Pith. sign in

REVIEW 3 major objections 4 minor 2 cited by

Implication of the existence of $J^{PC}=0^{--}$ $\bar{D}_sDK$ bound state on nature of $D_{s0}^*(2317)$ and new configuration of exotic state

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper predicts that three mesons—$\bar D_s$, $D$, and $K$—bind into a $J^{PC}=0^{--}$ hadronic molecule at about 4310 MeV, decoupled from ordinary quarkonium and searchable in LHCb data.

desk verdict A genuinely exotic three-body molecule prediction with a clean search channel, but the binding rests on weakly constrained input potentials; worth refereeing, not yet a secure prediction. read the letter →

arxiv 2501.11358 v2 pith:7WHU6ODN submitted 2025-01-20 hep-ph

Tian-Wei Wu , Ming-Zhu Liu , Li-Sheng Geng This is my paper · ORCID
classification hep-ph
keywords hadronicmoleculethree-bodyboundstateD_s0*(2317)exotichadronJ^PC=0^BmesondecaysLHCbsearchcontact-rangeEFT
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper's central claim is that the $\bar D_s D K$ three-meson system forms a bound hadronic molecule with quantum numbers $J^{PC}=0^{--}$, a combination that ordinary quark-antiquark charmonia cannot have. The predicted mass is about $4310^{+14}_{-24}$ MeV, roughly 21 MeV below the $\bar D_s D K$ threshold, and the state is dominated by a $DK$ pair bound to a $\bar D_s$. Because $0^{--}$ is exotic and the state does not mix with conventional charmonia or with the two-body $\bar D_s D_{s0}^*(2317)$ molecule, it would be a clean test of the hadronic-molecule idea. The paper also shows that this state, called $X(4310)$, should be produced in $B^+\to D^{*\pm}D^\mp K^+$ decays with branching fraction around $5\times 10^{-7}$, making it observable in upcoming high-luminosity LHCb data.

What carries the argument

The central object is the three-body wave function $\Psi_C = \frac{1}{\sqrt{2}}(\Psi_{\bar D_s D K} + C \Psi'_{D_s \bar D \bar K})$ with $C=\pm1$, solved with the Gaussian Expansion Method for the Schr\"odinger equation using contact-range potentials of Gaussian shape. The load-bearing input is the $DK$ potential, whose strength is fixed by reproducing the $D_{s0}^*(2317)$ mass under the assumption that $D_{s0}^*(2317)$ is a $DK$-$D_s\eta$ molecule with 70% molecular weight; the other potentials are then set by SU(3)-flavor ratios, and the $C$-parity dependent $\bar D_s D_{s0}^*$ interaction is added through $\eta$ exchange. What carries the argument is that the $DK$ attraction alone contributes about $-145$ MeV of the roughly $-200$ MeV total potential energy, making the three-body binding robust.

What would settle it

A concrete test: in the $B^+\to D^{*\pm}D^\mp K^+$ channel at LHCb with 350 fb$^{-1}$, look for a narrow peak near 4310 MeV in the $D_s D K$ invariant mass with a yield of order 100 events; the absence of such a peak at the predicted production rate would rule out the molecule, as would a lattice QCD spectrum of $\bar D_s D K$ showing no bound state below threshold.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes that a $J^{PC}=0^{--}$ $\bar D_s D K$ three-body hadronic molecule exists with mass $4310^{+14}_{-24}$ MeV and binding energy $21^{+24}_{-14}$ MeV. The calculation uses pairwise contact-range potentials whose relative strengths are fixed by the ratio $C^{DK}_a:C^{\bar D_s K}_a:C^{\bar D_s D}_a=1:0.5:0.1$, with the absolute $DK$ strength adjusted so that $D_{s0}^*(2317)$ emerges as a 70% molecular, 30% bare state. The resulting wave function is mainly the $(DK)-\bar D_s$ Jacobi channel, and the $\bar D_s D_{s0}^*$ subsystem, though repulsive in the negative-$C$ channel, still leaves the three-body state bound. The paper further claims that $X(4310)$ decays dominantly to $\bar D^* D$, with width ratio roughly $50:5:1$ against $\bar D_s D_s^*$ and $J/\psi\eta$, and is produced in $B$ decays at the $10^{-6}$ level, so the $B^+\to[X(4310)\to D^{*\pm}D^\mp]K^+$ branching fraction is about $5\times 10^{-7}$.

Load-bearing premise

The load-bearing input is the strength of the D-K attraction, which is not directly measured but fixed by assuming D_s0*(2317) has a 70% molecular component; if the true D-K attraction were weaker, or the regulator shape or three-body forces different, the predicted bound state could disappear.

Editorial extensions

If this is right

  • If $X(4310)$ exists, it provides the first unambiguous three-body hadronic molecule, since its $0^{--}$ quantum numbers veto mixing with ordinary charmonia.
  • A positive search in $B^+\to D^{*\pm}D^\mp K^+$ at LHCb would simultaneously validate the three-body mechanism and the molecular composition of $D_{s0}^*(2317)$.
  • The predicted decay pattern $\Gamma(X\to \bar D^* D):\Gamma(X\to \bar D_s D_s^*):\Gamma(X\to J/\psi\eta)\approx 50:5:1$ gives a distinctive experimental fingerprint.
  • The production-rate ratio between two-body and three-body molecules being independent of short-range interactions is a general regularity that can be checked with other three-meson systems.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper leaves implicit that the measured binding energy of $X(4310)$ could be inverted to extract the $DK$ scattering length, providing a model-independent handle on the $D_{s0}^*(2317)$ composition; this would be a natural follow-up once a peak is seen.
  • One could extend the same $C$-parity machinery to bottom analogues, such as $\bar B_s B K$, predicting analogous exotic three-body molecules that may be searched in $B$ or $\Upsilon$ decays.
  • A direct lattice QCD calculation of the $\bar D_s D K$ three-body spectrum near threshold would settle whether the binding survives without the contact-range approximations used here.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The manuscript predicts a J^{PC}=0^{--} \bar{D}_s D K three-body hadronic molecule, X(4310), with a mass of 4310^{+14}_{-24} MeV, using contact-range EFT pairwise interactions and solving the three-body Schrödinger equation with the Gaussian Expansion Method. The DK potential is fixed by reproducing the D_{s0}^*(2317) mass under the assumption that this resonance is a 70% DK-D_sη molecule and 30% bare c\bar{s} state; the \bar{D}_s K and \bar{D}_s D potentials are set by SU(3)-flavor ratios. The paper also computes strong decay widths and B-decay production rates and proposes B^+ \to D^{*\pm}D^\mp K^+ as a search channel.

Significance. If the prediction holds, X(4310) would be a genuinely three-body hadronic molecule with exotic quantum numbers, decoupled from conventional charmonia and from two-body molecular configurations, providing a new target for experimental searches. The paper's strengths are its use of a well-established numerical method (GEM), explicit propagation of input uncertainties via Monte Carlo sampling, and a scan of the D_{s0}^*(2317) molecular fraction. These make the result reproducible and falsifiable. However, the existence claim rests on an assumed two-body input (the DK potential) and on flavor-symmetry ratios for the other two potentials that are not directly constrained by data, so the significance is conditional on the robustness of those inputs.

major comments (3)
  1. [Table I and the paragraph after Eq. (2)] The three-body binding energy of 21^{+24}_{-14} MeV is the difference between a kinetic-energy expectation value of about 177 MeV and a total potential expectation value of about -200 MeV; within this balance, the \bar{D}_s K and \bar{D}_s D potentials contribute about -40 MeV and -14 MeV, respectively. These two potentials are fixed relative to the DK potential by the ratio C^{DK}:C^{\bar{D}_s K}:C^{\bar{D}_s D}=1:0.5:0.1, and the authors' uncertainty scan varies the molecular fraction of the D_{s0}^*(2317), which rescales all three potentials proportionally. The scan therefore does not test the uncertainty in the 0.5 and 0.1 ratios themselves. Because a reduction of even half of the adopted \bar{D}_s K attraction would substantially reduce the binding, the authors should vary these weak potentials independently over ranges compatible with the lattice and QCD sum-rule constraints cited in the Supplemental Material, and show the resulting binding-energy dependence. As it stands, the central existence claim is not yet shown to be robust to the least-constrained inputs.
  2. [Abstract and the paragraph following Eq. (2)] The abstract calls the DK potential 'model-independent,' but this potential is obtained by assuming the D_{s0}^*(2317) is a 70% DK-D_sη molecular admixture with a 30% bare c\bar{s} component, and the molecular fraction is then varied from 50% to 100%. This is a model assumption, not a direct extraction from data; lattice QCD analyses motivate the fraction, but the potential itself is a prediction of the assumed compositeness. The wording is therefore an overstatement and should be corrected, since the three-body prediction inherits the dependence on this assumption.
  3. [Fig. 2 and the text near Eq. (2)] The cutoff-dependence study in Fig. 2 shows a weak variation of the X mass with R_c, but the text does not state whether the DK potential strength is re-fitted to the D_{s0}^*(2317) mass at each value of R_c. In contact-range EFT, the low-energy constant must be renormalized as the cutoff is varied; if Fig. 2 instead keeps the potential strength fixed and only changes the Gaussian width, the mild R_c dependence does not demonstrate cutoff independence of the renormalized prediction. The authors should specify the renormalization procedure used for Fig. 2 and, if it was not done, repeat the scan with the DK potential re-determined at each R_c.
minor comments (4)
  1. [Paragraph after Eq. (2)] In the sentence 'forms a bound state with a binding energy of14 MeV', there is a missing space; it should read 'binding energy of 14 MeV'.
  2. [Supplement, Table I] The row for compositeness contains a duplicated 'Λ = 1.00' column entry; the table header should be corrected.
  3. [Fig. 2] The axes of Fig. 2 are difficult to read in the provided version; please ensure the printed figure clearly labels 'R_c (fm)' and 'Mass (MeV)'.
  4. [Eq. (9)] The Lorentz-index structure of the amplitude in Eq. (9) is not written explicitly (the contraction of the polarization vector and the metric is unclear); please rewrite it with explicit indices for readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the X(4310) binding energy is a genuine three-body output of fitted two-body potentials, not a refit of the target state.

full rationale

The derivation is not circular. The central output, the 21 MeV binding energy of the 0-- \bar D_s D K state, is obtained by solving the three-body Schr\"odinger equation (Eq. 5) with pair potentials fixed by independent two-body inputs: the DK potential is fitted to the experimental D_s0*(2317) mass under an explicit compositeness assumption, the \bar D_s K potential is taken as half of the DK potential from SU(3)-flavor symmetry, and the \bar D_s D potential is fixed by the X(3872) binding plus light-meson-saturation ratios. None of these inputs is the X(4310) state itself, and the X(4310) mass is never fed back into the potential determination. The molecular-fraction scan (50-100%) and cutoff scan alter the fitted strength but do not redefine the output. The fragility noted by the skeptic (small net of roughly 200 MeV attraction versus 177 MeV kinetic energy, and weakly constrained \bar D_s K and \bar D_s D strengths) is a model-dependence and robustness concern, not a circular reduction: varying those inputs would change the prediction rather than reproduce it by construction. Self-citations appear for the potential formalism and for earlier three-body studies, but the cited works fit different states and do not contain the claimed X(4310) result, so the prediction remains an independent dynamical output.

Assumptions & free parameters 5 free parameters · 8 assumptions · 1 invented entities

The central prediction rests on one measured anchor (the D_s0*(2317) and X(3872) masses used to calibrate the two-body potentials), one adopted-from-lattice anchor (the 70% molecular weight), and several model choices made by the authors (Gaussian regulator, SU(3) potential ratios, OBE eta exchange, naive factorization). The three-body binding is a genuine output of the Schrodinger equation, but the parameters above determine whether it appears. The X(4310) itself is the paper's one invented entity, and it carries a falsifiable mass and decay pattern.

free parameters (5)
  • D-K contact potential C_a(DK) = -2.06 fm^2 at Lambda = 1 GeV (momentum space); R_c = 0.472 fm (coordinate space)
    Fixed by reproducing the D_s0*(2317) mass in a coupled-channel D K - D_s eta contact EFT under the 70% molecular-weight assumption (Supplement Table I, third scenario). It provides the dominant attraction in the three-body system, <V_DK> ~ -145 MeV.
  • Bare-state mixing parameter beta = not quoted in the paper
    Eq. (12): V = beta(s - s_bar) is added to the D K - D_s eta potential; beta is determined by requiring the 70% molecular weight of D_s0*(2317). A number chosen by hand, not fitted to the three-body state.
  • Anti-D_s D contact potential C1a = -0.24 fm^2 at Lambda = 1 GeV; -0.60 to -0.11 fm^2 for Lambda = 0.5 to 2.0 GeV
    Obtained from reproducing the X(3872) mass as a D* anti-D bound state and applying light-meson-saturation ratios (Supplement). Contributes about -14 MeV to the binding, so it is not the dominant input.
  • Molecular weight of D_s0*(2317) = 70% (P_DK = 60%, P_Ds-eta = 10%, P_cs-bar = 30%)
    Adopted from lattice QCD reanalyses of the D_s0*(2317) wave function (Refs [2,4,6,9-11,14,26]); scanned 50-100% to estimate uncertainties. This assumption sets how attractive the extracted D-K potential is.
  • OBE dipole cut-off parameter alpha = 1 to 2 (scanned)
    Eq. (3), Lambda = alpha*Lambda_QCD + m_E; varied over the range used in prior heavy-hadron decay and molecule studies (Refs [27,55,56]). It sets the C-parity potential and the decay widths, and is the source of the bands in Figs. 5-6.
assumptions (8)
  • domain assumption Contact-range EFT with the Gaussian regulator V(r) = C_a exp(-(r/R_c)^2)/(pi^{3/2} R_c^3) describes the two-body hadron interactions.
    Eq. (2). The regulator shape and range R_c ~ 0.44-0.51 fm are model choices; the paper's only check is the weak cutoff dependence in Fig. 2.
  • domain assumption The anti-D_s K potential equals half of the D-K potential by SU(3)-flavor symmetry.
    Main text and Supplement: V(anti-D_s K) = (1/2) V(DK), citing Refs [11,49-51]. This ratio is not directly measured.
  • domain assumption The anti-D_s D potential is weak (0.1 of the D-K potential) and inherited from an X(3872) fit via light-meson-saturation ratios.
    Supplement: C_DK : C_anti-DsK : C_anti-DsD = 1 : 0.5 : 0.1. The alternative lattice-based value C1a = -0.44 to -0.64 fm^2 (Ref [73]) is larger, which the paper notes.
  • domain assumption D_s0*(2317) is a 70% D K - D_s eta molecule and 30% bare c-sbar state.
    Main text: 'we assume that the molecular and bare components account for 70% and 30%'. Taken from lattice QCD reanalyses, not from a direct measurement.
  • domain assumption The C-parity interaction is described by one-eta exchange between the anti-D_s and D_s0* in the OBE model.
    Eq. (4): attractive for C = + and repulsive for C = -, with magnitude only 2-4 MeV (Table I). Other contributions to the three-body force are neglected.
  • domain assumption The three-body Hamiltonian contains only pairwise potentials; no genuine three-body forces are included.
    Eq. (5). In contact EFT with two-body binding, a three-body force is generally needed for cutoff independence; the mild R_c dependence in Fig. 2 is the only check that omitted terms are small.
  • ad hoc to paper B production of X(4310) is dominated by the chain B -> anti-D* D_s0* followed by rescattering into anti-D_s D K (Fig. 4b).
    The production calculation assumes this hadronization chain and no competing mechanism. The resulting branching fraction, of order 10^-6, is therefore a model estimate.
  • domain assumption The weak decay B -> anti-D* D_s0* is described by naive factorization with covariant light-front form factors.
    Supplement Eq. (15) and the form factors of Ref [81]. Standard but model-dependent; a 10% form-factor uncertainty is quoted following Ref [82].
invented entities (1)
  • X(4310), a J^PC = 0^-- anti-D_s D K three-body hadronic molecule independent evidence
    purpose: The predicted bound state and the central result of the paper; used to demonstrate a new configuration of exotic hadronic matter and to motivate an LHCb search.
    The model gives a falsifiable handle outside the paper: a specific mass (4286-4324 MeV), specific dominant decays (anti-D* D at about 10^3 keV, anti-D_s D_s* at about 10^2 keV, J/psi eta at about 10^1 keV), and a search channel, B+ -> D*±D∓K+, with predicted event counts (about 10 and 100 for 50 and 350 fb^-1). The caveat is that every one of these rates is computed within the same molecular model that predicts the state.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Implication of the existence of $J^{PC}=0^{--}$ $\bar{D}_sDK$ bound state on nature of $D_{s0}^*(2317)$ and new configuration of exotic state." pith.science (2026). https://pith.science/paper/7WHU6ODN

@misc{pith2026250111358,
  author       = {Pith},
  title        = {Pith review of: Implication of the existence of $J^PC=0^--$ $\barD_sDK$ bound state on nature of $D_s0^*(2317)$ and new configuration of exotic state},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7WHU6ODN}},
  note         = {Machine review of arXiv:2501.11358}
}
abstract

The discovery of numerous new hadrons over the past two decades has provided unprecedented opportunities to understand the non-perturbative QCD and hadron structure. Hadronic molecule picture plays an important role in explaining these new hadrons and enriching the configurations of exotic hadronic states. In this letter, using the model-independent $DK$ potential extracted from the relevant experimental data, a $J^{PC}=0^{--}$ $\bar{D}_sDK$ three-body hadronic molecule is predicted with a mass of $4310^{+14}_{-24}$ MeV. This state shows decoupling to conventional $c\bar{c}$ charmonia or the $\bar{D}_s D_{s0}^*(2317)$ two-body molecular state. It can be regarded as a compelling three-body hadronic molecular candidate. We further demonstrate that the $B^+ \to {D}^{*\pm}D^\mp K^+$ decays could be promising channels for searching for the predicted state in future high-luminosity LHCb runs.

Figures

Figures reproduced from arXiv: 2501.11358 by the authors.

Figure 2
Figure 2. FIG. 2. Mass of [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 1
Figure 1. FIG. 1. Three permutations of the Jacobi coordinates for the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Triangle diagrams of the [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (5 more)
Figure 1
Figure 1. Figure 1: The results are shown in Table I, the 0 −− D¯ sDK system is predicted to be a bound state with a binding energy of 21+24 −14 MeV. Our results indicate that when the DK − Dsη molecu￾lar component of the D∗ s0 (2317) ranges from 50% to 100%, the D¯ sDK system always rema…
Figure 5
Figure 5. Figure 5: FIG. 5. Partial decay widths of [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 7
Figure 7. Figure 7: FIG. 7. With the [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]
Figure 1
Figure 1. Figure 1: FIG. 1. Partial widths of the decays [PITH_FULL_IMAGE:figures/full_fig_p011_1.png]
Figure 2
Figure 2. Figure 2: FIG. 2. Branching fraction of the decays [PITH_FULL_IMAGE:figures/full_fig_p012_2.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Probing the structure of the $D_{s 0}^*(2317)$ and $X(3872)$ states through correlation functions

    hep-ph 2025-06 conditional novelty 6.0 of 10

    Femtoscopic correlation functions for D0K+ and D0Dbar*0 pairs are predicted to be sensitive to the molecular versus bare-state composition of D_s0*(2317) and X(3872).

  2. Decay constants of the two-pole $D_0^*(2300)$

    hep-ph 2026-07 conditional novelty 4.0 of 10

    Molecular two-pole D0*(2300) decay constants are 65 and 81 MeV—much smaller than compact c¯q estimates—and imply Cabibbo-favored b-hadron branching fractions of order 10^{-5}.

Reference graph

Works this paper leans on

88 extracted references · 13 canonical work pages · cited by 2 Pith papers

  1. [1]

    P. G. Ortega, J. Segovia, D. R. Entem, and F. Fernandez, Phys. Rev. D 94, 074037 (2016), arXiv:1603.07000 [hep-ph]

    arXiv 2016

  2. [2]

    Albaladejo, P

    M. Albaladejo, P. Fernandez-Soler, J. Nieves, and P. G. Ortega, Eur. Phys. J. C 78, 722 (2018), arXiv:1805.07104 [hep-ph]

    arXiv 2018

  3. [3]

    S.-Q. Luo, B. Chen, X. Liu, and T. Matsuki, Phys. Rev. D 103, 074027 (2021), arXiv:2102.00679 [hep-ph]

    arXiv 2021

  4. [4]

    Yang, G.-J

    Z. Yang, G.-J. Wang, J.-J. Wu, M. Oka, and S.-L. Zhu, Phys. Rev. Lett. 128, 112001 (2022), arXiv:2107.04860 [hep-ph]

    arXiv 2022

  5. [5]

    Near Mass Degeneracy in the Scalar Meson Sector: Implications for $B^*_{(s)0}$ and $B'_{(s)1}$ Mesons

    H.-Y . Cheng and F.-S. Yu, Phys. Rev. D 89, 114017 (2014), arXiv:1404.3771 [hep-ph]

    work page Pith review arXiv 2014

  6. [6]

    Mart´ınez Torres, E

    A. Mart´ınez Torres, E. Oset, S. Prelovsek, and A. Ramos, JHEP 05, 153 (2015), arXiv:1412.1706 [hep-lat]

    arXiv 2015

  7. [7]

    Guo, U.-G

    Z.-H. Guo, U.-G. Meißner, and D.-L. Yao, Phys. Rev. D 92, 094008 (2015), arXiv:1507.03123 [hep-ph]

    arXiv 2015

  8. [8]

    Yao, M.-L

    D.-L. Yao, M.-L. Du, F.-K. Guo, and U.-G. Meißner, JHEP 11, 058 (2015), arXiv:1502.05981 [hep-ph]

    arXiv 2015

Show all 88 references
  1. [9]

    Guo, PoS LATTICE2022, 232 (2023)

    F.-K. Guo, PoS LATTICE2022, 232 (2023)

    2023

  2. [10]

    Gil-Dom ´ınguez and R

    F. Gil-Dom ´ınguez and R. Molina, Phys. Rev. D 109, 096002 (2024), arXiv:2306.01848 [hep-ph]

    2024 arXiv

  3. [11]

    L. Liu, K. Orginos, F.-K. Guo, C. Hanhart, and U.-G. Meissner, Phys. Rev. D87, 014508 (2013), arXiv:1208.4535 [hep-lat]

    2013 arXiv

  4. [12]

    Mohler, C

    D. Mohler, C. B. Lang, L. Leskovec, S. Prelovsek, and R. M. Woloshyn, Phys. Rev. Lett. 111, 222001 (2013), arXiv:1308.3175 [hep-lat]

    2013 arXiv

  5. [13]

    C. B. Lang, L. Leskovec, D. Mohler, S. Prelovsek, and R. M. Woloshyn, Phys. Rev. D 90, 034510 (2014), arXiv:1403.8103 [hep-lat]

    2014 arXiv

  6. [14]

    G. S. Bali, S. Collins, A. Cox, and A. Sch ¨afer, Phys. Rev. D96, 074501 (2017), arXiv:1706.01247 [hep-lat]

    2017 arXiv

  7. [15]

    Alexandrou, J

    C. Alexandrou, J. Berlin, J. Finkenrath, T. Leontiou, and M. Wagner, Phys. Rev. D 101, 034502 (2020), arXiv:1911.08435 [hep-lat]

    2020 arXiv

  8. [16]

    X.-Y . Guo, Y . Heo, and M. F. M. Lutz, Phys. Rev. D98, 014510 (2018), arXiv:1801.10122 [hep-lat]

    2018 arXiv

  9. [17]

    H.-L. Fu, H. W. Grießhammer, F.-K. Guo, C. Hanhart, and U.- G. Meißner, Eur. Phys. J. A 58, 70 (2022), arXiv:2111.09481 [hep-ph]

    2022 arXiv

  10. [18]

    F. S. Navarra, M. Nielsen, E. Oset, and T. Sekihara, Phys. Rev. D 92, 014031 (2015), arXiv:1501.03422 [hep-ph]

    2015 arXiv

  11. [19]

    Albaladejo, D

    M. Albaladejo, D. Jido, J. Nieves, and E. Oset, Eur. Phys. J. C 76, 300 (2016), arXiv:1604.01193 [hep-ph]

    2016 arXiv

  12. [20]

    Liu, X.-Z

    M.-Z. Liu, X.-Z. Ling, L.-S. Geng, En-Wang, and J.-J. Xie, Phys. Rev. D 106, 114011 (2022), arXiv:2209.01103 [hep-ph]

    2022 arXiv

  13. [21]

    Aubert et al

    B. Aubert et al. (BaBar), Phys. Rev. Lett. 90, 242001 (2003), arXiv:hep-ex/0304021

    2003 arXiv

  14. [22]

    Godfrey and N

    S. Godfrey and N. Isgur, Phys. Rev. D 32, 189 (1985)

    1985

  15. [23]

    W. Hao, Y . Lu, and B.-S. Zou, Phys. Rev. D 106, 074014 (2022), arXiv:2208.10915 [hep-ph]

    2022 arXiv

  16. [24]

    J.-J. Yang, W. Hao, X. Wang, D.-M. Li, Y .-X. Li, and E. Wang, Eur. Phys. J. C 83, 1098 (2023), arXiv:2303.11815 [hep-ph]

    2023 arXiv

  17. [25]

    Ni, J.-J

    R.-H. Ni, J.-J. Wu, and X.-H. Zhong, Phys. Rev. D109, 116006 (2024), arXiv:2312.04765 [hep-ph]

    2024 arXiv

  18. [26]

    G. K. C. Cheung, C. E. Thomas, D. J. Wilson, G. Moir, M. Pear- don, and S. M. Ryan (Hadron Spectrum), JHEP02, 100 (2021), arXiv:2008.06432 [hep-lat]

    2021 arXiv

  19. [27]

    Liu, Y .-W

    M.-Z. Liu, Y .-W. Pan, Z.-W. Liu, T.-W. Wu, J.-X. Lu, and L.-S. Geng, Phys. Rept. 1108, 1 (2025), arXiv:2404.06399 [hep-ph]

    2025 arXiv

  20. [28]

    Martinez Torres, K

    A. Martinez Torres, K. P. Khemchandani, D. Gamermann, and E. Oset, Phys. Rev. D 80, 094012 (2009), arXiv:0906.5333 [nucl-th]

    2009 arXiv

  21. [29]

    L. Ma, Q. Wang, and U.-G. Meißner, Chin. Phys. C 43, 014102 (2019), arXiv:1711.06143 [hep-ph]

    2019 arXiv

  22. [30]

    Wu, M.-Z

    T.-W. Wu, M.-Z. Liu, L.-S. Geng, E. Hiyama, and M. P. Valder- rama, Phys. Rev. D 100, 034029 (2019), arXiv:1906.11995 [hep-ph]

    2019 arXiv

  23. [31]

    Martinez Torres, K

    A. Martinez Torres, K. P. Khemchandani, L. Roca, and E. Oset, Few Body Syst. 61, 35 (2020), arXiv:2005.14357 [nucl-th]

    2020 arXiv

  24. [32]

    Wei, Q.-H

    X. Wei, Q.-H. Shen, and J.-J. Xie, Eur. Phys. J. C 82, 718 (2022), arXiv:2205.12526 [hep-ph]

    2022 arXiv

  25. [33]

    Y . Tan, X. Liu, X. Chen, Y . Yang, H. Huang, and J. Ping, Phys. Rev. D 110, 016005 (2024), arXiv:2404.02048 [hep-ph]

    2024 arXiv

  26. [34]

    Zhang, X.-Y

    Z. Zhang, X.-Y . Hu, G. He, J. Liu, J.-A. Shi, B.-N. Lu, and Q. Wang, (2024), arXiv:2409.01325 [hep-ph]

    2024 arXiv

  27. [35]

    C. W. Xiao, M. Bayar, and E. Oset, Phys. Rev. D 84, 034037 (2011), arXiv:1106.0459 [hep-ph]

    2011 arXiv

  28. [36]

    V . R. Debastiani, J. M. Dias, and E. Oset, Phys. Rev. D 96, 016014 (2017), arXiv:1705.09257 [hep-ph]

    2017 arXiv

  29. [37]

    Martinez Torres, K

    A. Martinez Torres, K. P. Khemchandani, and L.-S. Geng, Phys. Rev. D 99, 076017 (2019), arXiv:1809.01059 [hep-ph]

    2019 arXiv

  30. [38]

    Pang, J.-J

    J.-Y . Pang, J.-J. Wu, and L.-S. Geng, Phys. Rev. D102, 114515 (2020), arXiv:2008.13014 [hep-lat]

    2020 arXiv

  31. [39]

    Li et al

    Y . Li et al. (Belle), Phys. Rev. D 102, 112001 (2020), arXiv:2008.13341 [hep-ex]

    2020 arXiv

  32. [40]

    Wu, M.-Z

    T.-W. Wu, M.-Z. Liu, and L.-S. Geng, Phys. Rev. D 103, L031501 (2021), arXiv:2012.01134 [hep-ph]

    2021 arXiv

  33. [41]

    Wu and L.-S

    T.-C. Wu and L.-S. Geng, Phys. Rev. D 108, 014015 (2023), arXiv:2211.01846 [hep-ph]

    2023 arXiv

  34. [42]

    Sanchez Sanchez, L.-S

    M. Sanchez Sanchez, L.-S. Geng, J.-X. Lu, T. Hyodo, and M. P. Valderrama, Phys. Rev.D98, 054001 (2018), arXiv:1707.03802 [hep-ph]

    2018 arXiv

  35. [43]

    Ji, X.-K

    T. Ji, X.-K. Dong, F.-K. Guo, and B.-S. Zou, Phys. Rev. Lett. 129, 102002 (2022), arXiv:2205.10994 [hep-ph]

    2022 arXiv

  36. [44]

    Karliner and J

    M. Karliner and J. L. Rosner, Nucl. Phys. A 954, 365 (2016), arXiv:1601.00565 [hep-ph]

    2016 arXiv

  37. [45]

    Shen, X.-L

    L.-L. Shen, X.-L. Chen, Z.-G. Luo, P.-Z. Huang, S.-L. Zhu, P.-F. Yu, and X. Liu, Eur. Phys. J. C70, 183 (2010), arXiv:1005.0994 [hep-ph]

    2010 arXiv

  38. [46]

    Aaij et al

    R. Aaij et al. (LHCb), Phys. Rev. Lett. 133, 131902 (2024), arXiv:2406.03156 [hep-ex]

    2024

  39. [47]

    Hidalgo-Duque, J

    C. Hidalgo-Duque, J. Nieves, and M. P. Valderrama, Phys. Rev. D 87, 076006 (2013), arXiv:1210.5431 [hep-ph]

    2013 arXiv

  40. [48]

    Liu, X.-Z

    M.-Z. Liu, X.-Z. Ling, and L.-S. Geng, Phys. Rev. D 109, 056014 (2024), arXiv:2312.01433 [hep-ph]

    2024 arXiv

  41. [49]

    Guo, P.-N

    F.-K. Guo, P.-N. Shen, H.-C. Chiang, R.-G. Ping, and B.- S. Zou, Phys. Lett. B641, 278 (2006), arXiv:hep-ph/0603072 [hep-ph]

    2006 arXiv

  42. [50]

    F.-K. Guo, C. Hanhart, and U.-G. Meissner, Eur. Phys. J. A 40, 171 (2009), arXiv:0901.1597 [hep-ph]

    2009 arXiv

  43. [51]

    Altenbuchinger, L

    M. Altenbuchinger, L. S. Geng, and W. Weise, Phys. Rev. D 89, 014026 (2014), arXiv:1309.4743 [hep-ph]

    2014 arXiv

  44. [52]

    Ji, X.-K

    T. Ji, X.-K. Dong, M. Albaladejo, M.-L. Du, F.-K. Guo, J. Nieves, and B.-S. Zou, (2022), 10.1016/j.scib.2023.02.034, arXiv:2212.00631 [hep-ph]

    2022 arXiv

  45. [53]

    Liu, Z.-G

    X. Liu, Z.-G. Luo, and S.-L. Zhu, Phys. Lett. B 699, 341 (2011), [Erratum: Phys.Lett.B 707, 577 (2012)], arXiv:1011.1045 [hep-ph]

    2011 arXiv

  46. [54]

    N. A. Tornqvist, Z. Phys. C61, 525 (1994), arXiv:hep- ph/9310247 [hep-ph]

    1994

  47. [55]

    Cheng, C.-K

    H.-Y . Cheng, C.-K. Chua, and A. Soni, Phys. Rev. D 71, 014030 (2005), arXiv:hep-ph/0409317

    2005 arXiv

  48. [56]

    Yu, H.-Y

    F.-S. Yu, H.-Y . Jiang, R.-H. Li, C.-D. L ¨u, W. Wang, and Z.- X. Zhao, Chin. Phys. C42, 051001 (2018), arXiv:1703.09086 [hep-ph]

    2018 arXiv

  49. [57]

    Hiyama, Y

    E. Hiyama, Y . Kino, and M. Kamimura, Prog. Part. Nucl. Phys. 51, 223 (2003)

    2003

  50. [58]

    Soriano and J

    M. Soriano and J. J. Palacios, Phys. Rev. B 90, 075128 (2014)

    2014

  51. [59]

    Ring and P

    P. Ring and P. Schuck, The Nuclear Many-Body Problem, 1st ed., Texts and Monographs in Physics (Springer-Verlag, Berlin 7 Heidelberg New York, 1980) 3rd printing 2004

    1980

  52. [60]

    Faessler, T

    A. Faessler, T. Gutsche, V . E. Lyubovitskij, and Y .-L. Ma, Phys. Rev. D 76, 014005 (2007), arXiv:0705.0254 [hep-ph]

    2007 arXiv

  53. [61]

    Chen, Phys

    H.-X. Chen, Phys. Rev. D 105, 094003 (2022), arXiv:2103.08586 [hep-ph]

    2022 arXiv

  54. [62]

    Li and B.-S

    X.-Q. Li and B.-S. Zou, Phys. Lett. B 399, 297 (1997), arXiv:hep-ph/9611223

    1997 arXiv

  55. [63]

    Du, X.-Q

    D.-S. Du, X.-Q. Li, Z.-T. Wei, and B.-S. Zou, Eur. Phys. J. A 4, 91 (1999), arXiv:hep-ph/9805260

    1999 arXiv

  56. [64]

    Dai, D.-S

    Y .-S. Dai, D.-S. Du, X.-Q. Li, Z.-T. Wei, and B.-S. Zou, Phys. Rev. D 60, 014014 (1999), arXiv:hep-ph/9903204

    1999 arXiv

  57. [65]

    Ablikim, D.-S

    M. Ablikim, D.-S. Du, and M.-Z. Yang, Phys. Lett. B 536, 34 (2002), arXiv:hep-ph/0201168

    2002 arXiv

  58. [66]

    Lu, Y .-L

    C.-D. Lu, Y .-L. Shen, and W. Wang, Phys. Rev. D 73, 034005 (2006), arXiv:hep-ph/0511255

    2006 arXiv

  59. [67]

    Y . Cao, Y . Cheng, and Q. Zhao, Phys. Rev. D 109, 073002 (2024), arXiv:2303.00535 [hep-ph]

    2024 arXiv

  60. [68]

    Faessler, T

    A. Faessler, T. Gutsche, S. Kovalenko, and V . E. Lyubovitskij, Phys. Rev. D 76, 014003 (2007), arXiv:0705.0892 [hep-ph]

    2007 arXiv

  61. [69]

    del Amo Sanchez et al

    P. del Amo Sanchez et al. (BaBar), Phys. Rev. D 83, 032004 (2011), arXiv:1011.3929 [hep-ex]

    2011 arXiv

  62. [70]

    Aaij et al

    R. Aaij et al. (LHCb), JHEP 12, 139 (2020), arXiv:2005.10264 [hep-ex]

    2020

  63. [71]

    Ikeno, G

    N. Ikeno, G. Toledo, and E. Oset, Phys. Lett. B 847, 138281 (2023), arXiv:2305.16431 [hep-ph]

    2023 arXiv

  64. [72]

    Peng, M.-Z

    F.-Z. Peng, M.-Z. Liu, M. S ´anchez S ´anchez, and M. Pavon Valderrama, Phys. Rev. D 102, 114020 (2020), arXiv:2004.05658 [hep-ph]

    2020 arXiv

  65. [73]

    P.-P. Shi, M. Albaladejo, M.-L. Du, F.-K. Guo, and J. Nieves, (2024), arXiv:2410.19563 [hep-ph]

    2024 arXiv

  66. [74]

    Liu, F.-Z

    M.-Z. Liu, F.-Z. Peng, M. S ´anchez S´anchez, and M. P. Valder- rama, Phys. Rev. D98, 114030 (2018), arXiv:1811.03992 [hep- ph]

    2018 arXiv

  67. [75]

    Ablikim et al

    M. Ablikim et al. (BESIII), Phys. Rev. D 97, 051103 (2018), arXiv:1711.08293 [hep-ex]

    2018 arXiv

  68. [76]

    Godfrey, Phys

    S. Godfrey, Phys. Lett. B 568, 254 (2003), arXiv:hep- ph/0305122

    2003

  69. [77]

    Colangelo and F

    P. Colangelo and F. De Fazio, Phys. Lett. B 570, 180 (2003), arXiv:hep-ph/0305140

    2003 arXiv

  70. [78]

    Colangelo, F

    P. Colangelo, F. De Fazio, and A. Ozpineci, Phys. Rev. D 72, 074004 (2005), arXiv:hep-ph/0505195

    2005 arXiv

  71. [79]

    Y .-s. Oh, T. Song, and S. H. Lee, Phys. Rev. C 63, 034901 (2001), arXiv:nucl-th/0010064

    2001 arXiv

  72. [80]

    M. E. Bracco, M. Chiapparini, F. S. Navarra, and M. Nielsen, Prog. Part. Nucl. Phys. 67, 1019 (2012), arXiv:1104.2864 [hep- ph]

    2012 arXiv

  73. [81]

    R. C. Verma, J. Phys. G 39, 025005 (2012), arXiv:1103.2973 [hep-ph]

    2012 arXiv

  74. [82]

    Wu, M.-Z

    Q. Wu, M.-Z. Liu, and L.-S. Geng, Eur. Phys. J. C 84, 147 (2024), arXiv:2304.05269 [hep-ph]

    2024 arXiv

  75. [83]

    Aubert et al

    B. Aubert et al. (BaBar), Phys. Rev. Lett. 93, 041801 (2004), arXiv:hep-ex/0402025

    2004 arXiv

  76. [84]

    Iwashita et al

    T. Iwashita et al. (Belle), PTEP 2014, 043C01 (2014), arXiv:1310.2704 [hep-ex]

    2014 arXiv

  77. [85]

    Aaij et al

    R. Aaij et al. (LHCb), JHEP 04, 046 (2022), arXiv:2202.04045 [hep-ex]

    2022

  78. [86]

    Navas et al

    S. Navas et al. (Particle Data Group), Phys. Rev. D110, 030001 (2024). 1 SUPPLEMENTAL MATERIAL We provide details on determining the contact-range potentials and relevant Lagrangians of the Feynman diagrams in Figs. 3 and 4(b) in the main manuscript here. In addition, we prese...

    2024

  79. [88]

    The form factors of A0(t), A1(t), and A2(t) with t ≡ q2 1 can be parameterized as [81] X(t) = X(0) 1 − a (t/m2 B) + b (t2/m4 B)

    − 2mD∗ A0(q2 1)]}, where GF = 1.166 × 10−5 GeV−2, Vcb = 0.0395, Vcs = 0.991, fD∗ s0 = 59 MeV , anda1 = 1.07. The form factors of A0(t), A1(t), and A2(t) with t ≡ q2 1 can be parameterized as [81] X(t) = X(0) 1 − a (t/m2 B) + b (t2/m4 B) . (16) For these form factors, we adopt ...

  80. [2003]

    A remarkable feature of the spectrum of these heavy hadrons is that most are near the threshold of a pair of hadrons. The recent studies from the unquenched quark model [1–4], effective field theories [5–10], and lattice QCD [11–15] indi- cate that the heavy hadrons have stron...

    2025 arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.