\begin{document}$ cs\bar{c}\bar{s} $\end{document} tetraquark states with \begin{document}$ J^{PC}=1^{++} $\end{document} and \begin{document}$ 1^{+-} $\end{document} in both symmetric \begin{document}$ \mathbf{6}_{cs}\otimes\bar{\mathbf{6}}_{\bar{c}\bar{s}} $\end{document} and antisymmetric \begin{document}$ \bar{\mathbf{3}}_{cs}\otimes\mathbf{3}_{\bar{c}\bar{s}} $\end{document} color configurations using the QCD sum rule method. We construct the D-wave diquark-antidiquark type of \begin{document}$ cs\bar{c}\bar{s} $\end{document} tetraquark interpolating currents in various excitation structures with \begin{document}$(L_\lambda,L_\rho\{l_{\rho_1},l_{\rho_2}\})=(2,0\{0,0\}),\,(1,1\{1,0\}),\,(1,1\{0,1\}),\,(0,2\{1,1\}),\,(0,2\{2,0\}),\,(0,2\{0,2\})$\end{document}. Our results support the interpretation of the recently observed \begin{document}$ X(4685) $\end{document} resonance as a D-wave \begin{document}$ cs\bar{c}\bar{s} $\end{document} tetraquark state with \begin{document}$ J^{PC}=1^{++} $\end{document} in the \begin{document}$ (2,0\{0,0\}) $\end{document} or \begin{document}$ (0,2\{2,0\}) $\end{document} excitation mode, although some other possible excitation structures cannot be excluded exhaustively within theoretical errors. Moreover, our results provide the mass relations \begin{document}$ 6_{\rho\rho}<3_{\lambda\lambda}<3_{\lambda\rho}<3_{\rho\rho} $\end{document} and \begin{document}$ 6_{\rho\rho}<3_{\lambda\lambda}<6_{\lambda\lambda}< 3_{\rho\rho} $\end{document} for the positive and negative \begin{document}$ \mathbb{C} $\end{document}-parity D-wave \begin{document}$ cs\bar{c}\bar{s} $\end{document} tetraquarks, respectively. We suggest searching for these possible D-wave \begin{document}$ cs\bar{c}\bar{s} $\end{document} tetraquarks in both the hidden-charm channels \begin{document}$ J/\psi\phi $\end{document} and \begin{document}$ \eta_c\phi $\end{document}, as well as open-charm channels such as \begin{document}$ D_s\bar{D}_s^* $\end{document} and \begin{document}$ D_{s}\bar{D}_{s1}^* $\end{document} ."> <i>D</i>-wave excited <inline-formula><tex-math id="M1">\begin{document}${\boldsymbol{ cs}\bar{\boldsymbol c}\bar{\boldsymbol s}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/dae51669-f826-4438-9a21-064cd553b8a4/CPC-2022-0629_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/dae51669-f826-4438-9a21-064cd553b8a4/CPC-2022-0629_M1.png"/></alternatives></inline-formula> tetraquark states with <inline-formula><tex-math id="M2">\begin{document}${ \boldsymbol{J^{PC}}=\bf 1^{\bf ++}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/dae51669-f826-4438-9a21-064cd553b8a4/CPC-2022-0629_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/dae51669-f826-4438-9a21-064cd553b8a4/CPC-2022-0629_M2.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}${\bf 1^{\bf +-}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/dae51669-f826-4438-9a21-064cd553b8a4/CPC-2022-0629_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/dae51669-f826-4438-9a21-064cd553b8a4/CPC-2022-0629_M3.png"/></alternatives></inline-formula> -
  • [1]

    M. Gell-Mann, Phys. Lett.8, 214 (1964)

  • [2]

    G. Zweig, in: D. Lichtenberg, S.P.Rosen (Eds.),Developments in the Quark Theory of Hadrons, VOL. 1. 1964 - 1978: pp. 22–101, 1964

  • [3]

    R. L. Workmanet al. (Particle Data Group), PTEP2022, 083C01 (2022)

  • [4]

    R. Aaijet al. (LHCb), Phys. Rev. Lett.115, 072001 (2015)

  • [5]

    R. Aaijet al. (LHCb), Phys. Rev. Lett.122(22), 222001 (2019)

  • [6]

    R. Aaijet al. (LHCb), Sci. Bull.66, 1278-1287 (2021)

  • [7]

    R. Aaijet al. (LHCb), Phys. Rev. Lett.128(6), 062001 (2022)

  • [8]

    R. Aaijet al. (LHCb), Nature Phys.18(7), 751 (2022)

  • [9]

    R. Aaijet al. (LHCb), Nature Commun.13(1), 3351 (2022)

  • [10]

    R. Aaijet al. (LHCb), Sci. Bull.65(23), 1983-1993 (2020)

  • [11]

    H. X. Chen, W. Chen, X. Liuet al., Phys. Rept.639, 1-121 (2016)

  • [12]

    A. Esposito, A. Pilloni, and A. D. Polosa, Phys. Rept.668, 1-97 (2017)

  • [13]

    F. K. Guo, C. Hanhart, U. G. Meißneret al., Rev. Mod. Phys.90(1), 015004 (2018)

  • [14]

    Y. R. Liu, H. X. Chen, W. Chenet al., Prog. Part. Nucl. Phys.107, 237-320 (2019)

  • [15]

    N. Brambilla, S. Eidelman, C. Hanhartet al., Phys. Rept.873, 1-154 (2020)

  • [16]

    H. X. Chen, W. Chen, X. Liuet al., Rept. Prog. Phys.86(2), 026201 (2023)

  • [17]

    L. Meng, B. Wang, G. J. Wang et al., arXiv:2204.08716[hep-ph]

  • [18]

    R. Aaijet al., Phys. Rev. D95, 012002 (2017)

  • [19]

    R. Aaijet al., Phys. Rev. Lett.118, 022003 (2017)

  • [20]

    T. Aaltonenet al. (CDF), Phys. Rev. Lett.102, 242002 (2009)

  • [21]

    T. Aaltonenet al. (CDF), Mod. Phys. Lett. A32(26), 1750139 (2017)

  • [22]

    S. Chatrchyanet al. (CMS), Phys. Lett. B734, 261 (2014)

  • [23]

    V. M. Abazovet al. (D0), Phys. Rev. D89, 012004 (2014)

  • [24]

    J. P. Leeset al. (BABAR), Phys.Rev.D91, 012003 (2015)

  • [25]

    W. Chen and S.-L. Zhu, Phys. Rev. D83, 034010 (2011)

  • [26]

    Fl. Stancu,J. Phys. G37, 075017 (2010)[Erratum: J. Phys. G46, 019501 (2019)]

  • [27]

    H.-X. Chen, E.-L. Cui, W. Chenet al., Eur. Phys. J. C77, 160 (2017)

  • [28]

    D. Ebert, R. N. Faustov, and V. O. Galkin, Eur. Phys. J. C58, 399 (2008)

  • [29]

    Q.-F. Lü and Y.-B. Dong, Phys. Rev. D94, 074007 (2016)

  • [30]

    J. Wu, Y.-R. Liu, K. Chenet al., Phys. Rev. D94, 094031 (2016)

  • [31]

    X. Liu, H. Huang, J. Pinget al., Eur. Phys. J. C81(10), 950 (2021)

  • [32]

    C. Deng, J. Ping, and H. Huang, Phys. Rev. D98, 014026 (2018)

  • [33]

    Z.-G. Wang, Eur. Phys. J. C77, 78 (2017)

  • [34]

    R. Aaijet al. (LHCb), Phys. Rev. Lett.127(8), 082001 (2021)

  • [35]

    C. Deng, H. Chen, and J. Ping, Phys. Rev. D101, 054039 (2020)

  • [36]

    A. Türkan, J. Y. Süngü, and E. V. Veliev, arXiv:2103.05515

  • [37]

    Z.-G. Wang, Adv. High Energy Phys.2021, 4426163 (2021)

  • [38]

    L. J. Reinders, H. Rubinstein, and S. Yazaki, Phys. Rep.127, 1 (1985)

  • [39]

    M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Nucl. Phys. B147, 385 (1979)

  • [40]

    L. J. Reinders, H. R. Rubinstein, and S. Yazaki, Nucl. Phys. B186, 109-146 (1981)

  • [41]

    M. Shifman and T.M. Aliev, Phys. Lett. B112, 401 (1982)

  • [42]

    Y.-B. Dai, C.-S. Huang, M.-Q. Liuet al., Phys. Lett. B390, 350 (1997)

  • [43]

    H. X. Chen, W. Chen, Q. Maoet al., Phys. Rev. D91(5), 054034 (2015)

  • [44]

    J. R. Zhang and M. Q. Huang, JHEP11, 057 (2010)

  • [45]

    J. R. Zhang and M. Q. Huang, Phys. Rev. D83, 036005 (2011)

  • [46]

    H.-X. Chen, E.-L. Cui, W. Chenet al., Eur. Phys. J. C77, 3 (2017)

  • [47]

    S. Narison, World Sci. Lect. Notes Phys.26, 1-527 (1989)

  • [48]

    M. Jamin, J. A. Oller, and A. Pich, Eur. Phys. J. C24, 237 (2002)

  • [49]

    M. Jamin and A. Pich, Nucl. Phys. B Proc. Suppl.74, 300 (1999)

  • [50]

    B. L. Ioffe,Nucl. Phys. B188, 317 (1981)[Erratum: Nucl. Phys. B191, 591–592 (1981)]

  • [51]

    Y. Chung, H. G. Dosch, M. Kremeret al., Z. Phys. C25, 151 (1984)

  • [52]

    H. G. Dosch, M. Jamin, and S. Narison, Phys. Lett. B220, 251 (1989)

  • [53]

    A. Khodjamirian, T. Mannel, N. Offenet al., Phys. Rev. D83, 094031 (2011)

  • [54]

    M. Tanabashiet al. (Particle Data Group), Phys. Rev. D98, 030001 (2018)

  • [55]

    A. Francis, R. J. Hudspith, R. Lewiset al., Phys. Rev. D99, 054505 (2019)

  • [56]

    C. Deng, H. Chen, and J. Ping, Phys. Rev. D103, 014001 (2021)

  • [57]

    G.-J. Wang, L. Meng, M. Okaet al., Phys. Rev. D104, 036016 (2021)

  • [58]

    Z.-Y. Yang, Q.-N. Wang, W. Chenet al., Phys. Rev. D104, 014003 (2021)

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