- Open Access
Prediction of doubly charm hadronic molecules with double strange quarks
Phys. Rev. D 114, 054037 – Published 18 September, 2026
DOI: https://doi.org/10.1103/x5nz-vxjc
Abstract
In this work, we investigate whether the -doublet charmed-strange mesons and their antiparticles can form hidden-charm hidden-strangeness molecular tetraquarks by applying the one-boson-exchange model. We identify (), (), and () as promising hidden-charm hidden-strangeness molecular tetraquark candidates. Notably, the state with possesses exotic spin-parity quantum numbers forbidden for conventional mesons, providing a clean experimental signature for exotic hadrons. Moreover, the state with is a rare high-spin hadronic molecule. We then extend the same framework to discuss the binding properties of the systems and construct the mass spectrum of corresponding doubly charm doubly strangeness molecular tetraquarks. The promising candidates are (), (), and (), all of which are absolutely flavor-exotic. We encourage experimental searches for these predicted hadronic molecules, which would be a crucial step toward establishing doubly charm molecular tetraquarks with strangeness or 2.
Physics Subject Headings (PhySH)
Article Text
References (106)
- X. Liu, An overview of new particles, Chin. Sci. Bull. 59, 3815 (2014).
- H. X. Chen, W. Chen, X. Liu, and S. L. Zhu, The hidden-charm pentaquark and tetraquark states, Phys. Rep. 639, 1 (2016).
- A. Hosaka, T. Iijima, K. Miyabayashi, Y. Sakai, and S. Yasui, Exotic hadrons with heavy flavors: , , , and related states, Prog. Theor. Exp. Phys. 2016, 062C01 (2016).
- J. M. Richard, Exotic hadrons: Review and perspectives, Few Body Syst. 57, 1185 (2016).
- R. F. Lebed, R. E. Mitchell, and E. S. Swanson, Heavy-quark QCD exotica, Prog. Part. Nucl. Phys. 93, 143 (2017).
- S. L. Olsen, T. Skwarnicki, and D. Zieminska, Nonstandard heavy mesons and baryons: Experimental evidence, Rev. Mod. Phys. 90, 015003 (2018).
- F. K. Guo, C. Hanhart, and U. G. Meißner, Q. Wang, Q. Zhao, and B. S. Zou, Hadronic molecules, Rev. Mod. Phys. 90, 015004 (2018).
- Y. R. Liu, H. X. Chen, W. Chen, X. Liu, and S. L. Zhu, Pentaquark and tetraquark states, Prog. Part. Nucl. Phys. 107, 237 (2019).
- N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev, C. P. Shen, C. E. Thomas, A. Vairo, and C. Z. Yuan, The states: Experimental and theoretical status and perspectives, Phys. Rep. 873, 1 (2020).
- L. Meng, B. Wang, G. J. Wang, and S. L. Zhu, Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules, Phys. Rep. 1019, 1 (2023).
- H. X. Chen, W. Chen, X. Liu, Y. R. Liu, and S. L. Zhu, An updated review of the new hadron states, Rep. Prog. Phys. 86, 026201 (2023).
- M. Z. Liu, Y. W. Pan, Z. W. Liu, T. W. Wu, J. X. Lu, and L. S. Geng, Three ways to decipher the nature of exotic hadrons: Multiplets, three-body hadronic molecules, and correlation functions, Phys. Rep. 1108, 1 (2025).
- Z. G. Wang, Review of the QCD sum rules for exotic states, Front. Phys. 21, 016300 (2026).
- X. Wang, X. Liu, and Y. Gao, Colloquium: Hadron production in open-charm meson pairs at colliders, Rev. Mod. Phys. 98, 021001 (2026).
- Z. Y. Bai, D. Y. Chen, Q. Huang, X. Liu, S. Q. Luo, and J. Z. Wang, Unquenched charmonium and beyond, Phys. Rep. 1204, 1 (2027).
- R. Aaij et al. (LHCb Collaboration), Observation of a resonant structure near the threshold in the decay, Phys. Rev. Lett. 131, 071901 (2023).
- T. Aaltonen et al. (CDF Collaboration), Evidence for a narrow near-threshold structure in the mass spectrum in decays, Phys. Rev. Lett. 102, 242002 (2009).
- T. Ji, X. K. Dong, M. Albaladejo, M. L. Du, F. K. Guo, and J. Nieves, Establishing the heavy quark spin and light flavor molecular multiplets of the , , and , Phys. Rev. D 106, 094002 (2022).
- H. Mutuk, Molecular interpretation of as state, Eur. Phys. J. C 82, 1142 (2022).
- Q. Xin, Z. G. Wang, and X. S. Yang, Analysis of the and related tetraquark molecular states via the QCD sum rules, AAPPS Bull. 32, 37 (2022).
- M. Bayar, A. Feijoo, and E. Oset, seen in as the state seen in , Phys. Rev. D 107, 034007 (2023).
- Z. M. Ding and J. He, Combined analysis on nature of , , and , Eur. Phys. J. C 83, 806 (2023).
- F. Z. Peng, M. J. Yan, and M. Pavon Valderrama, Heavy- and light-flavor symmetry partners of the , the , and the from light-meson exchange saturation, Phys. Rev. D 108, 11 (2023).
- S. S. Agaev, K. Azizi, and H. Sundu, Near-threshold structures in the mass distribution of the decay , Phys. Rev. D 107, 094018 (2023).
- Y. Chen, H. Chen, C. Meng, H. R. Qi, and H. Q. Zheng, On the nature of , Eur. Phys. J. C 83, 381 (2023).
- J. J. Qi, Z. Y. Wang, Z. F. Zhang, and X. H. Guo, The properties of the -wave bound state, Chin. Phys. C 50, 022001 (2026).
- N. Mahajan, : Possible options, Phys. Lett. B 679, 228 (2009).
- G. J. Ding, Possible Molecular states of system and , Eur. Phys. J. C 64, 297 (2009).
- T. Branz, T. Gutsche, and V. E. Lyubovitskij, Hadronic molecule structure of the and , Phys. Rev. D 80, 054019 (2009).
- R. M. Albuquerque, M. E. Bracco, and M. Nielsen, A QCD sum rule calculation for the narrow structure, Phys. Lett. B 678, 186 (2009).
- R. Molina and E. Oset, The , and the as dynamically generated resonances from the vector-vector interaction, Phys. Rev. D 80, 114013 (2009).
- X. Liu, Oddball as the molecular cousin of , Chin. Phys. C 34, 1405 (2010).
- J. R. Zhang and M. Q. Huang, molecular states from QCD sum rules: A view on , J. Phys. G 37, 025005 (2010).
- X. Liu and S. L. Zhu, is probably a molecular partner of , Phys. Rev. D 80, 017502 (2009); 85, 019902(E) (2012).
- Z. G. Wang, Reanalysis of the , , , and as molecular states with QCD sum rules, Eur. Phys. J. C 74, 2963 (2014).
- X. Chen, X. Lü, R. Shi, and X. Guo, Mass of in Bethe-Salpeter equation for quarks, arXiv:1512.06483.
- R. Aaij et al. (LHCb Collaboration), Observation of structures consistent with exotic states from amplitude analysis of decays, Phys. Rev. Lett. 118, 022003 (2017).
- S. Jia et al. (Belle Collaboration), Observation of a vector charmoniumlike state in ., Phys. Rev. D 100, 111103 (2019).
- R. Aaij et al. (LHCb Collaboration), Observation of new resonances decaying to and , Phys. Rev. Lett. 127, 082001 (2021).
- S. I. Finazzo, M. Nielsen, and X. Liu, QCD sum rule calculation for the charmonium-like structures in the and invariant mass spectra, Phys. Lett. B 701, 101 (2011).
- X. Liu, Z. G. Luo, and S. L. Zhu, Novel charmonium-like structures in the and invariant mass spectra, Phys. Lett. B 699, 341 (2011); 707, 577(E) (2012).
- J. He and P. L. Lü, Understanding and in the invariant mass spectrum, Nucl. Phys. A919, 1 (2013).
- J. He, Understanding spin parity of and in a hadronic molecular state picture, Phys. Rev. D 95, 074004 (2017).
- H. W. Ke, X. H. Liu, and X. Q. Li, Study on the possible molecular state composed of within the Bethe-Salpeter framework, Chin. Phys. C 44, 093104 (2020).
- J. He, Y. Liu, J. T. Zhu, and D. Y. Chen, as a molecular state from interaction , Eur. Phys. J. C 80, 246 (2020).
- F. Z. Peng, M. J. Yan, M. Sánchez Sánchez, and M. Pavon Valderrama, Light- and heavy-quark symmetries and the , , , , and resonances, Phys. Rev. D 107, 016001 (2023).
- X. D. Yang, F. L. Wang, Z. W. Liu, and X. Liu, Newly observed : A new charmoniumlike molecule, Eur. Phys. J. C 81, 807 (2021).
- Z. G. Wang, Assignments of the , , , and based on the QCD sum rules, Adv. High Energy Phys. 2021, 4426163 (2021).
- S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
- X. Q. Li and X. Liu, A possible global group structure for exotic states, Eur. Phys. J. C 74, 3198 (2014).
- M. Karliner and J. L. Rosner, New exotic meson and baryon resonances from doubly-heavy hadronic molecules, Phys. Rev. Lett. 115, 122001 (2015).
- R. Aaij et al. (LHCb Collaboration), Observation of an exotic narrow doubly charmed tetraquark, Nat. Phys. 18, 751 (2022).
- R. Aaij et al. (LHCb Collaboration), Study of the doubly charmed tetraquark , Nat. Commun. 13, 3351 (2022).
- R. Molina, T. Branz, and E. Oset, A new interpretation for the and the prediction of novel exotic charmed mesons, Phys. Rev. D 82, 014010 (2010).
- A. V. Manohar and M. B. Wise, Exotic states in QCD, Nucl. Phys. B399, 17 (1993).
- T. E. O. Ericson and G. Karl, Strength of pion exchange in hadronic molecules, Phys. Lett. B 309, 426 (1993).
- N. A. Tornqvist, From the deuteron to deusons, an analysis of deuteronlike meson-meson bound states, Z. Phys. C 61, 525 (1994).
- D. Janc and M. Rosina, The molecular state, Few Body Syst. 35, 175 (2004).
- G. J. Ding, J. F. Liu, and M. L. Yan, Dynamics of hadronic molecule in one-boson exchange approach and possible heavy flavor molecules, Phys. Rev. D 79, 054005 (2009).
- S. Ohkoda, Y. Yamaguchi, S. Yasui, K. Sudoh, and A. Hosaka, Exotic mesons with double charm and bottom flavor, Phys. Rev. D 86, 034019 (2012).
- N. Li, Z. F. Sun, X. Liu, and S. L. Zhu, Coupled-channel analysis of the possible and molecular states, Phys. Rev. D 88, 114008 (2013).
- H. Xu, B. Wang, Z. W. Liu, and X. Liu, potentials in chiral perturbation theory and possible molecular states, Phys. Rev. D 99, 014027 (2019).
- L. Tang, B. D. Wan, K. Maltman, and C. F. Qiao, Doubly heavy tetraquarks in QCD sum rules, Phys. Rev. D 101, 094032 (2020).
- M. Z. Liu, T. W. Wu, M. Pavon Valderrama, J. J. Xie, and L. S. Geng, Heavy-quark spin and flavor symmetry partners of the revisited: What can we learn from the one boson exchange model?, Phys. Rev. D 99, 094018 (2019).
- Z. M. Ding, H. Y. Jiang, and J. He, Molecular states from and interactions, Eur. Phys. J. C 80, 1179 (2020).
- M. B. Wise, Chiral perturbation theory for hadrons containing a heavy quark, Phys. Rev. D 45, R2188 (1992).
- G. J. Ding, Are and or hadronic molecules?, Phys. Rev. D 79, 014001 (2009).
- H. Y. Cheng and K. C. Yang, Charmless hadronic decays into a tensor meson, Phys. Rev. D 83, 034001 (2011).
- R. Casalbuoni, A. Deandrea, N. Di Bartolomeo, R. Gatto, F. Feruglio, and G. Nardulli, Light vector resonances in the effective chiral Lagrangian for heavy mesons, Phys. Lett. B 292, 371 (1992).
- R. Casalbuoni, A. Deandrea, N. Di Bartolomeo, R. Gatto, F. Feruglio, and G. Nardulli, Phenomenology of heavy meson chiral Lagrangians, Phys. Rep. 281, 145 (1997).
- T. M. Yan, H. Y. Cheng, C. Y. Cheung, G. L. Lin, Y. C. Lin, and H. L. Yu, Heavy quark symmetry and chiral dynamics, Phys. Rev. D 46, 1148 (1992); 55, 5851(E) (1997).
- M. Bando, T. Kugo, and K. Yamawaki, Nonlinear realization and hidden local symmetries, Phys. Rep. 164, 217 (1988).
- M. Harada and K. Yamawaki, Hidden local symmetry at loop: A new perspective of composite gauge boson and chiral phase transition, Phys. Rep. 381, 1 (2003).
- R. Machleidt, K. Holinde, and C. Elster, The Bonn meson exchange model for the nucleon nucleon interaction, Phys. Rep. 149, 1 (1987).
- R. Machleidt, The High precision, charge dependent Bonn nucleon-nucleon potential (CD-Bonn), Phys. Rev. C 63, 024001 (2001).
- X. Cao, B. S. Zou, and H. S. Xu, Phenomenological analysis of the double pion production in nucleon-nucleon collisions up to 2.2 GeV, Phys. Rev. C 81, 065201 (2010).
- D. O. Riska and G. E. Brown, Nucleon resonance transition couplings to vector mesons, Nucl. Phys. A679, 577 (2001).
- F. L. Wang, R. Chen, Z. W. Liu, and X. Liu, Possible triple-charm molecular pentaquarks from interactions, Phys. Rev. D 99, 054021 (2019).
- Z. Y. Wang, J. J. Qi, J. Xu, and X. H. Guo, Studying the molecule in the Bethe-Salpeter equation approach, Phys. Rev. D 102, 036008 (2020).
- J. J. Qi, Z. Y. Wang, Z. F. Zhang, and X. H. Guo, Studying the molecule in the Bethe–Salpeter equation approach, Eur. Phys. J. C 81, 639 (2021).
- Y. Y. Cui, R. Chen, and Q. Huang, Molecular pentaquarks composed of a ground octet baryon and a -wave anti-charmed meson, Phys. Rev. D 113, 114034 (2026).
- Y. R. Liu, X. Liu, W. Z. Deng, and S. L. Zhu, Is really a molecular state?, Eur. Phys. J. C 56, 63 (2008).
- X. Liu, Z. G. Luo, Y. R. Liu, and S. L. Zhu, and other possible heavy molecular states, Eur. Phys. J. C 61, 411 (2009).
- X. Liu, Y. R. Liu, W. Z. Deng, and S. L. Zhu, Is a loosely bound molecular state?, Phys. Rev. D 77, 034003 (2008).
- X. Liu, Y. R. Liu, W. Z. Deng, and S. L. Zhu, as a molecular state, Phys. Rev. D 77, 094015 (2008).
- F. L. Wang and X. Liu, Exotic doubly-charm molecular states with hidden or open strangeness and around 4.5–4.7 GeV, Phys. Rev. D 102, 094006 (2020).
- B. Hu, X. L. Chen, Z. G. Luo, P. Z. Huang, S. L. Zhu, P. F. Yu, and X. Liu, Possible heavy molecular states composed of a pair of excited charm-strange mesons, Chin. Phys. C 35, 113 (2011).
- L. L. Shen, X. L. Chen, Z. G. Luo, P. Z. Huang, S. L. Zhu, P. F. Yu, and X. Liu, The molecular systems composed of the charmed mesons in the doublet, Eur. Phys. J. C 70, 183 (2010).
- Y. R. Liu, Heavy quark spin selection rules in Meson-Antimeson states, Phys. Rev. D 88, 074008 (2013).
- Z. F. Sun, X. Liu, M. Nielsen, and S. L. Zhu, Hadronic molecules with both open charm and bottom, Phys. Rev. D 85, 094008 (2012).
- M. T. Li, W. L. Wang, Y. B. Dong, and Z. Y. Zhang, A study of one - and one -wave heavy meson interaction in a chiral quark model, Commun. Theor. Phys. 63, 63 (2015).
- M. T. Li, W. L. Wang, Y. B. Dong, and Z. Y. Zhang, A study of -wave heavy meson interactions in a chiral quark model, arXiv:1303.4140.
- X. K. Dong, F. K. Guo, and B. S. Zou, A survey of heavy-antiheavy hadronic molecules, Progr. Phys. 41, 65 (2021).
- R. Chen, X. Liu, Y. R. Liu, and S. L. Zhu, Predictions of the hidden-charm molecular states with four-quark component, Eur. Phys. J. C 76, 319 (2016).
- F. L. Wang, X. D. Yang, R. Chen, and X. Liu, Correlation of the hidden-charm molecular tetraquarks and the charmoniumlike structures existing in the process, Phys. Rev. D 104, 094010 (2021).
- V. B. Berestetsky, E. M. Lifshitz, and L. P. Pitaevsky, Quantum Electrodynamics (Pergamon Press, New York, 1982).
- E. Epelbaum, H. W. Hammer, and U. G. Meissner, Modern theory of nuclear forces, Rev. Mod. Phys. 81, 1773 (2009).
- A. Esposito, A. L. Guerrieri, F. Piccinini, A. Pilloni, and A. D. Polosa, Four-quark hadrons: An updated review, Int. J. Mod. Phys. A 30, 1530002 (2015).
- N. A. Tornqvist, On deusons or deuteron-like meson-meson bound states, Nuovo Cimento Soc. Ital. Fis. 107A, 2471 (1994).
- F. L. Wang and X. Liu, Surveying the mass spectra and the electromagnetic properties of the molecular pentaquarks, Phys. Rev. D 109, 014043 (2024).
- R. Aaij et al. (LHCb Collaboration), Observation of a narrow pentaquark state, , and of two-peak structure of the , Phys. Rev. Lett. 122, 222001 (2019).
- J. J. Wu, R. Molina, E. Oset, and B. S. Zou, Prediction of narrow and resonances with hidden charm above 4 GeV, Phys. Rev. Lett. 105, 232001 (2010).
- W. L. Wang, F. Huang, Z. Y. Zhang, and B. S. Zou, and states in a chiral quark model, Phys. Rev. C 84, 015203 (2011).
- Z. C. Yang, Z. F. Sun, J. He, X. Liu, and S. L. Zhu, The possible hidden-charm molecular baryons composed of anti-charmed meson and charmed baryon, Chin. Phys. C 36, 6 (2012).
- J. J. Wu, T.-S. H. Lee, and B. S. Zou, Nucleon resonances with hidden charm in coupled-channel Models, Phys. Rev. C 85, 044002 (2012).
- R. Chen, X. Liu, X. Q. Li, and S. L. Zhu, Identifying exotic hidden-charm pentaquarks, Phys. Rev. Lett. 115, 132002 (2015).