arxiv: 2605.03320 · v1 · submitted 2026-05-05 · ✦ hep-ph

Recognition: unknown

Does psi(4660) exist?

Xian-Chen Wang , Quanxing Ye , Qian Wang

Authors on Pith no claims yet

Pith reviewed 2026-05-07 16:10 UTC · model grok-4.3

classification ✦ hep-ph

keywords charmonium resonancescoupled-channel effectsψ(4660)BESIIIBelleRiemann sheetsLippmann-Schwinger

0 comments

The pith

The ψ(4660) resonance corresponds to a bare pole on the real axis in coupled-channel fits to both Belle and BESIII data.

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

The paper tests the existence of the ψ(4660) by building a model of e+ e- annihilation into open-charm pairs and other states using coupled channels. Short-range contact interactions and two bare charmonium states are included, then the Lippmann-Schwinger equation is solved to match cross-section data. The results show that the ψ(4660) pole on the unphysical sheet links back to a bare state on the real axis for both experimental datasets, even as the lower ψ(4360) changes character between them. This matters because it helps decide whether observed peaks in the charmonium region are conventional quark states or arise purely from channel couplings.

Core claim

The ψ(4660) pole found on the unphysical Riemann sheet above the Λc+ Λc- threshold is associated with a bare pole on the real axis in both the Belle and BESIII fits when two explicit bare 4S and 5S charmonium states are included in the coupled-channel framework.

What carries the argument

Lippmann-Schwinger equation solved with short-ranged contact potentials in the heavy-quark limit that explicitly include two bare S-wave charmonium states (assigned as 4S and 5S).

Load-bearing premise

Short-ranged contact potentials in the heavy-quark limit plus explicit inclusion of two bare 4S and 5S states suffice to describe the coupled-channel dynamics.

What would settle it

New high-precision cross-section data showing a zero value exactly at the Λc+Λc- threshold or a lineshape that cannot be fit with a real-axis bare pole for ψ(4660).

Figures

Figures reproduced from arXiv: 2605.03320 by Qian Wang, Quanxing Ye, Xian-Chen Wang.

**Figure 1.** Figure 1: FIG. 1: Feynman diagrams for view at source ↗

**Figure 2.** Figure 2: FIG. 2: Comparison of the fitted lineshapes with experimental measurements for the Belle [ view at source ↗

**Figure 3.** Figure 3: FIG. 3: Panels (a) and (b): Pole trajectories of view at source ↗

**Figure 4.** Figure 4: FIG. 4: Prediction of the Ξ view at source ↗

**Figure 5.** Figure 5: FIG. 5: Line shapes of the two separate fits compared with experimental data after replacing the Gaussian form view at source ↗

read the original abstract

We investigate $S$-wave coupled-channel effects in $e^+e^-$ annihilation in the energy region $\sqrt{s}\in[4.0,5.5]\,\mathrm{GeV}$, including the open-charm final states $\Lambda_c^+\bar{\Lambda}_c^-$, $\Xi_c^+\bar{\Xi}_c^-$, $\Xi_c^0\bar{\Xi}_c^0$, and $\psi(2S)\pi^+\pi^-$. Motivated by the recent high-precision BESIII measurements of the $e^+e^-\to\Lambda_c^+\bar{\Lambda}_c^-$ cross section, which shows a nearly flat lineshape around $4.66~\mathrm{GeV}$ and a non-zero value right at threshold, in striking contrast to earlier Belle observation, we construct an effective coupled-channel framework by using short-ranged contact potentials in the heavy-quark limit.Two charmonium states, i.e. the $\psi(4360)$ and $\psi(4660)$, assigned as the $4S$ and $5S$ excitations, respectively, are explicitly included. The scattering amplitudes are obtained by solving the Lippmann-Schwinger equation.The Belle and BESIII $e^+e^-\to\Lambda_c^+\bar{\Lambda}_c^-$ and $e^+e^-\to\psi(2S)\pi^+\pi^-$ cross-sections reveal markedly different pole structures for the $\psi(4360)$. It emerges as a dynamically generated state for the Belle data, whereas it appears as a bare state in the BESIII fit. In contrast, the $\psi(4660)$ pole found on the unphysical Riemann sheet above the $\Lambda_c^+\bar{\Lambda}_c^-$ threshold is associated with a bare pole on the real axis in both fits.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Fits to Belle vs BESIII ΛcΛc data show ψ(4660) tied to the input bare 5S pole in both cases, while ψ(4360) flips between dynamically generated and bare.

read the letter

The main point is that this paper runs the same short-range contact-potential coupled-channel model on the new BESIII e+e- to Λc+Λc- cross section and the older Belle data, and finds the ψ(4660) pole on the unphysical sheet stays linked to the explicit bare 5S state in both fits, whereas the ψ(4360) changes character depending on which dataset is used. They also fold in Ξc channels and ψ(2S)π+π- and solve the Lippmann-Schwinger equation in the heavy-quark limit with two bare states as inputs. That contrast is the concrete new observation here, and it is useful because the BESIII lineshape is flatter and non-zero at threshold, which the model accommodates by shifting the lower pole. The method itself is standard and the execution looks competent on the evidence given. The soft spots are the usual ones for this style of work. The bare masses and couplings are free parameters tuned to data, so the claim that the observed pole is “associated with” the bare 5S state is partly by construction. The model omits long-range pion exchange between the charmed baryons and any additional states; if those matter near the ΛcΛc threshold the pole could pick up more dynamical character and the conclusion would shift. The abstract gives no fit values, errors, or stability checks, so the robustness is hard to judge without the full numbers. This is for people who follow charmonium assignments and coupled-channel fits to e+e- data. A reader who wants to see how the latest BESIII measurement updates the 4S/5S picture will find the comparison worth the time. It deserves a serious referee because the data contrast is timely and the calculation is reproducible, even if the model assumptions are open to debate and the central association is not an independent prediction.

Referee Report

2 major / 2 minor

Summary. The paper claims that in a coupled-channel model using short-ranged contact interactions in the heavy-quark limit and explicitly incorporating bare ψ(4360) (4S) and ψ(4660) (5S) states, the solution of the Lippmann-Schwinger equation fitted to Belle and BESIII data shows that the ψ(4660) resonance, appearing as a pole on the unphysical Riemann sheet above the Λ_c^+ Λ_c^- threshold, is associated with the bare 5S state in both datasets. In contrast, the ψ(4360) is dynamically generated for Belle data but bare for BESIII data. This leads to the conclusion that the ψ(4660) exists as the 5S charmonium state.

Significance. This result, if the model assumptions hold, would support the conventional charmonium assignment for ψ(4660) and demonstrate the utility of explicit bare-state inclusion for distinguishing resonance origins. The approach of solving the Lippmann-Schwinger equation with fitted bare parameters provides a clear framework for pole analysis, and the dataset-dependent findings for ψ(4360) underscore the importance of precise experimental inputs. Such analyses contribute to clarifying the spectrum of vector charmonia above the open-charm threshold.

major comments (2)

The association of the ψ(4660) pole with the bare 5S state is presented as a key finding, but since the bare pole positions are free parameters in the effective model (as implied by the construction of the framework), this association appears to be by construction rather than an emergent prediction. This is load-bearing for the claim that ψ(4660) 'exists' as the 5S state.
The model relies on the sufficiency of short-ranged contact potentials plus exactly two bare states. Given that the ψ(4360) interpretation changes with the dataset, the robustness of the ψ(4660) conclusion under variations such as inclusion of long-range forces or additional states is not addressed, which is critical for the central claim.

minor comments (2)

The abstract would benefit from including quantitative details such as the extracted pole positions, residues, or goodness-of-fit measures to allow readers to evaluate the quality of the fits.
Clarification on how the bare states are assigned as 4S and 5S (e.g., via mass matching or quantum numbers) would improve the presentation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive comments on our manuscript. We address the major comments point by point below.

read point-by-point responses

Referee: The association of the ψ(4660) pole with the bare 5S state is presented as a key finding, but since the bare pole positions are free parameters in the effective model (as implied by the construction of the framework), this association appears to be by construction rather than an emergent prediction. This is load-bearing for the claim that ψ(4660) 'exists' as the 5S state.

Authors: We respectfully disagree that the association is by construction. Although the bare pole positions are fitted parameters, the Lippmann-Schwinger equation is solved in the presence of the coupled-channel contact interactions, which can generate new poles or substantially shift the bare ones. This flexibility is demonstrated by the ψ(4360), whose interpretation changes from dynamically generated (Belle data) to bare (BESIII data). The fact that the ψ(4660) resonance pole remains associated with the bare 5S state in fits to both independent datasets indicates that this outcome is selected by the data rather than imposed a priori. We will add explicit clarification on the procedure used to associate dressed poles with bare states in the revised manuscript. revision: yes
Referee: The model relies on the sufficiency of short-ranged contact potentials plus exactly two bare states. Given that the ψ(4360) interpretation changes with the dataset, the robustness of the ψ(4660) conclusion under variations such as inclusion of long-range forces or additional states is not addressed, which is critical for the central claim.

Authors: We agree that the robustness of the ψ(4660) result under extensions of the model (e.g., long-range forces or additional bare states) has not been explicitly tested and that the dataset dependence seen for the ψ(4360) makes such checks relevant. Our analysis is restricted to the minimal framework of short-ranged contact interactions in the heavy-quark limit with two explicit bare states. Within this setup the ψ(4660) conclusion is consistent across both datasets. We will add a dedicated paragraph discussing these model limitations and the desirability of future robustness studies in the revised manuscript. revision: partial

Circularity Check

1 steps flagged

Association of ψ(4660) pole with bare 5S state follows by construction from explicit inclusion and fitting of bare poles

specific steps

fitted input called prediction [Abstract]
"Two charmonium states, i.e. the ψ(4360) and ψ(4660), assigned as the 4S and 5S excitations, respectively, are explicitly included. [...] the ψ(4660) pole found on the unphysical Riemann sheet above the Λc+Λc- threshold is associated with a bare pole on the real axis in both fits."

The bare 5S state is introduced as an adjustable input parameter whose position and couplings are fitted to the e+e- cross-section data. The subsequent claim that the dressed ψ(4660) pole 'is associated with' this bare pole is then enforced by the model definition and the fitting procedure itself.

full rationale

The paper's central result—that the ψ(4660) pole is associated with a bare 5S state on the real axis in both Belle and BESIII fits—reduces directly to the model's inputs. The effective framework is defined by adding two bare charmonium states (explicitly assigned as 4S and 5S) plus short-ranged contact potentials, then solving the Lippmann-Schwinger equation and fitting the bare-pole parameters to the cross-section data. The reported association is therefore a direct consequence of this construction rather than an independent dynamical prediction. No other circular steps (self-citation chains, ansatz smuggling, or renaming) are identifiable from the provided text.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

Model depends on multiple fitted parameters for contact potentials and bare-state masses plus the heavy-quark limit approximation; no independent evidence is supplied for the bare states beyond the fit itself.

free parameters (2)

bare masses and couplings of psi(4360) and psi(4660)
Introduced explicitly as 4S and 5S states and adjusted to reproduce the observed lineshapes.
strengths of short-range contact potentials
Fitted parameters in each channel to solve the Lippmann-Schwinger equation.

axioms (1)

domain assumption Heavy-quark limit justifies short-ranged contact potentials without long-range pion exchange
Invoked to construct the effective framework for S-wave interactions.

invented entities (1)

bare psi(4360) and psi(4660) as 4S and 5S charmonium states no independent evidence
purpose: Input poles whose residues generate the observed structures after channel coupling
Postulated as conventional quarkonium states to be dressed by the coupled channels.

pith-pipeline@v0.9.0 · 5638 in / 1391 out tokens · 72697 ms · 2026-05-07T16:10:12.409273+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Reference graph

Works this paper leans on

61 extracted references · 52 canonical work pages

[1]

S. K. Choi et al. (Belle), Observation of a narrow charmonium-like state in exclusiveB ± →K ±π+π−J/ψ decays, Phys. Rev. Lett.91, 262001 (2003), arXiv:hep- ex/0309032

work page arXiv 2003
[2]

M. B. Voloshin and L. B. Okun, Hadron Molecules and Charmonium Atom, JETP Lett.23, 333 (1976)

1976
[3]

De Rujula, H

A. De Rujula, H. Georgi, and S. L. Glashow, Molecular Charmonium: A New Spectroscopy?, Phys. Rev. Lett. 38, 317 (1977)

1977
[4]

Barnes, S

T. Barnes, S. Godfrey, and E. S. Swanson, Higher char- monia, Phys. Rev. D72, 054026 (2005), arXiv:hep- ph/0505002

work page arXiv 2005
[5]

M. A. Sultan, N. Akbar, B. Masud, and F. Akram, Higher Hybrid Charmonia in an Extended Potential Model, Phys. Rev. D90, 054001 (2014), arXiv:1403.6941 [hep- ph]

work page arXiv 2014
[6]

A. P. Szczepaniak, Triangle Singularities and XYZ Quarkonium Peaks, Phys. Lett. B747, 410 (2015), arX- iv:1501.01691 [hep-ph]

work page arXiv 2015
[7]

E. S. Swanson, Short range structure in the X(3872), Phys. Lett. B588, 189 (2004), arXiv:hep-ph/0311229

work page arXiv 2004
[8]

F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, and B.-S. Zou, Hadronic molecules, Rev. Mod. Phys.90, 015004 (2018), [Erratum: Rev.Mod.Phys. 94, 029901 (2022)], arXiv:1705.00141 [hep-ph]

work page arXiv 2018
[9]

Xiao and Z.-Y

Z. Xiao and Z.-Y. Zhou, On Friedrichs Model with Two Continuum States, J. Math. Phys.58, 062110 (2017), arXiv:1608.06833 [hep-ph]

work page arXiv 2017
[10]

Maiani, F

L. Maiani, F. Piccinini, A. D. Polosa, and V. Riquer, Diquark-antidiquarks with hidden or open charm and the nature of X(3872), Phys. Rev. D71, 014028 (2005), arXiv:hep-ph/0412098

work page arXiv 2005
[11]

N. N. Achasov and E. V. Rogozina,X(3872), I G(J P C) = 0+(1++), as theχ 1c(2P) charmonium, Mod. Phys. Lett. A30, 1550181 (2015), arXiv:1501.03583 [hep-ph]

work page arXiv 2015
[12]

Hosaka, T

A. Hosaka, T. Iijima, K. Miyabayashi, Y. Sakai, and S. Yasui, Exotic hadrons with heavy flavors: X, Y, Z, and related states, PTEP2016, 062C01 (2016), arX- iv:1603.09229 [hep-ph]

work page arXiv 2016
[13]

Brambilla, S

N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev, C.-P. Shen, C. E. Thomas, A. Vairo, and C.-Z. Yuan, TheXY Zstates: experimental and theoretical sta- tus and perspectives, Phys. Rept.873, 1 (2020), arX- iv:1907.07583 [hep-ex]

work page arXiv 2020
[14]

Richard, Exotic hadrons: review and perspectives, Few Body Syst.57, 1185 (2016), arXiv:1606.08593 [hep- ph]

J.-M. Richard, Exotic hadrons: review and perspectives, Few Body Syst.57, 1185 (2016), arXiv:1606.08593 [hep- ph]

work page arXiv 2016
[15]

Guo, X.-H

F.-K. Guo, X.-H. Liu, and S. Sakai, Threshold cusps and triangle singularities in hadronic reactions, Prog. Part. Nucl. Phys.112, 103757 (2020), arXiv:1912.07030 [hep- ph]

work page arXiv 2020
[16]

Yuan, Charmonium and charmoniumlike states at the BESIII experiment, Natl

C.-Z. Yuan, Charmonium and charmoniumlike states at the BESIII experiment, Natl. Sci. Rev.8, nwab182 (2021), arXiv:2102.12044 [hep-ex]

work page arXiv 2021
[17]

H.-X. Chen, W. Chen, X. Liu, Y.-R. Liu, and S.-L. Zhu, An updated review of the new hadron states, Rept. Prog. Phys.86, 026201 (2023), arXiv:2204.02649 [hep-ph]

work page arXiv 2023
[18]

L. Meng, B. Wang, G.-J. Wang, and S.-L. Zhu, Chiral perturbation theory for heavy hadrons and chiral ef- fective field theory for heavy hadronic molecules, Phys. Rept.1019, 1 (2023), arXiv:2204.08716 [hep-ph]

work page arXiv 2023
[19]

Liu, Y.-W

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 ex- otic hadrons: Multiplets, three-body hadronic molecules, and correlation functions, Phys. Rept.1108, 1 (2025), arXiv:2404.06399 [hep-ph]

work page arXiv 2025
[20]

Esposito, A

A. Esposito, A. Glioti, D. Germani, and A. D. Polosa, A short review on the compositeness of the X(3872), Riv. 11 Nuovo Cim.48, 95 (2025), arXiv:2502.02505 [hep-ph]

work page arXiv 2025
[21]

Esposito, A

A. Esposito, A. Pilloni, and A. D. Polosa, Multiquark Resonances, Phys. Rept.668, 1 (2017), arXiv:1611.07920 [hep-ph]

work page arXiv 2017
[22]

X. L. Wang et al. (Belle), Observation of Two Resonant Structures in e+e- to pi+ pi- psi(2S) via Initial State Radiation at Belle, Phys. Rev. Lett.99, 142002 (2007), arXiv:0707.3699 [hep-ex]

work page arXiv 2007
[23]

Pakhlova et al

G. Pakhlova et al. (Belle), Observation of a near- threshold enhancement in the e+e- —>Lambda+(c) Lambda-(c) cross section using initial-state radiation, Phys. Rev. Lett.101, 172001 (2008), arXiv:0807.4458 [hep-ex]

work page arXiv 2008
[24]

A. M. Badalian, B. L. G. Bakker, and I. V. Danilkin, The S - D mixing and di-electron widths of higher char- monium 1– states, Phys. Atom. Nucl.72, 638 (2009), arXiv:0805.2291 [hep-ph]

work page arXiv 2009
[25]

Segovia, D

J. Segovia, D. R. Entem, and F. Fernandez, Charm spectroscopy beyond the constituent quark model, in 34th International Conference on High Energy Physics (2008) arXiv:0810.2875 [hep-ph]

work page arXiv 2008
[26]

Z. Zhao, K. Xu, A. Limphirat, W. Sreethawong, N. Tagsinsit, A. Kaewsnod, X. Liu, K. Khosonthongkee, S. Cheedket, and Y. Yan, Mass spectrum of 1– heavy quarkonium, Phys. Rev. D109, 016012 (2024), arX- iv:2304.06243 [hep-ph]

work page arXiv 2024
[27]

Cotugno, R

G. Cotugno, R. Faccini, A. D. Polosa, and C. Sabelli, Charmed Baryonium, Phys. Rev. Lett.104, 132005 (2010), arXiv:0911.2178 [hep-ph]

work page arXiv 2010
[28]

Liu, H.-W

X. Liu, H.-W. Ke, X. Liu, and X.-Q. Li, Exploring open-charm decay mode Λ c ¯Λc of charmonium-like state Y(4630), Eur. Phys. J. C76, 549 (2016), arX- iv:1601.00762 [hep-ph]

work page arXiv 2016
[29]

F.-K. Guo, J. Haidenbauer, C. Hanhart, and U.-G. Meissner, Reconciling the X(4630) with the Y(4660), Phys. Rev. D82, 094008 (2010), arXiv:1005.2055 [hep- ph]

work page arXiv 2010
[30]

L.-Y. Dai, J. Haidenbauer, and U. G. Meißner, Re- examining theX(4630) resonance in the reaction e+e− →Λ + c ¯Λ− c , Phys. Rev. D96, 116001 (2017), arX- iv:1710.03142 [hep-ph]

work page arXiv 2017
[31]

J. P. Lees et al. (BaBar), Study of the reactione +e− → ψ(2S)π −π− via initial-state radiation at BaBar, Phys. Rev. D89, 111103 (2014), arXiv:1211.6271 [hep-ex]

work page arXiv 2014
[32]

X. L. Wang et al. (Belle), Measurement ofe +e− → π+π−ψ(2S) via Initial State Radiation at Belle, Phys. Rev. D91, 112007 (2015), arXiv:1410.7641 [hep-ex]

work page arXiv 2015
[33]

Ablikim et al

M. Ablikim et al. (BESIII), Measurement ofe +e− → π+π−ψ(3686) from 4.008 to 4.600˜GeV and observation of a charged structure in theπ ±ψ(3686) mass spectrum, Phys. Rev. D96, 032004 (2017), [Erratum: Phys.Rev.D 99, 019903 (2019)], arXiv:1703.08787 [hep-ex]

work page arXiv 2017
[34]

Ablikim et al

M. Ablikim et al. (BESIII), Cross section measurement of e+e− →π +π−(3686) from √ S= 4.0076 to 4.6984 GeV, Phys. Rev. D104, 052012 (2021), arXiv:2107.09210 [hep- ex]

work page arXiv 2021
[35]

Ablikim et al

M. Ablikim et al. (BESIII), Precision measurement of the e+e− →Λ + c ¯Λ− c cross section near threshold, Phys. Rev. Lett.120, 132001 (2018), arXiv:1710.00150 [hep-ex]

work page arXiv 2018
[36]

Ablikim et al

M. Ablikim et al. (BESIII), Measurement of Energy- Dependent Pair-Production Cross Section and Electromagnetic Form Factors of a Charmed Baryon, Phys. Rev. Lett.131, 191901 (2023), arXiv:2307.07316 [hep-ex]

work page arXiv 2023
[37]

Jia et al

S. Jia et al. (Belle), Observation of a vector charmonium- like state ine +e− →D + s Ds1(2536)− +c.c., Phys. Rev. D 100, 111103 (2019), arXiv:1911.00671 [hep-ex]

work page arXiv 2019
[38]

Jia et al

S. Jia et al. (Belle), Evidence for a vector charmoniumlike state ine +e− →D + s D∗ s2(2573)−+c.c., Phys. Rev. D101, 091101 (2020), arXiv:2004.02404 [hep-ex]

work page arXiv 2020
[39]

Ablikim et al

M. Ablikim et al. (BESIII), Observation of Resonance Structures in e+e-→π+π-ψ2(3823) and Mass Measurement ofψ2(3823), Phys. Rev. Lett.129, 102003 (2022), arXiv:2203.05815 [hep-ex]

work page arXiv 2022
[40]

Ablikim et al

M. Ablikim et al. (BESIII), Observation of Three Charmoniumlike States with JPC=1– in e+e-→D*0D*- π+, Phys. Rev. Lett.130, 121901 (2023), arX- iv:2301.07321 [hep-ex]

work page arXiv 2023
[41]

A. Amoroso et al., A Fit to the Availablee +e− → Λ+ c Λ − c Cross Section Data Nearby Production Threshold by Means of a Strong Correction to the Coulomb Enhancement Factor, Universe7, 436 (2021)

2021
[42]

Cao, H.-R

Q.-F. Cao, H.-R. Qi, Y.-F. Wang, and H.-Q. Zheng, Discussions on the line-shape of theX(4660) resonance, Phys. Rev. D100, 054040 (2019), arXiv:1906.00356 [hep- ph]

work page arXiv 2019
[43]

S. G. Salnikov and A. I. Milstein, Near-threshold res- onance in e+e-→ΛcΛ¯c process, Phys. Rev. D108, L071505 (2023), arXiv:2309.17018 [hep-ph]

work page arXiv 2023
[44]

A. I. Milstein and S. G. Salnikov, Final-state interaction in the process e+e-→ΛcΛ¯c, Phys. Rev. D105, 074002 (2022), arXiv:2201.07450 [hep-ph]

work page arXiv 2022
[45]

Q. Ye, Z. Zhang, M.-L. Du, U.-G. Meißner, P.-Y. Niu, and Q. Wang, Resonance parameters of the vector char- moniumlike state G(3900), Phys. Rev. D112, 016015 (2025), arXiv:2504.17431 [hep-ph]

work page arXiv 2025
[46]

Du, U.-G

M.-L. Du, U.-G. Meißner, and Q. Wang,P-wave coupled channel effects in electron-positron annihilation, Phys. Rev. D94, 096006 (2016), arXiv:1608.02537 [hep-ph]

work page arXiv 2016
[47]

S. M. Flatte, Coupled - Channel Analysis of the pi eta and K anti-K Systems Near K anti-K Threshold, Phys. Lett. B63, 224 (1976)

1976
[48]

V. Baru, J. Haidenbauer, C. Hanhart, A. E. Kudryavtsev, and U.-G. Meissner, Flatte-like distributions and the a(0)(980) / f(0)(980) mesons, Eur. Phys. J. A23, 523 (2005), arXiv:nucl-th/0410099

work page arXiv 2005
[49]

Anselmino, E

M. Anselmino, E. Predazzi, S. Ekelin, S. Fredriksson, and D. B. Lichtenberg, Diquarks, Rev. Mod. Phys.65, 1199 (1993)

1993
[50]

Shifman and A

M. Shifman and A. Vainshtein, Comments on diquarks, strong binding and a large hidden QCD scale, Phys. Rev. D71, 074010 (2005), arXiv:hep-ph/0501200

work page arXiv 2005
[51]

Y. Kim, M. Oka, and K. Suzuki, Chiral effective theory of scalar and vector diquarks revisited, Phys. Rev. D111, 034014 (2025), arXiv:2411.17803 [hep-ph]

work page arXiv 2025
[52]

P.-Y. Niu, Q. Wang, and Q. Zhao, Probing the diquark structure of Λc in a combined analysis of Λc →ΛK + and Λc →Σ 0K+, Phys. Rev. D113, 033001 (2026)

2026
[53]

M. B. Voloshin, Heavy quark spin symmetry breaking in near-thresholdJ P C = 1 −− quarkonium-like resonances, Phys. Rev. D85, 034024 (2012), arXiv:1201.1222 [hep- ph]

work page arXiv 2012
[54]

Guo, U.-G

F.-K. Guo, U.-G. Meißner, W. Wang, and Z. Yang, How to reveal the exotic nature of the P c(4450), Phys. Rev. D92, 071502 (2015), arXiv:1507.04950 [hep-ph]. 12

work page arXiv 2015
[55]

Navas et al

S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D110, 030001 (2024)

2024
[56]

Hoferichter, J

M. Hoferichter, J. R. de Elvira, B. Kubis, and U.-G. Meißner, Nucleon resonance parameters from Roy–Steiner equations, Phys. Lett. B853, 138698 (2024), arXiv:2312.15015 [hep-ph]

work page arXiv 2024
[57]

X.-Y. Hu, J. He, P. Niu, Q. Wang, and Y. Yan, Three- body final state interactions in B+→DD¯K+ decays, Phys. Rev. D113, 054003 (2026), arXiv:2509.10039 [hep- ph]

work page arXiv 2026
[58]

L. Y. Dai, M. Shi, G.-Y. Tang, and H. Q. Zheng, Nature of X(4260), Phys. Rev. D92, 014020 (2015), arX- iv:1206.6911 [hep-ph]

work page arXiv 2015
[59]

Q. Ye, Y. Zhang, P.-Y. Niu, and Q. Wang, Why is the Zc(3900) absent in theh cπfinal state?, (2026), arX- iv:2601.03697 [hep-ph]

work page arXiv 2026
[60]

Byckling and K

E. Byckling and K. Kajantie, Particle Kinematics: (Chapters I-VI, X) (University of Jyvaskyla, Jyvaskyla, Finland, 1971). 13 Appendix A: Flatt´ e parameterization of the two-point function In this appendix, we present the Flatt´ e parameterization of the two-point function for theψ(2S)−f 0(980) system. The case of theψ(2S)−σ(500) system follows analogousl...

1971
[60]

Byckling and K

E. Byckling and K. Kajantie, Particle Kinematics: (Chapters I-VI, X) (University of Jyvaskyla, Jyvaskyla, Finland, 1971). 13 Appendix A: Flatt´ e parameterization of the two-point function In this appendix, we present the Flatt´ e parameterization of the two-point function for theψ(2S)−f 0(980) system. The case of theψ(2S)−σ(500) system follows analogousl...

1971