Open Access

Existence of the $D D^{} {\bar{K}}^{}$ and $B B^{} K^{}$ three-body molecular states

Yan-Ke Chen ¹, Lu Meng ^2,*, Jun-Zhang Wang ^3,†, and Shi-Lin Zhu ^1,‡

¹School of Physics and Center of High Energy Physics, Peking University, Beijing 100871, China
²School of Physics, Southeast University, Nanjing 211189, China
³Department of Physics and Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, Chongqing 401331, China

^*Contact author: lmeng@seu.edu.cn
^†Contact author: wangjzh@cqu.edu.cn
^‡Contact author: zhusl@pku.edu.cn

Phys. Rev. D 114, 014048 – Published 22 July, 2026

DOI: https://doi.org/10.1103/xxsq-d5sm

Abstract

We investigate the existence of the three-body molecular state composed of $D D^{*} {\bar{K}}^{*}$ within the one-boson-exchange model. A major challenge is that while the pseudoscalar-meson couplings are well determined, the couplings for scalar- and vector-meson exchanges render significant model dependence. To ensure the reliability of our predictions and reduce model dependence, we recalibrate the coupling constants of the one-boson-exchange model. We treat the pole position of $Z_{c} (3900)$ , or equivalently the scalar $σ$ -exchange coupling constant, as the only unknown parameter. The coupling constants for the vector $ρ$ and $ω$ exchanges are determined by the pole positions of the well-established states $X (3872)$ and $T_{c c} (3875)$ . We demonstrate that these parameter sets also successfully describe the $T_{c s 0} (2870)$ without further tuning. For the three-body system, our results indicate that an $I (J^{P}) = 1 / 2 (0^{-})$ three-body molecular bound state exists when $Z_{c} (3900)$ is a virtual state located within approximately $- 10 MeV$ of the $D {\bar{D}}^{*}$ threshold. Furthermore, we extend our analysis to the complex energy plane using the complex scaling method to search for molecular resonances, though no evidence of resonances is found in considered channels. We also apply this formalism to the bottom analog $B B^{*} K^{*}$ system. In this sector, the conditions for the existence of a three-body bound state are more relaxed, as a $Z_{c} (3900)$ virtual state located within $- 25 MeV$ below the threshold suffices, although three-body molecular resonances remain absent. We suggest that future experiments precisely measure the pole position of $Z_{c} (3900)$ or search for the three-body bound state in $D D \bar{K} π π$ and $D D \bar{K}$ channels, as these efforts would mutually illuminate the nature of the associated states.

Physics Subject Headings (PhySH)

Article Text

References (117)

H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, The hidden-charm pentaquark and tetraquark states, Phys. Rep. 639, 1 (2016).
A. Esposito, A. Pilloni, and A. D. Polosa, Multiquark resonances, Phys. Rep. 668, 1 (2017).
R. F. Lebed, R. E. Mitchell, and E. S. Swanson, Heavy-quark QCD exotica, Prog. Part. Nucl. Phys. 93, 143 (2017).
A. Ali, J. S. Lange, and S. Stone, Exotics: Heavy pentaquarks and tetraquarks, Prog. Part. Nucl. Phys. 97, 123 (2017).
F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, and B.-S. Zou, Hadronic molecules, Rev. Mod. Phys. 90, 015004 (2018); 94, 029901(E) (2022).
S. L. Olsen, T. Skwarnicki, and D. Zieminska, Nonstandard heavy mesons and baryons: Experimental evidence, Rev. Mod. Phys. 90, 015003 (2018).
M. Karliner, J. L. Rosner, and T. Skwarnicki, Multiquark states, Annu. Rev. Nucl. Part. Sci. 68, 17 (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 $X Y Z$ states: Experimental and theoretical status and perspectives, Phys. Rep. 873, 1 (2020).
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).
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).
T.-W. Wu, Y.-W. Pan, M.-Z. Liu, and L.-S. Geng, Multi-hadron molecules: Status and prospect, Sci. Bull. 67, 1735 (2022).
S. K. Choi et al. (Belle Collaboration), Observation of a narrow charmonium-like state in exclusive $B^{\pm} \to K^{\pm} π^{+} π^{-} J / ψ$ decays, Phys. Rev. Lett. 91, 262001 (2003).
M. Ablikim et al. (BESIII Collaboration), Observation of a charged charmoniumlike structure in $e^{+} e^{-} \to π^{+} π^{-} J / ψ$ at $\sqrt{s} = 4.26 GeV$ , Phys. Rev. Lett. 110, 252001 (2013).
Z. Q. Liu et al. (Belle Collaboration), Study of $e^{+} e^{-} \to π^{+} π^{-} J / ψ$ and observation of a charged charmoniumlike state at Belle, Phys. Rev. Lett. 110, 252002 (2013); 111, 019901(E) (2013).
R. Aaij et al. (LHCb Collaboration), A model-independent study of resonant structure in $B^{+} \to D^{+} D^{-} K^{+}$ decays, Phys. Rev. Lett. 125, 242001 (2020).
R. Aaij et al. (LHCb Collaboration), Amplitude analysis of the $B^{+} \to D^{+} D^{-} K^{+}$ decay, Phys. Rev. D 102, 112003 (2020).
R. Aaij et al. (LHCb Collaboration), Observation of new charmonium or charmoniumlike states in $B^{+} \to D^{* \pm} D^{\mp} K^{+}$ decays, Phys. Rev. Lett. 133, 131902 (2024).
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 $T_{c c}^{+}$ , Nat. Commun. 13, 3351 (2022).
S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
Q.-H. Shen and J.-J. Xie, Faddeev fixed-center approximation to the $η K^{*} {\bar{K}}^{*}$ , $π K^{*} {\bar{K}}^{*}$ , and $K K^{*} \bar{K}$ systems, Phys. Rev. D 107, 034019 (2023).
X. Zhang, C. Hanhart, U.-G. Meißner, and J.-J. Xie, Remarks on non-perturbative three–body dynamics and its application to the $K K \bar{K}$ system, Eur. Phys. J. A 58, 20 (2022).
T.-W. Wu, Y.-W. Pan, M.-Z. Liu, S.-Q. Luo, L.-S. Geng, and X. Liu, Discovery of the doubly charmed $T_{c c}^{+}$ state implies a triply charmed $H_{c c c}$ hexaquark state, Phys. Rev. D 105, L031505 (2022).
S.-Q. Luo, T.-W. Wu, M.-Z. Liu, L.-S. Geng, and X. Liu, Triple-charm molecular states composed of $D^{*} D^{*} D$ and $D^{*} D^{*} D^{*}$ , Phys. Rev. D 105, 074033 (2022).
M. Bayar, A. Martinez Torres, K. P. Khemchandani, R. Molina, and E. Oset, Exotic states with triple charm, Eur. Phys. J. C 83, 46 (2023).
Y.-W. Pan, T.-W. Wu, M.-Z. Liu, and L.-S. Geng, Hadronic molecules composed of a doubly charmed tetraquark state and a charmed meson, Eur. Phys. J. C 82, 908 (2022).
P. G. Ortega, Exploring the Efimov effect in the $D^{*} D^{*} D^{*}$ system, Phys. Rev. D 110, 034015 (2024).
H.-L. Fu, Y.-H. Lin, F.-K. Guo, H.-W. Hammer, U.-G. Meißner, A. Rusetsky, and X. Zhang, Exploring Efimov states in $D^{*} D^{*} D^{*}$ and ${DD}^{*} D^{*}$ three-body systems, J. High Energy Phys. 07 (2025) 081.
Y. Tan, X. Liu, X. Chen, Y. Yang, H. Huang, and J. Ping, Dynamical study of $D^{*} D K$ and $D^{*} D \bar{D}$ systems at quark level, Phys. Rev. D 110, 016005 (2024).
M. P. Valderrama, $D^{*} D^{*} \bar{D}$ and $D^{*} D^{*} {\bar{D}}^{*}$ three-body systems, Phys. Rev. D 98, 034017 (2018).
J. M. Dias, L. Roca, and S. Sakai, Prediction of new states from $D^{(*)} B^{(*)} {\bar{B}}^{(*)}$ three-body interactions, Phys. Rev. D 97, 056019 (2018).
L. Ma, Q. Wang, and U.-G. Meißner, Trimeson bound state $B B B^{*}$ via a delocalized $π$ bond, Phys. Rev. D 100, 014028 (2019).
L. Ma, Q. Wang, and U.-G. Meißner, Double heavy tri-hadron bound state via delocalized $π$ bond, Chin. Phys. C 43, 014102 (2019).
X.-L. Ren, B. B. Malabarba, L.-S. Geng, K. P. Khemchandani, and A. Martínez Torres, $K^{*}$ mesons with hidden charm arising from $K X (3872)$ and $K Z_{c} (3900)$ dynamics, Phys. Lett. B 785, 112 (2018).
X.-L. Ren and Z.-F. Sun, Possible bound states with hidden bottom from ${\bar{K}}^{(*)} B^{(*)} {\bar{B}}^{(*)}$ systems, Phys. Rev. D 99, 094041 (2019).
T.-W. Wu, M.-Z. Liu, L.-S. Geng, E. Hiyama, and M. P. Valderrama, $D K$ , $D D K$ , and $D D D K$ molecules–understanding the nature of the $D_{s 0}^{*} (2317)$ , Phys. Rev. D 100, 034029 (2019).
Z.-Y. Di and Z.-G. Wang, Analysis of the $D {\bar{D}}^{*} K$ system with QCD sum rules, Adv. High Energy Phys. 2019, 8958079 (2019).
N. Ikeno, M. Bayar, and E. Oset, Molecular states of $D^{*} D^{*} {\bar{K}}^{*}$ nature, Phys. Rev. D 107, 034006 (2023).
Z. Zhang, X.-Y. Hu, G. He, J. Liu, J.-A. Shi, B.-N. Lu, and Q. Wang, Binding of the three-hadron $D D^{*} K$ system from the lattice effective field theory, Phys. Rev. D 111, 036002 (2025).
Q.-Y. Zhai, R. Molina, E. Oset, and L.-S. Geng, Study of the exotic three-body $N D^{*} {\bar{K}}^{*}$ system, Phys. Rev. D 111, 034039 (2025).
X.-L. Ren, K. P. Khemchandani, and A. Martínez Torres, Heavy $K^{*}$ mesons with open charm from $K D^{(*)} D^{*}$ interactions, Eur. Phys. J. C 84, 1297 (2024).
Y.-W. Pan, J.-X. Lu, E. Hiyama, L.-S. Geng, and A. Hosaka, Effect of a repulsive three-body interaction on the $D D^{(*)} K$ molecule, Phys. Rev. D 111, 114006 (2025).
D. L. Canham, H. W. Hammer, and R. P. Springer, On the scattering of $D$ and $D^{*}$ mesons off the X(3872), Phys. Rev. D 80, 014009 (2009).
Y.-H. Lin, E. Wilbring, H.-L. Fu, H.-W. Hammer, and U.-G. Meißner, Three-body universality in the $B$ meson sector, J. Phys. G 52, 105005 (2025).
A. Martinez Torres, K. P. Khemchandani, L. Roca, and E. Oset, Few-body systems consisting of mesons, Few Body Syst. 61, 35 (2020).
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).
R. Molina, T. Branz, and E. Oset, A new interpretation for the $D_{s 2}^{*} (2573)$ and the prediction of novel exotic charmed mesons, Phys. Rev. D 82, 014010 (2010).
H.-X. Chen, W. Chen, R.-R. Dong, and N. Su, $X_{0} (2900)$ and $X_{1} (2900)$ : Hadronic molecules or compact tetraquarks, Chin. Phys. Lett. 37, 101201 (2020).
J. He and D.-Y. Chen, Molecular picture for $X_{0} (2900)$ and $X_{1} (2900)$ , Chin. Phys. C 45, 063102 (2021).
M.-Z. Liu, J.-J. Xie, and L.-S. Geng, $X_{0} (2866)$ as a $D^{*} {\bar{K}}^{*}$ molecular state, Phys. Rev. D 102, 091502 (2020).
M.-W. Hu, X.-Y. Lao, P. Ling, and Q. Wang, $X_{0} (2900)$ and its heavy quark spin partners in molecular picture, Chin. Phys. C 45, 021003 (2021).
S. S. Agaev, K. Azizi, and H. Sundu, New scalar resonance $X_{0} (2900)$ as a molecule: Mass and width, J. Phys. G 48, 085012 (2021).
B. Wang and S.-L. Zhu, How to understand the X(2900)?, Eur. Phys. J. C 82, 419 (2022).
P. G. Ortega, D. R. Entem, F. Fernandez, and J. Segovia, Novel $T_{c s}$ and $T_{c \bar{s}}$ candidates in a constituent-quark-model-based meson-meson coupled-channels calculation, Phys. Rev. D 108, 094035 (2023).
B. Wang, K. Chen, L. Meng, and S.-L. Zhu, Spectrum of the molecular tetraquarks: Unraveling the $T_{c s 0} (2900)$ and $T_{c \bar{s} 0}^{a} (2900)$ , Phys. Rev. D 109, 034027 (2024).
N. A. Tornqvist, Possible large deuteron—like meson meson states bound by pions, Phys. Rev. Lett. 67, 556 (1991).
N. A. Tornqvist, From the deuteron to deusons, an analysis of deuteron—like meson meson bound states, Z. Phys. C 61, 525 (1994).
D. Gamermann, E. Oset, D. Strottman, and M. J. Vicente Vacas, Dynamically generated open and hidden charm meson systems, Phys. Rev. D 76, 074016 (2007).
Y.-R. Liu, X. Liu, W.-Z. Deng, and S.-L. Zhu, Is $X (3872)$ really a molecular state?, Eur. Phys. J. C 56, 63 (2008).
X. Liu, Y.-R. Liu, W.-Z. Deng, and S.-L. Zhu, $Z^{+} (4430)$ as a $D_{1}^{'} D^{*} (D_{1} D^{*})$ molecular state, Phys. Rev. D 77, 094015 (2008).
C. E. Thomas and F. E. Close, Is X(3872) a molecule?, Phys. Rev. D 78, 034007 (2008).
X. Liu, Z.-G. Luo, Y.-R. Liu, and S.-L. Zhu, X(3872) and other possible heavy molecular states, Eur. Phys. J. C 61, 411 (2009).
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).
I. W. Lee, A. Faessler, T. Gutsche, and V. E. Lyubovitskij, X(3872) as a molecular $D D^{*}$ state in a potential model, Phys. Rev. D 80, 094005 (2009).
Z.-F. Sun, J. He, X. Liu, Z.-G. Luo, and S.-L. Zhu, $Z_{b} (10610)^{\pm}$ and $Z_{b} (10650)^{\pm}$ as the $B^{*} \bar{B}$ and $B^{*} {\bar{B}}^{*}$ molecular states, Phys. Rev. D 84, 054002 (2011).
N. Li and S.-L. Zhu, Isospin breaking, coupled-channel effects and Diagnosis of X(3872), Phys. Rev. D 86, 074022 (2012).
N. Li, Z.-F. Sun, X. Liu, and S.-L. Zhu, Coupled-channel analysis of the possible $D^{(*)} D^{(*)}, {\bar{B}}^{(*)} {\bar{B}}^{(*)}$ and $D^{(*)} {\bar{B}}^{(*)}$ molecular states, Phys. Rev. D 88, 114008 (2013).
R. Chen, A. Hosaka, and X. Liu, Heavy molecules and one- $σ / ω$ -exchange model, Phys. Rev. D 96, 116012 (2017).
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 X(3872) revisited: What can we learn from the one boson exchange model?, Phys. Rev. D 99, 094018 (2019).
R. Chen and Q. Huang, $Z_{c s} (3985)^{-}$ : A strange hidden-charm tetraquark resonance or not?, Phys. Rev. D 103, 034008 (2021).
R. Chen, Q. Huang, X. Liu, and S.-L. Zhu, Predicting another doubly charmed molecular resonance $T_{c c}^{' +} (3876)$ , Phys. Rev. D 104, 114042 (2021).
X.-K. Dong, F.-K. Guo, and B.-S. Zou, A survey of heavy–heavy hadronic molecules, Commun. Theor. Phys. 73, 125201 (2021).
X.-K. Dong, F.-K. Guo, and B.-S. Zou, A survey of heavy-antiheavy hadronic molecules, Prog. Phys. 41, 65 (2021).
Z.-Y. Lin, J.-B. Cheng, and S.-L. Zhu, $T_{c c}^{+}$ and $χ_{c 1} (3872)$ with the complex scaling method and $D D (\bar{D}) π$ three-body effect, Phys. Rev. D 110, 054008 (2024).
J.-B. Cheng, Z.-Y. Lin, and S.-L. Zhu, Double-charm tetraquark under the complex scaling method, Phys. Rev. D 106, 016012 (2022).
F.-Z. Peng, M.-J. Yan, and M. Pavon Valderrama, Heavy- and light-flavor symmetry partners of the $T_{c c}^{+} (3875)$ , the $X (3872)$ , and the $X (3960)$ from light-meson exchange saturation, Phys. Rev. D 108, 114001 (2023).
Z.-Y. Lin, J.-Z. Wang, J.-B. Cheng, L. Meng, and S.-L. Zhu, Identification of the $G (3900)$ as the P-wave $D {\bar{D}}^{*} / \bar{D} D^{*}$ resonance, Phys. Rev. Lett. 133, 241903 (2024).
J.-Z. Wang, Z.-Y. Lin, B. Wang, L. Meng, and S.-L. Zhu, Double pole structures of $X_{1} (2900)$ as the $P$ -wave ${\bar{D}}^{*} K^{*}$ resonances, Phys. Rev. D 110, 114003 (2024).
J.-Z. Wang, Z.-Y. Lin, J.-B. Cheng, L. Meng, and S.-L. Zhu, Emergence of new heavy quarkoniumlike states: $Y (10600)$ and $Y (10650)$ , arXiv:2505.02742.
J.-B. Cheng, Z.-Y. Lin, J.-Z. Wang, and S.-L. Zhu, Decoding $Z_{c} (4430)$ and $Z_{c} (4200)$ : The role of $P$ -wave charmed mesons, Phys. Rev. D 113, 096001 (2026).
H.-X. Zhu, L. Meng, Y. Ma, N. Li, W. Chen, and S.-L. Zhu, Constraining the $D D D^{*}$ three-body bound state via the $Z_{c} (3900)$ pole, Phys. Rev. D 111, 094022 (2025).
E. Hiyama, Y. Kino, and M. Kamimura, Gaussian expansion method for few-body systems, Prog. Part. Nucl. Phys. 51, 223 (2003).
J. Aguilar and J. M. Combes, A class of analytic perturbations for one-body Schroedinger Hamiltonians, Commun. Math. Phys. 22, 269 (1971).
E. Balslev and J. M. Combes, Spectral properties of many-body Schroedinger operators with dilatation-analytic interactions, Commun. Math. Phys. 22, 280 (1971).
N. Moiseyev, Quantum theory of resonances: Calculating energies, widths and cross-sections by complex scaling, Phys. Rep. 302, 212 (1998).
S. Aoyama, T. Myo, K. Katō, and K. Ikeda, The complex scaling method for many-body resonances and its applications to three-body resonances, Prog. Theor. Phys. 116, 1 (2006).
H. Georgi, Comment on heavy baryon weak form-factors, Nucl. Phys. B348, 293 (1991).
T. Mannel, W. Roberts, and Z. Ryzak, Baryons in the heavy quark effective theory, Nucl. Phys. B355, 38 (1991).
A. F. Falk, Hadrons of arbitrary spin in the heavy quark effective theory, Nucl. Phys. B378, 79 (1992).
M. B. Wise, Chiral perturbation theory for hadrons containing a heavy quark, Phys. Rev. D 45, R2188 (1992).
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).
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).
C. Isola, M. Ladisa, G. Nardulli, and P. Santorelli, Charming penguins in $B \to K^{*} π$ , $K (ρ, ω, ϕ)$ decays, Phys. Rev. D 68, 114001 (2003).
M. Albaladejo, F.-K. Guo, C. Hidalgo-Duque, and J. Nieves, $Z_{c} (3900)$ : What has been really seen?, Phys. Lett. B 755, 337 (2016).
A. Pilloni, C. Fernandez-Ramirez, A. Jackura, V. Mathieu, M. Mikhasenko, J. Nys, and A. P. Szczepaniak (JPAC Collaboration), Amplitude analysis and the nature of the $Z_{c} (3900)$ , Phys. Lett. B 772, 200 (2017).
S. X. Nakamura, X. H. Li, H. P. Peng, Z. T. Sun, and X. R. Zhou, Global coupled-channel analysis of $e^{+} e^{-} \to c \bar{c}$ processes in $\sqrt{s} = 3.75$ to 4.7 GeV, Phys. Rev. D 112, 054027 (2025).
K. Yu, G.-J. Wang, J.-J. Wu, and Z. Yang, Three-coupled-channel analysis of $Z_{c} (3900)$ involving $D {\bar{D}}^{*}$ , $π J / ψ$ , and $ρ η c$ , Phys. Rev. D 110, 114029 (2024).
Y.-H. Chen, M.-L. Du, and F.-K. Guo, Precise determination of the pole position of the exotic $Z_{c} (3900)$ , Sci. China Phys. Mech. Astron. 67, 291011 (2024).
N. Kalantar-Nayestanaki, E. Epelbaum, J. G. Messchendorp, and A. Nogga, Signatures of three-nucleon interactions in few-nucleon systems, Rep. Prog. Phys. 75, 016301 (2012).
E. Epelbaum and J. Gegelia, Regularization, renormalization and ‘peratization’ in effective field theory for two nucleons, Eur. Phys. J. A 41, 341 (2009).
R. Machleidt and D. R. Entem, Chiral effective field theory and nuclear forces, Phys. Rep. 503, 1 (2011).
U. van Kolck, Few nucleon forces from chiral Lagrangians, Phys. Rev. C 49, 2932 (1994).
H.-W. Hammer, A. Nogga, and A. Schwenk, Three-body forces: From cold atoms to nuclei, Rev. Mod. Phys. 85, 197 (2013).
Y.-W. Pan, M.-Z. Liu, and L.-S. Geng, Probing the three-body force in hadronic systems with specific charge parity, Phys. Rev. Lett. 136, 151901 (2026).
Q. Meng, E. Hiyama, A. Hosaka, M. Oka, P. Gubler, K. U. Can, T. T. Takahashi, and H. S. Zong, Stable double-heavy tetraquarks: Spectrum and structure, Phys. Lett. B 814, 136095 (2021).
L. Meng, Y.-K. Chen, Y. Ma, and S.-L. Zhu, Tetraquark bound states in constituent quark models: Benchmark test calculations, Phys. Rev. D 108, 114016 (2023).
J. Carbonell, A. Deltuva, A. C. Fonseca, and R. Lazauskas, Bound state techniques to solve the multiparticle scattering problem, Prog. Part. Nucl. Phys. 74, 55 (2014).
E. Hiyama, R. Lazauskas, J. Carbonell, and M. Kamimura, Possibility of generating a 4-neutron resonance with a $T = 3 / 2$ isospin 3-neutron force, Phys. Rev. C 93, 044004 (2016).
A. Doté, T. Inoue, and T. Myo, Fully coupled-channel study of $K^{-} p p$ resonance in a chiral SU(3)-based $\bar{K} N$ potential, Phys. Lett. B 784, 405 (2018).
L. Happ, P. Naidon, and E. Hiyama, Mass ratio dependence of three-body resonance lifetimes in 1D and 3D, Few Body Syst. 65, 38 (2024).
Y.-K. Chen, L. Meng, Z.-Y. Lin, and S.-L. Zhu, Virtual states in the coupled-channel problems with an improved complex scaling method, Phys. Rev. D 109, 034006 (2024).
Y.-K. Chen, W.-L. Wu, L. Meng, and S.-L. Zhu, Unified description of the $Q s \bar{q} \bar{q}$ molecular bound states, molecular resonances, and compact tetraquark states in the quark potential model, Phys. Rev. D 109, 014010 (2024).
Q. Meng, G.-J. Wang, and M. Oka, Mass spectra of full-heavy and double-heavy tetraquark states in the conventional quark model, Phys. Rev. D 111, 014018 (2025).
Y. Ma, W.-L. Wu, L. Meng, Y.-K. Chen, and S.-L. Zhu, Fully strange tetraquark resonant states as the cousins of X(6900), Phys. Rev. D 110, 074026 (2024).
W.-L. Wu, Y.-K. Chen, L. Meng, and S.-L. Zhu, Benchmark calculations of fully heavy compact and molecular tetraquark states, Phys. Rev. D 109, 054034 (2024).
W.-L. Wu, Y. Ma, Y.-K. Chen, L. Meng, and S.-L. Zhu, Doubly heavy tetraquark bound and resonant states, Phys. Rev. D 110, 094041 (2024).

Phys. Rev. D 114, 014048– Published 22 July, 2026

Vol. 114, Iss. 1 — 1 July 2026

Received 6 March 2026
Accepted 12 June 2026

DOI: https://doi.org/10.1103/xxsq-d5sm

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physical Review D

Reuse & Permissions

Export citation

Export citation

Existence of the $D D^{} {\bar{K}}^{}$ and $B B^{} K^{}$ three-body molecular states

Abstract

Physics Subject Headings (PhySH)

Article Text

References (117)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

Existence of the DD*K¯* and BB*K* three-body molecular states

Abstract

Physics Subject Headings (PhySH)

Article Text

References (117)

Existence of the $D D^{} {\bar{K}}^{}$ and $B B^{} K^{}$ three-body molecular states