• [1]

    G. Buchalla, A. J. Buras, and M. E. Lautenbacher, Rev. Mod. Phys. 68, 1125 (1996)

  • [2]

    K. S. F. F. Guimarães, I. Bediaga, A. Delfino et al., Nucl. Phys. Proc. Suppl. 199, 341 (2010)

  • [3]

    P. C. Magalhães, M. R. Robilotta, K. S. F. F. Guimaraes et al., Phys. Rev. D 84, 094001 (2011)

  • [4]

    J. R. Peláez and A. Rodas, Eur. Phys. J. C 78, 897 (2018)

  • [5]

    I. Bediaga and P. C. Magalhães, arXiv: 1512.09284

  • [6]

    I. Bediaga, T. Frederico, and O. Lourenço, Phys. Rev. D 89, 094013 (2014)

  • [7]

    J. R. Peláez and F. J. Ynduráin, Phys. Rev. D 71, 074016 (2005)

  • [8]

    G. Breit and E. Wigner, Phys. Rev. 49, 519 (1936)

  • [9]

    G. N. Fleming, Phys. Rev. 135, B551 (1964)

  • [10]

    D. Morgan, Phys. Rev. 166, 1731 (1968)

  • [11]

    D. Herndon, P. Soding, and R. J. Cashmore, Phys. Rev. D 11, 3165 (1975)

  • [12]

    R. H. Dalitz, Phys. Rev. 94, 1046 (1954)

  • [13]

    Y. Y. Keum, H. n. Li, and A. I. Sanda, Phys. Lett. B 504, 6 (2001)

  • [14]

    Y. Y. Keum, H. n. Li, and A. I. Sanda, Phys. Rev. D 63, 054008 (2001)

  • [15]

    C. D. Lü, K. Ukai, and M. Z. Yang, Phys. Rev. D 63, 074009 (2001)

  • [16]

    H. n. Li, Prog. Part. Nucl. Phys. 51, 85 (2003)

  • [17]

    W. F. Wang and H. n. Li, Phys. Lett. B 763, 29 (2016)

  • [18]

    Y. Li, A. J. Ma, W. F. Wang et al., Phys. Rev. D 95, 056008 (2017)

  • [19]

    W. F. Wang and J. Chai, Phys. Lett. B 791, 342 (2019)

  • [20]

    W. F. Wang, J. Chai, and A. J. Ma, JHEP 03, 162 (2020)

  • [21]

    Z. T. Zou, Y. Li, and H. n. Li, Phys. Rev. D 103, 013005 (2021)

  • [22]

    Y. Li et al., Phys. Rev. D 102, 056017 (2020)

  • [23]

    W. F. Wang, Phys. Rev. D 101, 111901 (R) (2020), arXiv: 2004.09027[hep-ph]

  • [24]

    A. J. Ma and W. F. Wang, Phys. Rev. D 103, 016002 (2021)

  • [25]

    W. F. Wang, Phys. Rev. D 103, 056021 (2021)

  • [26]

    W. F. Wang, L. F. Yang, A. J. Ma et al., Phys. Rev. D 109, 116009 (2024)

  • [27]

    A. J. Ma and W. F. Wang, Chin. Phys. C 46, 053104 (2022)

  • [28]

    Y. S. Ren, A. J. Ma and W. F. Wang, JHEP 01, 047 (2024)

  • [29]

    A. J. Ma and W. F. Wang, Phys. Rev. D 109, 056017 (2024)

  • [30]

    Q. Chang, L. Yang, Z. T. Zou et al., Eur. Phys. J. C 84, 753 (2024)

  • [31]

    J. W. Zhang, B. Y. Cui, X. G. Wu et al., Phys. Rev. D 110, 036015 (2024)

  • [32]

    L. L. Mu and X. Q. Yu, Phys. Rev. D 111, 016002 (2025)

  • [33]

    Y. X. Wang, J. P. Wang, Y. Li and Z. T. Zou, Phys. Rev. D 111, 053009 (2025)

  • [34]

    A. J. Ma and W. F. Wang, arXiv: 2508.09578[hep-ph]

  • [35]

    R. H. Dalitz, Strange particles and strong interactions (Oxford Press, London, 1962)

  • [36]

    A. Astier et al., Phys. Lett. B 25, 294 (1967)

  • [37]

    R. Aaij et al. (LHCb Collaboration), Phys. Rev. D 94, 072001 (2016)

  • [38]

    R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 123, 231802 (2019)

  • [39]

    S. H. Zhou, X. X. Hai, R. H. Li et al., Phys. Rev. D 107, 116023 (2023)

  • [40]

    S. H. Zhou, R. H. Li, and X. Y. Lü, Phys. Rev. D 110, 056001 (2024)

  • [41]

    B. Delcourt et al., Phys. Lett. B 99, 257 (1981)

  • [42]

    P. M. Ivanov et al., Phys. Lett. B 107, 297 (1981)

  • [43]

    D. Bisello et al. (DM2 Collaboration), Z. Phys. C 39, 13 (1988)

  • [44]

    M. N. Achasov et al., Phys. Rev. D 76, 072012 (2007)

  • [45]

    R. R. Akhmetshin et al. (CMD-2 Collaboration), Phys. Lett. B 669, 217 (2008)

  • [46]

    J. P. Lees et al. (BABAR Collaboration), Phys. Rev. D 88, 032013 (2013)

  • [47]

    M. N. Achasov et al., Phys. Rev. D 94, 112006 (2016)

  • [48]

    E. A. Kozyrev et al., Phys. Lett. B 779, 64 (2018)

  • [49]

    M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 99, 032001 (2019)

  • [50]

    F. Mané et al., Phys. Lett. B 99, 261 (1981)

  • [51]

    M. N. Achasov et al., Phys. Rev. D 63, 072002 (2001)

  • [52]

    R. R. Akhmetshin et al., Phys. Lett. B 551, 27 (2003)

  • [53]

    M. N. Achasov et al., J. Exp. Theor. Phys. 103, 720 (2006)

  • [54]

    J. P. Lees et al. (BABAR Collaboration), Phys. Rev. D 89, 092002 (2014)

  • [55]

    E. A. Kozyrev et al. (CMD-3 Collaboration), Phys. Lett. B 760, 314 (2016)

  • [56]

    A. Abele et al. (CMD-3 Collaboration), Phys. Lett. B 468, 178 (1999)

  • [57]

    M. Albrecht et al. (Crystal Barrel Collaboration), Eur. Phys. J. C 80, 453 (2020)

  • [58]

    A. J. Pawlicki et al., Phys. Rev. D 15, 3196 (1977)

  • [59]

    D. Cohen et al., Phys. Rev. D 22, 2595 (1980)

  • [60]

    S. Ryu et al. (Belle Collaboration), Phys. Rev. D 89, 072009 (2014)

  • [61]

    J. P. Lees et al. (BABAR Collaboration), Phys. Rev. D 98, 032010 (2018)

  • [62]

    T. E. Coan et al. (CLEO Collaboration), Phys. Rev. D 53, 6037 (1996)

  • [63]

    S. Gonzàlez-Solís and P. Roig, Eur. Phys. J. C 79, 436 (2019)

  • [64]

    D. Matvienko et al. (Belle Collaboration), Phys. Rev. D 92, 012013 (2015)

  • [65]

    M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 107, 052010 (2023)

  • [66]

    W. F. Wang, J. Y. Xu, S. H. Zhou et al., arXiv: 2502.11159 [hep-ph]

  • [67]

    H. Y. Cheng, C. K. Chua, and A. Soni, Phys. Rev. D 72, 094003 (2005)

  • [68]

    C. K. Chua, W. S. Hou, S. Y. Shiau et al., Phys. Rev. D 67, 034012 (2003)

  • [69]

    C. Bruch, A. Khodjamirian, and J. H. Kühn, Eur. Phys. J. C 39, 41 (2005)

  • [70]

    S. A. Ivashyn and A. Y. Korchin, Eur. Phys. J. C 49, 697 (2007)

  • [71]

    H. Czyż, A. Grzelińska, and J. H. Kühn, Phys. Rev. D 81, 094014 (2010)

  • [72]

    M. Gronau and J. L. Rosner, Phys. Lett. B 564, 90 (2003)

  • [73]

    G. Engelhard, Y. Nir, and G. Raz, Phys. Rev. D 72, 075013 (2005)

  • [74]

    M. Gronau and J. L. Rosner, Phys. Rev. D 72, 094031 (2005)

  • [75]

    M. Imbeault and D. London, Phys. Rev. D 84, 056002 (2011)

  • [76]

    M. Gronau, Phys. Lett. B 727, 136 (2013)

  • [77]

    B. Bhattacharya, M. Gronau, and J. L. Rosner, Phys. Lett. B 726, 337 (2013)

  • [78]

    B. Bhattacharya, M. Gronau, M. Imbeault et al., Phys. Rev. D 89, 074043 (2014)

  • [79]

    D. Xu, G. N. Li, and X. G. He, Phys. Lett. B 728, 579 (2014)

  • [80]

    X. G. He, G. N. Li, and D. Xu, Phys. Rev. D 91, 014029 (2015)

  • [81]

    T. Huber, J. Virto, and K.K. Vos, JHEP 11, 103 (2020)

  • [82]

    T. Mannel, K. Olschewsky, and K. K. Vos, JHEP 06, 073 (2020)

  • [83]

    S. Kränkl, T. Mannel, and J. Virto, Nucl. Phys. B 899, 247 (2015)

  • [84]

    A. Furman, R. Kamiński, L. Leśniak et al., Phys. Lett. B 699, 102 (2011)

  • [85]

    A. Furman, R. Kamiński, L. Leśniak et al., Phys. Lett. B 622, 207 (2005)

  • [86]

    B. El-Bennich et al., Phys. Rev. D 79, 094005 (2009); 83, 039903 (2011)

  • [87]

    H. Y. Cheng and C. K. Chua, Phys. Rev. D 88, 114014 (2013)

  • [88]

    H. Y. Cheng and C. K. Chua, Phys. Rev. D 89, 074025 (2014)

  • [89]

    H. Y. Cheng, C. K. Chua, and Z. Q. Zhang, Phys. Rev. D 94, 094015 (2016)

  • [90]

    H. Y. Cheng and C. K. Chua, Phys. Rev. D 102, 053006 (2020)

  • [91]

    Y. Li, Phys. Rev. D 89, 094007 (2014)

  • [92]

    Z. H. Zhang, X. H. Guo, and Y. D. Yang, Phys. Rev. D 87, 076007 (2013)

  • [93]

    C. Wang, Z. H. Zhang, Z. Y. Wang et al., Eur. Phys. J. C 75, 536 (2015)

  • [94]

    J. J. Qi, Z. Y. Wang, Z. H. Zhang et al., Eur. Phys. J. C 78, 845 (2018)

  • [95]

    J. J. Qi, Z. Y. Wang, X. H. Guo et al., Phys. Rev. D 99, 076010 (2019)

  • [96]

    Z. H. Zhang, Phys. Lett. B 820, 136537 (2021)

  • [97]

    R. Hu and Z. H. Zhang, Phys. Rev. D 105, 093007 (2022)

  • [98]

    H. n. Li, Phys. Rev. D 52, 3958 (1995)

  • [99]

    D. Scora and N. Isgur, Phys. Rev. D 40, 1491 (1989)

  • [100]

    T. Hurth, A. Khodjamirian, F. Mahmoudi et al., arXiv: 2512.10868

  • [101]

    A. Bazavov et al. (Fermilab Lattice and MILC Collaborations), Eur. Phys. J. C 82, 1141 (2022)

  • [102]

    M. Beneke, P. Böer, G. Finauri et al., JHEP 10, 223 (2021)

  • [103]

    P. Böer, T. Feldmann, and D. van Dyk, JHEP 02, 133 (2017)

  • [104]

    J. Gasser and H. Leutwyler, Nucl. Phys. B 250, 517 (1985)

  • [105]

    D. Boito et al., Phys. Rev. D 96, 113003 (2017)

  • [106]

    J. H. Kühn and A. Santamaria, Z. Phys. C 48, 445 (1990)

  • [107]

    R. Aaij et al. (LHCb Collaboration), Phys. Rev. D 101, 012006 (2020)

  • [108]

    J. M. Blatt and V. F. Weisskopf, Theoretical nuclear physics (Springer, New York, 1952).

  • [109]

    B. Aubert et al. (BaBar Collaboration), Phys. Rev. D 72, 072003 (2005) [Erratum: Phys. Rev. D 74, 099903 (2006)]

  • [110]

    R. Aaij et al. (LHCb Collaboration), Phys. Rev. D 92, 012012 (2015)

  • [111]

    R. Aaij et al. (LHCb Collaboration), Phys. Rev. D 90, 072003 (2014)

  • [112]

    R. Aaij et al. (LHCb Collaboration), Phys. Rev. D 91, 092002 (2015) [Erratum: Phys. Rev. D 93, 119901 (2016)]

  • [113]

    S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

  • [114]

    C. H. Chen and H. n. Li, Phys. Lett. B 561, 258 (2003)

  • [115]

    W. F. Wang, H. C. Hu, H. n. Li et al., Phys. Rev. D 89, 074031 (2014)

  • [116]

    A. Ali et al., Phys. Rev. D 76, 074018 (2007)

  • [117]

    B. Aubert et al. (BaBar Collaboration), Phys. Rev. D 78, 011107 (2008)

  • [118]

    C. H. Wang et al. (Belle Collaboration), Phys. Rev. D 75, 092005 (2007)

  • [119]

    T. Feldmann, P. Kroll, and B. Stech, Phys. Rev. D 58, 114006 (1998)

  • [120]

    T. Feldmann, P. Kroll, and B. Stech, Phys. Lett. B 449, 339 (1999)

  • [121]

    M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 108, 092003 (2023)

  • [122]

    P. Ball, JHEP 01, 010 (1999)

  • [123]

    P. Ball and R. Zwicky, Phys. Rev. D 71, 014015 (2005)

  • [124]

    Y. Y. Charng, T. Kurimoto, and H. n. Li, Phys. Rev. D 74, 074024 (2006); 78, 059901(E) (2008).

  • [125]

    M. Beneke and T. Feldmann, Nucl. Phys. B 592, 3 (2001)

  • [126]

    W. F. Wang, H. n. Li, W. Wang et al., Phys. Rev. D 91, 094024 (2015)

  • [127]

    A. Bharucha, D. M. Straub, and R. Zwicky, JHEP 08, 098 (2016)

  • [128]

    C. Allton et al. (RBC-UKQCD Collaboration), Phys. Rev. D 78, 114509 (2008)