• [1]

    C. A. Baker et al., Phys. Rev. Lett. 97, 131801 (2006), arXiv: hep-ex/0602020

  • [2]

    C. Abel et al., Phys. Rev. Lett. 124, 081803 (2020), arXiv: 2001.11966

  • [3]

    R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38, 1440 (1977)

  • [4]

    R. D. Peccei and H. R. Quinn, Phys. Rev. D 16, 1791 (1977)

  • [5]

    S. Weinberg, Phys. Rev. Lett. 40, 223 (1978)

  • [6]

    F. Wilczek, Phys. Rev. Lett. 40, 279 (1978)

  • [7]

    J. E. Kim, Phys. Rev. Lett. 43, 103 (1979)

  • [8]

    M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Nucl. Phys. B 166, 493 (1980)

  • [9]

    A. R. Zhitnitsky, Sov. J. Nucl. Phys. 31, 260 (1980)

  • [10]

    M. Dine, W. Fischler, and M. Srednicki, Phys. Lett. B 104, 199 (1981)

  • [11]

    J. Quevillon and C. Smith, Eur. Phys. J. C 79, 822 (2019), arXiv: 1903.12559

  • [12]

    A. Hook, S. Kumar, Z. Liu et al., Phys. Rev. Lett. 124, 221801 (2020), arXiv: 1911.12364

  • [13]

    P. Svrcek and E. Witten, JHEP 06, 051 (2006), arXiv: hep-th/0605206

  • [14]

    I. G. Irastorza and J. Redondo, Prog. Part. Nucl. Phys. 102, 89 (2018), arXiv: 1801.08127

  • [15]

    L. Di Luzio, M. Giannotti, E. Nardi et al., Phys. Rept. 870, 1 (2020), arXiv: 2003.01100

  • [16]

    K. Choi, S.H. Im, and C. Sub Shin, Ann. Rev. Nucl. Part. Sci. 71, 225 (2021), arXiv: 2012.05029

  • [17]

    M. I. Vysotsky, Y. B. Zeldovich, M. Y. Khlopov et al., Pisma Zh. Eksp. Teor. Fiz. 27, 533 (1978)

  • [18]

    Z. G. Berezhiani and M. Y. Khlopov, Z. Phys. C 49, 73 (1991)

  • [19]

    Z. G. Berezhiani, A. S. Sakharov, and M. Y. Khlopov, Sov. J. Nucl. Phys. 55, 1063 (1992)

  • [20]

    A. S. Sakharov and M. Y. Khlopov, Phys. Atom. Nucl. 57, 485 (1994)

  • [21]

    A. S. Sakharov, D. D. Sokoloff, and M. Y. Khlopov, Phys. Atom. Nucl. 59, 1005 (1996)

  • [22]

    M. Y. Khlopov, A. S. Sakharov, and D. D. Sokoloff, Nucl. Phys. B Proc. Suppl. 72, 105 (1999)

  • [23]

    M. Y. Khlopov, S. G. Rubin, and A. S. Sakharov, Astropart. Phys. 23, 265 (2005), arXiv: astro-ph/0401532

  • [24]

    K. Mimasu and V. Sanz, JHEP 06, 173 (2015), arXiv: 1409.4792

  • [25]

    J. Jaeckel and M. Spannowsky, Phys. Lett. B 753, 482 (2016), arXiv: 1509.00476

  • [26]

    G. Galanti and M. Roncadelli, Universe 8, 253 (2022), arXiv: 2205.00940

  • [27]

    J. Liu, L. T. Wang, X. P. Wang et al., Phys. Rev. D 97, 095044 (2018), arXiv: 1712.07237

  • [28]

    M. Bauer, M. Neubert, and A. Thamm, JHEP 12, 044 (2017), arXiv: 1708.00443

  • [29]

    M. J. Dolan, T. Ferber, C. Hearty et al., JHEP 12, 094 (2017), arXiv: 1709.00009

  • [30]

    M. Bauer, M. Heiles, M. Neubert et al., Eur. Phys. J. C 79, 74 (2019), arXiv: 1808.10323

  • [31]

    M. B. Gavela, J. M. No, V. Sanz et al., Phys. Rev. Lett. 124, 051802 (2020), arXiv: 1905.12953

  • [32]

    D. d'Enterria, Collider constraints on axion-like particles, in Workshop on Feebly Interacting Particles, 2, (2021), arXiv: 2102.08971

  • [33]

    P. Agrawal et al., Eur. Phys. J. C 81, 1015 (2021), arXiv: 2102.12143

  • [34]

    H. Y. Zhang, C. X. Yue, Y. C. Guo et al., Phys. Rev. D 104, 096008 (2021)

  • [35]

    M. Tian, Z. S. Wang, and K. Wang, Search for long-lived axions with far detectors at future lepton colliders, arXiv: 2201.08960

  • [36]

    F. A. Ghebretinsaea, Z. S. Wang, and K. Wang, JHEP 07, 070 (2022), arXiv: 2203.01734

  • [37]

    A. de Giorgi, L. Merlo, and J. L. Tastet, Fortsch. Phys. 71, 2300027 (2023), arXiv: 2212.11290

  • [38]

    H. Wang, C. X. Yue, Y. C. Guo et al., J. Phys. G 49, 115002 (2022)

  • [39]

    R. Schäfer, F. Tillinger, and S. Westhoff, Phys. Rev. D 107, 076022 (2023), arXiv: 2202.11714

  • [40]

    K. Cheung and C. J. Ouseph, Phys. Rev. D 108, 035003 (2023), arXiv: 2303.16514

  • [41]

    C. Antel et al., Eur. Phys. J. C 83, 1122 (2023), arXiv: 2305.01715

  • [42]

    P. S. B. Dev, J. F. Fortin, S. P. Harris et al., Phys. Rev. Lett. 132, 101003 (2024), arXiv: 2305.01002

  • [43]

    T. Biswas, JHEP 05, 081 (2024), arXiv: 2312.05992

  • [44]

    C. X. Yue, H. Wang, X. J. Cheng et al., Phys. Rev. D 107, 115025 (2023), arXiv: 2305.19561

  • [45]

    C. X. Yue, H. Wang, and Y. Q. Wang, Phys. Lett. B 848, 138368 (2024), arXiv: 2311.16768

  • [46]

    R. Balkin, O. Hen, W. Li et al., JHEP 02, 123 (2024), arXiv: 2310.08827

  • [47]

    F. Esser, M. Madigan, V. Sanz et al., JHEP 09, 063 (2023), arXiv: 2303.17634

  • [48]

    Y. Lu, Y. n. Mao, K. Wang et al., LAYCAST: LAYered CAvern Surface Tracker at future electron-positron colliders, arXiv: 2406.05770

  • [49]

    Q. Qiu, Y. Gao, H. j. Tian et al., JCAP 02, 001 (2025), arXiv: 2404.18099

  • [50]

    K. Cheung, F. T. Chung, G. Cottin et al., JHEP 07, 209 (2024), arXiv: 2404.06126

  • [51]

    F. Esser, M. Madigan, A. Salas-Bernardez et al., JHEP 10, 164 (2024), arXiv: 2404.08062

  • [52]

    Z. Wang and Y. Gao, Phys. Rev. D 111, 043042 (2025), arXiv: 2409.02468

  • [53]

    M. B. Marcos, A. de Giorgi, L. Merlo et al., SciPost Phys. 18, 084 (2025), arXiv: 2407.14970

  • [54]

    G. Yang, T. Wang, and G. L. Wang, Chin. Phys. C 49, 013109 (2025), arXiv: 2407.05298

  • [55]

    H. Li, Q. Wu, and G. Zhang, Mod. Phys. Lett. A 39, 2450113 (2024)

  • [56]

    S.C. İnan and A.V. Kisselev, Analysis of axion-like particles in a top-quark pair production at the CLIC, arXiv: 2501.15500

  • [57]

    C. X. Yue, X. Y. Li, M. S. Y. Wang et al., Phys. Rev. D 111, 075015 (2025), arXiv: 2503.03179

  • [58]

    X. Ai et al., New Physics Search at the CEPC: a General Perspective, arXiv: 2505.24810

  • [59]

    S. Y. Wang, Y. P. Jiao, H. H. Zhang et al., Probing Long-Lived Photophobic Axion-Like Particles via Prompt Leptons and Mono- \begin{document}$gamma$\end{document} at FCC-ee and CEPC, arXiv: 2509.17718

  • [60]

    S. s. Bao, Y. Ma, Y. Wu et al., JHEP 10, 122 (2025), arXiv: 2505.10023

  • [61]

    J. Alda, M. Fuentes Zamoro, L. Merlo et al., Comprehensive ALP Searches in Meson Decays, arXiv: 2507.19578

  • [62]

    Z. Wang and Y. Gao, Axion Star Bosenova in Axion Miniclusters, arXiv: 2508.14535

  • [63]

    R. Bedi, T. Gherghetta, S. Kumar et al., Heavy QCD Axions at High-Energy Muon Colliders, arXiv: 2509.10605

  • [64]

    M. Figliolia, F. Grippa, G. Lambiase et al., Gravitational Signatures of Axion Dark Matter via Parity-Violating Interactions, arXiv: 2509.12038

  • [65]

    C. X. Yue, X. Y. Li, S. Yang et al., Searching for long-lived axion-like particles via displaced vertices at the HL-LHC, arXiv: 2510.24097

  • [66]

    F. Esser, A. Salas-Bernardez, M. Ubiali et al., A global analysis of ALP-mediated multiboson production at the LHC, arXiv: 2510.24873

  • [67]

    J. Butterworth, M. Cullingworth, J. Egan et al., Probing the coupling of axions to tops and gluons with LHC measurements, arXiv: 2508.21660

  • [68]

    S. Bhattacharya, S. Jahedi, S.K. Manna et al., Probing ALP-portal Fermionic Dark Matter at the \begin{document}$e.+e.-$\end{document} Colliders, arXiv: 2505.00478

  • [69]

    CMS Collaboration, Phys. Lett. B 797, 134826 (2019), arXiv: 1810.04602

  • [70]

    Belle-Ⅱ Collaboration, Phys. Rev. Lett. 125, 161806 (2020), arXiv: 2007.13071

  • [71]

    ATLAS Collaboration, JHEP 03, 243 (2021), arXiv: 2008.05355

  • [72]

    ATLAS Collaboration, JHEP 07, 155 (2023), arXiv: 2211.04172

  • [73]

    BESⅢ Collaboration, Phys. Lett. B 838, 137698 (2023), arXiv: 2211.12699

  • [74]

    BESⅢ Collaboration, Phys. Rev. D 110, L031101 (2024)

  • [75]

    CMS Collaboration, JHEP 08, 006 (2025), arXiv: 2412.15413

  • [76]

    C. O'HARE, cajohare/AxionLimits: AxionLimits, https://doi.org/10.5281/zenodo.3932429, (2024)

  • [77]

    N. Craig, A. Hook, and S. Kasko, JHEP 09, 028 (2018), arXiv: 1805.06538

  • [78]

    N. Fonseca, E. Morgante, and G. Servant, JHEP 10, 020 (2018), arXiv: 1805.04543

  • [79]

    A. Hook and G. Marques-Tavares, JHEP 12, 101 (2016), arXiv: 1607.01786

  • [80]

    J. Bonilla, I. Brivio, J. Machado-Rodríguez et al., JHEP 06, 113 (2022), arXiv: 2202.03450

  • [81]

    M. Aiko and M. Endo, JHEP 06, 194 (2024), arXiv: 2401.13323

  • [82]

    Z. Ding, Y. n. Mao, and K. Wang, JHEP 06, 087 (2025), arXiv: 2411.08660

  • [83]

    A. Dainese, M. Mangano, A.B. Meyer et al., Report on the Physics at the HL-LHC, and Perspectives for the HE-LHC, CERN Yellow Reports: Monographs, CERN, Geneva (2019), DOI: 10.23731/CYRM-2019-007

  • [84]

    Y. n. Mao, K. Wang, and Y. Xiong, Chin. Phys. C 49, 083106 (2025), arXiv: 2411.14041

  • [85]

    H. Georgi, D. B. Kaplan, and L. Randall, Phys. Lett. B 169, 73 (1986)

  • [86]

    H. Georgi, Phys. Lett. B 298, 187 (1993), arXiv: hep-ph/9207278

  • [87]

    I. Brivio, M. B. Gavela, L. Merlo et al., Eur. Phys. J. C 77, 572 (2017), arXiv: 1701.05379

  • [88]

    I. Brivio, O. J. P. Éboli, and M. C. Gonzalez-Garcia, Phys. Rev. D 104, 035027 (2021), arXiv: 2106.05977

  • [89]

    M. Aiko and M. Endo, JHEP 05, 147 (2023), arXiv: 2302.11377

  • [90]

    Particle Data Group Collaboration, Phys. Rev. D 110, 030001 (2024)

  • [91]

    J. Alwall, R. Frederix, S. Frixione et al., JHEP 07, 079 (2014), arXiv: 1405.0301

  • [92]

    R.D. Ball et al., Nucl. Phys. B 867, 244 (2013), arXiv: 1207.1303

  • [93]

    C. Degrande, C. Duhr, B. Fuks et al., Comput. Phys. Commun. 183, 1201 (2012), arXiv: 1108.2040

  • [94]

    C. Bierlich et al., SciPost Phys. Codeb. 2022, 8 (2022), arXiv: 2203.11601

  • [95]

    DELPHES 3 Collaboration, JHEP 02, 057 (2014), arXiv: 1307.6346

  • [96]

    CMS Collaboration, Phys. Lett. B 861, 139231 (2025), arXiv: 2406.05101

  • [97]

    TMVA Collaboration, TMVA - Toolkit for Multivariate Data Analysis, arXiv: physics/0703039

  • [98]

    G. Cowan, K. Cranmer, E. Gross et al., Eur. Phys. J. C 71, 1554 (2011), arXiv: 1007.1727

  • [99]

    G. Cowan, Discovery sensitivity for a counting experiment with background uncertainty, https://www.pp.rhul.ac.uk/cowan/stat/medsig/medsigNote.pdf, (2012)

  • [100]

    N. Kauer and G. Passarino, JHEP 08, 116 (2012), arXiv: 1206.4803