- Open Access
- Access by Xinjiang University
, , and other singly-heavy tetraquark states
Phys. Rev. D 114, 034047 – Published 24 August, 2026
DOI: https://doi.org/10.1103/6fc4-2frx
Abstract
We systematically study the mass spectra of -wave singly heavy tetraquark states (, ; , , ) in a mass splitting model. We adopt the assumption that the is the lowest tetraquark and use this state as a reference to determine the mass splittings. According to the obtained results, we also estimate the rearrangement decay widths of the tetraquarks within a simple scheme. We find that the recently observed states and by the LHCb Collaboration can be consistently interpreted as the second highest (, ) and the higher tetraquark states, respectively. We predict several narrow tetraquark candidates: the lowest and with and , and their bottom counterparts. The obtained information from mass spectrum and rearrangement decay properties will help search for the new singly heavy tetraquark states.
Physics Subject Headings (PhySH)
Article Text
References (95)
- R. Aaij et al. (LHCb Collaboration), First observation of a doubly charged tetraquark and its neutral partner, Phys. Rev. Lett. 131, 041902 (2023).
- R. Aaij et al. (LHCb Collaboration), Amplitude analysis of and decays, Phys. Rev. D 108, 012017 (2023).
- R. Aaij et al. (LHCb Collaboration), A model-independent study of resonant structure in decays, Phys. Rev. Lett. 125, 242001 (2020).
- R. Aaij et al. (LHCb Collaboration), Amplitude analysis of the decay, Phys. Rev. D 102, 112003 (2020).
- T. Gershon (LHCb Collaboration), Exotic hadron naming convention, arXiv:2206.15233.
- R. Aaij et al. (LHCb Collaboration), Observation of new charmonium or charmoniumlike states in decays, Phys. Rev. Lett. 133, 131902 (2024).
- R. Aaij et al. (LHCb Collaboration), Observation of the open-charm tetraquark candidate in the decay, Phys. Rev. Lett. 134, 101901 (2025).
- V. M. Abazov et al. (D0 Collaboration), Evidence for a state, Phys. Rev. Lett. 117, 022003 (2016).
- R. Aaij et al. (LHCb Collaboration), Search for structure in the invariant mass spectrum, Phys. Rev. Lett. 117, 152003 (2016).
- A. M. Sirunyan et al. (CMS Collaboration), Search for the X(5568) state decaying into in proton-proton collisions at , Phys. Rev. Lett. 120, 202005 (2018).
- T. Aaltonen et al. (CDF Collaboration), A search for the exotic meson with the Collider Detector at Fermilab, Phys. Rev. Lett. 120, 202006 (2018).
- M. Aaboud et al. (ATLAS Collaboration), Search for a structure in the invariant mass spectrum with the ATLAS experiment, Phys. Rev. Lett. 120, 202007 (2018).
- Y. R. Liu, X. Liu, and S. L. Zhu, and its partner states, Phys. Rev. D 93, 074023 (2016).
- S. S. Agaev, K. Azizi, and H. Sundu, Mass and decay constant of the newly observed exotic state, Phys. Rev. D 93, 074024 (2016).
- W. Wang and R. Zhu, Can be a tetraquark state?, Chin. Phys. C 40, 093101 (2016).
- Z. G. Wang, Analysis of the as scalar tetraquark state in the diquark-antidiquark model with QCD sum rules, Commun. Theor. Phys. 66, 335 (2016).
- C. M. Zanetti, M. Nielsen, and K. P. Khemchandani, QCD sum rule study of a charged bottom-strange scalar meson, Phys. Rev. D 93, 096011 (2016).
- W. Chen, H. X. Chen, X. Liu, T. G. Steele, and S. L. Zhu, Decoding the as a fully open-flavor tetraquark state, Phys. Rev. Lett. 117, 022002 (2016).
- S. S. Agaev, K. Azizi, and H. Sundu, Width of the exotic state through its strong decay to , Phys. Rev. D 93, 114007 (2016).
- J. M. Dias, K. P. Khemchandani, A. Martínez Torres, M. Nielsen, and C. M. Zanetti, A QCD sum rule calculation of the decay width, Phys. Lett. B 758, 235 (2016).
- Z. G. Wang, Analysis of the strong decay with QCD sum rules, Eur. Phys. J. C 76, 279 (2016).
- L. Tang and C. F. Qiao, Tetraquark states with open flavors, Eur. Phys. J. C 76, 558 (2016).
- Q. F. Lü and Y. B. Dong, Masses of open charm and bottom tetraquark states in a relativized quark model, Phys. Rev. D 94, 094041 (2016).
- W. Chen, H. X. Chen, X. Liu, T. G. Steele, and S. L. Zhu, Open-flavor charm and bottom and tetraquark states, Phys. Rev. D 95, 114005 (2017).
- J. R. Zhang, J. L. Zou, and J. Y. Wu, tetraquark states from improved QCD sum rules: Delving into , Chin. Phys. C 42, 043101 (2018).
- T. Guo, J. Li, J. Zhao, and L. He, Mass spectra and decays of open-heavy tetraquark states, Phys. Rev. D 105, 054018 (2022).
- J. R. Zhang, Open-charm tetraquark candidate: Note on , Phys. Rev. D 103, 054019 (2021).
- Z. G. Wang, Analysis of the as the scalar tetraquark state via the QCD sum rules, Int. J. Mod. Phys. A 35, 2050187 (2020).
- U. Özdem and K. Azizi, Magnetic moment of the state in the diquark–antidiquark picture, Eur. Phys. J. A 58, 171 (2022).
- Q. F. Lü, D. Y. Chen, and Y. B. Dong, Open charm and bottom tetraquarks in an extended relativized quark model, Phys. Rev. D 102, 074021 (2020).
- G. J. Wang, L. Meng, L. Y. Xiao, M. Oka, and S. L. Zhu, Mass spectrum and strong decays of tetraquark states, Eur. Phys. J. C 81, 188 (2021).
- G. Yang, J. Ping, and J. Segovia, tetraquarks in the chiral quark model, Phys. Rev. D 103, 074011 (2021).
- Y. Tan and J. Ping, X(2900) in a chiral quark model, Chin. Phys. C 45, 093104 (2021).
- S. Narison, A. Rabemananajara, and D. Rabetiarivony, DK and BK-like spectra from laplace sum rule at NLO, Nucl. Part. Phys. Proc. 318–323, 90 (2022).
- Y. Xue, X. Jin, H. Huang, and J. Ping, Tetraquarks with open charm flavor, Phys. Rev. D 103, 054010 (2021).
- H. T. An, Z. W. Liu, F. S. Yu, and X. Liu, Discovery of implies new charmed-strange pentaquark system, Phys. Rev. D 106, L111501 (2022).
- S. S. Agaev, K. Azizi, and H. Sundu, Modeling the resonance as a hadronic molecule , Phys. Rev. D 107, 094019 (2023).
- X. S. Yang, Q. Xin, and Z. G. Wang, Analysis of the and related tetraquark states with the QCD sum rules, Int. J. Mod. Phys. A 38, 2350056 (2023).
- P. G. Ortega, D. R. Entem, F. Fernandez, and J. Segovia, Novel and candidates in a constituent-quark-model-based meson-meson coupled-channels calculation, Phys. Rev. D 108, 094035 (2023).
- T. de Oliveira, D. Harnett, R. Kleiv, A. Palameta, and T. G. Steele, Light-quark flavour splitting of heavy-light constituent diquark masses and doubly strange diquarks from QCD sum-rules, Phys. Rev. D 108, 054036 (2023).
- D. K. Lian, W. Chen, H. X. Chen, L. Y. Dai, and T. G. Steele, Strong decays of as a fully open-flavor tetraquark state, Eur. Phys. J. C 84, 1 (2024).
- F. X. Liu, R. H. Ni, X. H. Zhong, and Q. Zhao, Charmed-strange tetraquarks and their decays in the potential quark model, Phys. Rev. D 107, 096020 (2023).
- H. Mutuk, Monte-Carlo based QCD sum rules analysis of and , J. Phys. G 48, 055007 (2021).
- B. Mohan and R. Dhir, A baryon-calibrated unified quark-diquark effective mass formalism for heavy multiquarks, arXiv:2603.04175.
- H. Mutuk, Exotic and states in the Born-Oppenheimer approximation, Phys. Rev. D 113, 034020 (2026).
- X. W. Kang and J. A. Oller, -wave coupled-channel scattering of and the puzzling , Phys. Rev. D 94, 054010 (2016).
- R. Chen and X. Liu, Is the newly reported a molecular state?, Phys. Rev. D 94, 034006 (2016).
- J. X. Lu, X. L. Ren, and L. S. Geng, — interactions in finite volume and , Eur. Phys. J. C 77, 94 (2017).
- B. X. Sun, F. Y. Dong, and J. L. Pang, Study of X(5568) in a unitary coupled-channel approximation of and , Chin. Phys. C 41, 074104 (2017).
- H. W. Ke, L. Gao, and X. Q. Li, The possible molecular state and its radiative decay, Eur. Phys. J. C 77, 285 (2017).
- R. Molina and E. Oset, Molecular picture for the as a state and related states, Phys. Lett. B 811, 135870 (2020); 837, 137645(E) (2023).
- M. W. Hu, X. Y. Lao, P. Ling, and Q. Wang, and its heavy quark spin partners in molecular picture, Chin. Phys. C 45, 021003 (2021).
- H. Chen, H. R. Qi, and H. Q. Zheng, as a molecule, Eur. Phys. J. C 81, 812 (2021).
- X. K. Dong and B. S. Zou, Prediction of possible bound states, Eur. Phys. J. A 57, 139 (2021).
- L. R. Dai, R. Molina, and E. Oset, Looking for the exotic and its partner in the reactions, Phys. Rev. D 105, 096022 (2022).
- J. He and D. Y. Chen, Molecular picture for and , Chin. Phys. C 45, 063102 (2021).
- M. Z. Liu, J. J. Xie, and L. S. Geng, as a molecular state, Phys. Rev. D 102, 091502 (2020).
- Y. Huang, J. X. Lu, J. J. Xie, and L. S. Geng, Strong decays of molecules and the newly observed states, Eur. Phys. J. C 80, 973 (2020).
- B. Wang and S. L. Zhu, How to understand the , Eur. Phys. J. C 82, 419 (2022).
- C. J. Xiao, D. Y. Chen, Y. B. Dong, and G. W. Meng, Study of the decays of wave hadronic molecules: The scalar and its spin partners , Phys. Rev. D 103, 034004 (2021).
- S. S. Agaev, K. Azizi, and H. Sundu, On the structures of new scalar resonances and , J. Phys. G 50, 055002 (2023).
- H. W. Ke, Y. F. Shi, X. H. Liu, and X. Q. Li, Possible molecular states of () and new exotic states , , and , Phys. Rev. D 106, 114032 (2022).
- M. Y. Duan, E. Wang, and D. Y. Chen, Searching for the open flavor tetraquark in the process , Eur. Phys. J. C 84, 681 (2024).
- Z. M. Ding, Q. Huang, and J. He, Roles of and molecular states in decay , Eur. Phys. J. C 85, 1133 (2025).
- M. Y. Duan, M. L. Du, Z. H. Guo, E. Wang, and D. Y. Chen, Coupled-channel interactions and the origin of , Phys. Rev. D 108, 074006 (2023).
- F. L. Wang and X. Liu, Five-flavor molecular pentaquarks in the and systems, Phys. Rev. D 113, 094037 (2026).
- J. Song, Z. Y. Yang, and E. Oset, Searching for the partner of the in the reaction, Phys. Rev. D 111, 094004 (2025).
- Z. Yu, Q. Wu, Z. L. Yue, and D. Y. Chen, production in the decays processes, Eur. Phys. J. C 86, 787 (2026).
- J. D. E. Yeo, C. E. Thomas, and D. J. Wilson, Exotic and states and coupled-channel scattering at the flavour symmetric point from lattice QCD, arXiv:2604.19553.
- X. H. Liu, M. J. Yan, H. W. Ke, G. Li, and J. J. Xie, Triangle singularity as the origin of and observed in , Eur. Phys. J. C 80, 1178 (2020).
- Y. H. Ge, X. H. Liu, and H. W. Ke, Possibility of as the resonance-like structure induced by threshold effects, Eur. Phys. J. C 82, 955 (2022).
- T. J. Burns and E. S. Swanson, Kinematical cusp and resonance interpretations of the , Phys. Lett. B 813, 136057 (2021).
- J. B. Cheng, S. Y. Li, Y. R. Liu, Y. N. Liu, Z. G. Si, and T. Yao, Spectrum and rearrangement decays of tetraquark states with four different flavors, Phys. Rev. D 101, 114017 (2020).
- J. Wu, Y. R. Liu, K. Chen, X. Liu, and S. L. Zhu, , , and and their tetraquark partners, Phys. Rev. D 94, 094031 (2016).
- S. Y. Li, Y. R. Liu, Y. N. Liu, Z. G. Si, and J. Wu, Pentaquark states with the configuration in a simple model, Eur. Phys. J. C 79, 87 (2019).
- J. Wu, X. Liu, Y. R. Liu, and S. L. Zhu, Systematic studies of charmonium-, bottomonium-, and -like tetraquark states, Phys. Rev. D 99, 014037 (2019).
- 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).
- J. Wu, Y. R. Liu, K. Chen, X. Liu, and S. L. Zhu, Hidden-charm pentaquarks and their hidden-bottom and -like partner states, Phys. Rev. D 95, 034002 (2017).
- J. Wu, Y. R. Liu, K. Chen, X. Liu, and S. L. Zhu, Heavy-flavored tetraquark states with the configuration, Phys. Rev. D 97, 094015 (2018).
- S. Y. Li, Y. R. Liu, Z. L. Man, Z. G. Si, and J. Wu, , , and other compact states, Chin. Phys. C 48, 063109 (2024).
- S. Y. Li, Y. R. Liu, Z. L. Man, Z. G. Si, and J. Wu, Hidden-charm pentaquark states in a mass splitting model, Phys. Rev. D 108, 056015 (2023).
- S. Y. Li, Y. R. Liu, Z. L. Man, C. R. Shu, Z. G. Si, and J. Wu, Triply heavy tetraquark states in a mass-splitting model, Symmetry 17, 170 (2025).
- S. Y. Li, Y. R. Liu, Z. L. Man, Z. G. Si, and J. Wu, Doubly heavy tetraquark states in a mass splitting model, Phys. Rev. D 110, 094044 (2024).
- H. Høgaasen, E. Kou, J. M. Richard, and P. Sorba, Isovector and hidden-beauty partners of the , Phys. Lett. B 732, 97 (2014).
- X. Z. Weng, X. L. Chen, and W. Z. Deng, Masses of doubly heavy-quark baryons in an extended chromomagnetic model, Phys. Rev. D 97, 054008 (2018).
- T. Hyodo, Y. R. Liu, M. Oka, K. Sudoh, and S. Yasui, Production of doubly charmed tetraquarks with exotic color configurations in electron-positron collisions, Phys. Lett. B 721, 56 (2013).
- K. Chen, X. Liu, J. Wu, Y. R. Liu, and S. L. Zhu, Triply heavy tetraquark states with the configuration, Eur. Phys. J. A 53, 5 (2017).
- S. Q. Luo, K. Chen, X. Liu, Y. R. Liu, and S. L. Zhu, Exotic tetraquark states with the configuration, Eur. Phys. J. C 77, 709 (2017).
- Q. S. Zhou, K. Chen, X. Liu, Y. R. Liu, and S. L. Zhu, Surveying exotic pentaquarks with the typical configuration, Phys. Rev. C 98, 045204 (2018).
- T. Aaltonen et al. (CDF Collaboration), Observation of the structure in the mass spectrum in decays, Mod. Phys. Lett. A 32, 1750139 (2017).
- R. Aaij et al. (LHCb Collaboration), Observation of new resonances decaying to and , Phys. Rev. Lett. 127, 082001 (2021).
- F. Stancu, Can be a tetraquark?, J. Phys. G 37, 075017 (2010); 46, 019501(E) (2019).
- J. B. Cheng and Y. R. Liu, , , and : Molecules or compact pentaquarks?, Phys. Rev. D 100, 054002 (2019).
- S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
- F. S. Yu, Weak-decay searches for tetraquarks Eur. Phys. J. C 82, 641 (2022).