchell, and E. S. Swanson, Prog. Part. and Nucl. Phys. 93, 143 (2017)

  • [18]

    F. K. Guo, C. Hanhart, U. G. Meißner et al., Rev. Mod. Phys. 90, 015004 (2018)

  • [19]

    R. M. Albuquerque, J. M. Dias, K. Khemchandani et al., J. Phys. G: Nucl. Part. Phys. 46, 093002 (2019)

  • [20]

    Y. Yamaguchi, A. Hosaka, S. Takeuchi et al., J. Phys. G: Nucl. Part. Phys. 47, 053001 (2020)

  • [21]

    F. K. Guo, X. H. Liu, and S. Sakai, Prog. Part. and Nucl. Phys. 112, 103757 (2020)

  • [22]

    N. Brambilla, S. Eidelman, C. Hanhart et al., Phys. Rep. 873, 1 (2020)

  • [23]

    S. J. Wetzel, R. G. Melko, J. Scott et al., Phys. Rev. Res. 2, 033499 (2020)

  • [24]

    M. Song, M. S. Oh, Y. Ahn et al., Chin. Phys. C 45, 073111 (2021)

  • [25]

    Y. D. Hezaveh, L. P. Levasseur, and P. J. Marshall, Nature 548, 555 (2017)

  • [26]

    S. Soma, L. Wang, S. Shi et al., Phys. Rev. D 107, 083028 (2023)

  • [27]

    L. G. Pang, K. Zhou, N. Su et al., Nature Commun. 9, 210 (2018)

  • [28]

    X. Chen and M. Huang, Phys. Rev. D 109, L051902 (2024)

  • [29]

    A. Radovic, M. Williams, D. Rousseau et al., Nature 560, 41 (2018)

  • [30]

    D. Guest, K. Cranmer, and D. Whiteson, Annu. Rev. Nucl. Part. Sci. 68, 161 (2018)

  • [31]

    K. Albertsson, P. Altoe, D. Anderson et al., Machine learning in high energy physics community white paper, Journal of Physics: Conference Series, Vol. 1085 (IOP Publishing, 2018), p. 022008

  • [32]

    J. Kim, G. Pederiva, and A. Shindler, Phys. Lett. B 856, 138894 (2024)

  • [33]

    K. Zhou, L. Wang, L. G. Pang et al., Prog. Part. and Nucl. Phys. 135, 104084 (2024)

  • [34]

    G. Aarts, K. Fukushima, T. Hatsuda et al., Nature Rev. Phys. 7, 154 (2025)

  • [35]

    L. Jiang, L. Wang, and K. Zhou, Phys. Rev. D 103, 116023 (2021)

  • [36]

    X. Chen and M. Huang, JHEP 2025(02), 123 (2025)

  • [37]

    M. Mansouri, K. Bitaghsir Fadafan, and X. Chen, Eur. Phys. J. C 86, 321 (2026)

  • [38]

    W. C. Dai, O. Y. Luo, B. Chen et al., Phys. Lett. B 877, 140511 (2026)

  • [39]

    J. Mei, L. Wang, and M. Huang, (2025), arXiv: 2507.22012

  • [40]

    P. Xiang, Y. S. Zhao, and X. G. Huang, Chin. Phys. C 46, 074110 (2022)

  • [41]

    X. K. Du, P. Guo, X. H. Wu et al., Chin. Phys. C 47, 074108 (2023)

  • [42]

    Y. Wu, L. Xiao, and Y. Zhang, Chin. Phys. C 50, 033105 (2026)

  • [43]

    J. Li and H. Sun, Chin. Phys. C 49, 093106 (2025)

  • [44]

    Y. Wu, K. Wang, C. Li et al., Chin. Phys. C 49, 013110 (2025)

  • [45]

    X. Tong, W. Feng, W. Xu et al., Chin. Phys. Lett. 43, 020201 (2026)

  • [46]

    X. Y. Wang, C. Dong, and X. Liu, Chin. Phys. Lett. 41, 031201 (2024)

  • [47]

    Z. Ding, F. Lin, and X. Wang, (2026), arXiv: 2603.29269

  • [48]

    S. Qu, J. Y. Zhang, and M. Bao, Chin. Phys. C 49, 104106 (2025)

  • [49]

    S. C. Bai and S. J. Ran, Chin. Phys. Lett. 41, 120701 (2024)

  • [50]

    Y. G. Ma, L. G. Pang, R. Wang et al., Chin. Phys. Lett. 40, 122101 (2023)

  • [51]

    X. Li, R. Guo, Y. Zhou et al., Chin. Phys. C 47, 034101 (2023)

  • [52]

    M. Raissi, P. Perdikaris, and G. E. Karniadakis, J. Comput. Phys. 378, 686 (2019)

  • [53]

    P. H. Chiu, J. C. Wong, C. Ooi et al., Comput. Methods Appl. Mech. Eng. 395, 114909 (2022)

  • [54]

    P. Wen, C. Lin, L. Yang et al., Chin. Phys. C 49, 084109 (2025)

  • [55]

    Z. Liu, Y. Wang, S. Vaidya et al., Kan: Kolmogorov– arnold networks, International conference on learning representations (2025)

  • [56]

    Z. Liu, P. Ma, Y. Wang et al., Phys. Rev. X 15, 041051 (2025)

  • [57]

    Z. Liu and M. Tegmark, Phys. Rev. Lett. 126, 180604 (2021)

  • [58]

    S.-M. Udrescu and M. Tegmark, Science Advances 6, eaay2631 (2020)

  • [59]

    M. Schmidt and H. Lipson, Science 324, 81 (2009)

  • [60]

    Z. Zhang, R. Ma, J. Hu et al., Chin. Phys. Lett. 39, 111201 (2022)

  • [61]

    O. Y. Luo, X. Chen, F. P. Li et al., Eur. Phys. J. C 85, 637 (2025)

  • [62]

    N. R. Panczyk, O. F. Erdem, and M. I. Radaideh, Energy and AI 22, 100595 (2025)

  • [63]

    C. Guo, L. Sun, S. Li et al., Physics of Fluids 37, 095120 (2025)

  • [64]

    H. Hao, X. Zhang, B. Li et al., (2024), arXiv: 2405.16494

  • [65]

    K. Nakamura, J. Phys. G: Nucl. Part. Phys. 37, 075021 (2010)

  • [66]

    T. Hastie, R. Tibshirani, J. Friedman et al., The elements of statistical learning, (2009)

  • [67]

    C. M. Bishop, Pattern recognition and machine learning by Christopher M. Bishop, Vol. 400 (Springer Science+ Business Media, LLC Berlin, Germany: 2006)

  • [68]

    I. Goodfellow, Y. Bengio, and A. Courville, Deep learning (MIT press Cambridge, 2016)

  • [69]

    S. Geman, E. Bienenstock, and R. Doursat, Neural Computation 4, 1 (1992)

  • [70]

    K. P. Murphy, Machine learning: a probabilistic perspective (MIT press, 2012)

  • [71]

    T. Hastie, R. Tibshirani, and J. Friedman, An introduction to statistical learning, (2009), course notes

  • [72]

    Y. F. Liu, W. J. Xing, X. Y. Wu et al., Phys. Rev. C 105, 044904 (2022)

  • [73]

    S. Katel, H. Li, Z. Zhao et al., (2024), arXiv: 2412.05333

  • [74]

    H. Garcilazo and A. Valcarce, Symmetry 17, 1324 (2025)

  • [75]

    T. Hyodo, (2025), arXiv: 2503.15376

  • [76]

    G. Yang, J. Ping, and J. Segovia, Symmetry 12, 1869 (2020)

  • [77]

    W. T. Lyu, L. J. Liu, and E. Wang, Eur. Phys. J. C 85, 503 (2025)

  • [78]

    P. D. Collins and E. J. Squires, Regge poles in particle physics, Vol. 45 (Springer, 2006)

  • [79]

    D. Jido, J. Oller, E. Oset et al., Nucl. Phys. A 725, 181 (2003)

  • [80]

    T. Hyodo and D. Jido, Prog. Part. and Nucl. Phys. 67, 55 (2012)

  • [81]

    J. Bulava, B. Cid-Mora, A. D. Hanlon et al, Phys. Rev. Lett. 132, 051901 (2024)

  • [82]

    J. M. Xie, Z. W. Liu, J. X. Lu et al., (2026), arXiv: 2604.00791

  • [83]

    Y. B. He, X. H. Liu, L. S. Geng et al., Phys. Rev. D 113, L051501 (2026)

  • [84]

    Y. Gao, X. Y. Wang, and X. Liu, (2026), arXiv: 2602.11480[nucl-th]

  • [85]

    J. S. Sucunza, T. Luu, and C. Urbach, The Lambda 1405 at the \begin{document}$SU(3)$\end{document} point in lattice QCD, Proceedings of the 42nd International Symposium on Lattice Field Theory (LATTICE2025), PoS, Vol. LATTICE2025 (Mumbai, India, 2025) p. 092, arXiv: 2602.19928[hep-lat]

  • [86]

    K. G. Wilson, Phys. Rev. D 10, 2445 (1974)

  • [87]

    S. Durr, Z. Fodor, J. Frison et al., Science 322, 1224 (2008)

  • [88]

    Y. Aoki, T. Blum, G. Colangelo et al., Eur. Phys. J. C 82, 869 (2022)

  • [89]

    A. Bazavov, T. Bhattacharya, C. DeTar et al., Phys. Rev. D 90, 094503 (2014)

  • [90]

    S. He, L. Li, Z. Li et al., Mechanics & Astronomy 67, 240411 (2024)

  • [91]

    L. Zhang and M. Huang, Phys. Rev. D 106, 096028 (2022)

  • [92]

    Y. Chen, D. Li, and M. Huang, Commun. Theor. Phys. 74, 097201 (2022)

  • [93]

    R. Li, S. Han, Z. Lin et al., Phys. Rev. D 111, 074026 (2025)

  • [94]

    K. Zhou, G. Endrődi, L. G. Pang et al., Phys. Rev. D 100, 011501 (2019)

  • [95]

    X. Chen, D. Li, and M. Huang, Chin. Phys. C 43, 023105 (2019)

  • [96]

    X. Chen, L. Zhang, D. Li et al., JHEP 03, 073 (2021)

  • [97]

    X. Chen, D. Li, D. Hou et al., JHEP 2021, 132 (2021)

  • [98]

    L. Zhu, X. Chen, K. Zhou et al., Phys. Rev. D 112, 026019 (2025)

  • [99]

    W. J. Xing, S. Cao, G. Y. Qin et al., Phys. Rev. Lett. 134, 052301 (2025)

  • [100]

    S. Cao and X. N. Wang, Rep. Prog. Phys. 84, 024301 (2021)

  • [101]

    W. Zhang, Z. Zhang, J. Hu et al., Chin. Phys. Lett. 42, 070202 (2025)

  • [102]

    H. A. Zeng, L. Wang, and M. Huang, (2025), arXiv: 2512.06044[hep-lat]

  • [103]

    D. Winney and A. P. Szczepaniak, (2025), arXiv: 2512.21805

  • [104]

    A. Inopin and G. Sharov, Phys. Rev. D 63, 054023 (2001)

  • [105]

    J. K. Chen, Eur. Phys. J. C 84, 356 (2024)