RECORD
Existence of the $DD^*\bar{K}^*$ and $BB^*K^*$ three-body molecular states
High Energy Physics - Phenomenology · Submitted 12 Feb 2026
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim For the three-body system, our results indicate that an $I\left(J^P\right)=1 / 2\left(0^{-}\right)$ three-body molecular bound state exists when $Z_c(3900)$ is a virtual state located within approximately $-10~\text{MeV}$ of the $D\bar{D}^*$ threshold.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
We investigate the existence of the three-body molecular state composed of $DD^*\bar{K}^*$ within the one-boson-exchange (OBE) 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 OBE model. We treat the pole position of $Z_c(3900)$, or equivalently the scalar $\sigma$-exchange coupling constant, as the only unknown parameter. The coupling constants for the vector $\rho$- and $\omega$-exchanges are determined by the pole positions of the well established states $X(3872)$ and $T_{cc}(3875)$. We demonstrate that these parameter sets also successfully describe the $T_{cs0}(2870)$ without further tuning. For the three-body system, our results indicate that an $I\left(J^P\right)=1 / 2\left(0^{-}\right)$ three-body molecular bound state exists when $Z_c(3900)$ is a virtual state located within approximately $-10~\text{MeV}$ 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 $BB^*K^*$ 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 $-25~\text{MeV}$ 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 $DD\bar{K}\pi\pi$ and $DD\bar{K}$ channels, as these efforts would mutually illuminate the nature of the associated states.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We investigate the existence of the three-body molecular state composed of $DD^*\bar{K}^*$ within the one-boson-exchange (OBE) model. | contribution 0.99 | 0.91 | 0.03 | unclear 0.87 |
| s1 | 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. | background 0.53 | 0.11 | 0.02 | asserted 1.00 |
| s2 | To ensure the reliability of our predictions and reduce model dependence, we recalibrate the coupling constants of the OBE model. | method 0.82 | 0.94 | 0.02 | asserted 0.94 |
| s3 | We treat the pole position of $Z_c(3900)$, or equivalently the scalar $\sigma$-exchange coupling constant, as the only unknown parameter. | method 0.97 | 0.83 | 0.03 | asserted 0.99 |
| s4 | The coupling constants for the vector $\rho$- and $\omega$-exchanges are determined by the pole positions of the well established states $X(3872)$ and $T_{cc}(3875)$. | method 0.97 | 0.76 | 0.02 | asserted 1.00 |
| s5 | We demonstrate that these parameter sets also successfully describe the $T_{cs0}(2870)$ without further tuning. | result 0.93 | 0.90 | 0.05 | asserted 1.00 |
| s6 | For the three-body system, our results indicate that an $I\left(J^P\right)=1 / 2\left(0^{-}\right)$ three-body molecular bound state exists when $Z_c(3900)$ is a virtual state located within approximately $-10~\text{MeV}$ of the $D\bar{D}^*$ threshold. | result 1.00 | 0.94 | 0.70 | hedged possibility 0.76 |
| s7 | 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. | result 0.66 | 0.96 | 0.06 | asserted 0.99 |
| s8 | We also apply this formalism to the bottom analog $BB^*K^*$ system. | contribution 0.98 | 0.93 | 0.03 | asserted 0.92 |
| s9 | 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 $-25~\text{MeV}$ below the threshold suffices, although three-body molecular resonances remain absent. | result 1.00 | 0.94 | 0.14 | asserted 0.89 |
| s10 | We suggest that future experiments precisely measure the pole position of $Z_c(3900)$ or search for the three-body bound state in $DD\bar{K}\pi\pi$ and $DD\bar{K}$ channels, as these efforts would mutually illuminate the nature of the associated states. | future work 1.00 | 0.12 | 0.10 | hedged possibility 0.98 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
We investigate the existence of the three-body molecular state composed of $DD^*\bar{K}^*$ within the one-boson-exchange (OBE) 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 OBE model. We treat the pole position of $Z_c(3900)$, or equivalently the scalar $\sigma$-exchange coupling constant, as the only unknown parameter. The coupling constants for the vector $\rho$- and $\omega$-exchanges are determined by the pole positions of the well established states $X(3872)$ and $T_{cc}(3875)$. We demonstrate that these parameter sets also successfully describe the $T_{cs0}(2870)$ without further tuning. For the three-body system, our results indicate that an $I\left(J^P\right)=1 / 2\left(0^{-}\right)$ three-body molecular bound state exists when $Z_c(3900)$ is a virtual state located within approximately $-10~\text{MeV}$ 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 $BB^*K^*$ 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 $-25~\text{MeV}$ 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 $DD\bar{K}\pi\pi$ and $DD\bar{K}$ channels, as these efforts would mutually illuminate the nature of the associated states.
Human review
References
How the literature uses it
2 arXiv papers cite this in 2 sentences
Papers citing it · 1 sentence without a confident label
Cites it as background 1 paper
-
Furthermore, $BK$, as the heavy-flavor partner of $DK$, has also been the subject of several dedicated investigations [ref] .
Coupled-channel study of the three-body $DDK$ and $D^{*}D^{*}K$ · Introduction · 0.95
What it cites · 67 sentences without a confident label
Uses the method or tool of 13 papers
-
To address the model dependence and make theoretical predictions more reliable, we adopt the approach from Ref. [ref] to recalibrate the model parameters.
Constraining the $DDD^*$ three-body bound state via the $Z_c(3900)$ pole · Introduction · 0.98
-
The combination of the GEM and the CSM has proven to be a powerful tool for investigating few-body resonances [ref] .
Bound state techniques to solve the multiparticle scattering problem · Methodology · 0.87
-
The combination of the GEM and the CSM has proven to be a powerful tool for investigating few-body resonances [ref] .
Fully coupled-channel study of $K^-pp$ resonance in a chiral SU(3)-based $\bar{K}N$ potential · Methodology · 0.87
Uses data or values from 3 papers
-
The values in the table are adopted from Refs. [ref] as a baseline, which are determined using vector meson dominance combined with results from lattice QCD and light cone sum rules [ref] .
Isospin breaking, coupled-channel effects, and X(3872) · Effective Lagrangians and potentials · 1.00
-
The values in the table are adopted from Refs. [ref] as a baseline, which are determined using vector meson dominance combined with results from lattice QCD and light cone sum rules [ref] .
Coupled-channel analysis of the possible $D^{(*)}D^{(*)}$, $\bar{B}^{(*)}\bar{B}^{(*)}$ and $D^{(*)}\bar{B}^{(*)}$ molecular states · Effective Lagrangians and potentials · 1.00
-
The values in the table are adopted from Refs. [ref] as a baseline, which are determined using vector meson dominance combined with results from lattice QCD and light cone sum rules [ref] .
Charming penguins in B => K* pi, K (rho,omega,phi) decays · Effective Lagrangians and potentials · 1.00
Cites as background 44 papers
-
Furthermore, three-body universality in the charmed and bottom sectors was investigated in Refs. [ref] .
Three-body universality in the B meson sector · Introduction · 0.93
-
Furthermore, three-body universality in the charmed and bottom sectors was investigated in Refs. [ref] .
On the scattering of D and D* mesons off the X(3872) · Introduction · 0.93
-
Theoretical studies of three-body hadronic molecules have been conducted on various systems, including three light-mesons [ref] , $D^(*)D^(*)D^(*)$ [ref] , $D^(*)D^(*)D̅^(*)$ [ref] , $D^(*)B^(*)B̅^(*)$ [ref] , $BBB^*$ [ref] , and systems where kaons replace one or more heavy mesons [ref] .
Discovery of the doubly charmed $T_{cc}^+$ state implies a triply charmed $H_{ccc}$ hexaquark state · Introduction · 0.95
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.