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S-wave two-hadron dynamics explain the charmed-strange axial mesons and predict a three-body state near 3265 MeV

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D1(2420) and the D_s1 states are modeled as two-hadron molecules, and a new n \bar D_s1(2460) three-body state at ~3265 MeV is predicted.

T0 review reviewed 2026-08-02 challenge →

load-bearing objection A proceedings summary of the authors' own molecular program: the two-body results are recycled from earlier papers, and the three-body prediction rests on an uncheckable equation as printed — but the physics is serious and the correlation signatures are falsifiable. the 4 major comments →

arxiv 2607.14389 v1 pith:YVJX2BTA submitted 2026-07-15 hep-ph nucl-th

Exotic states with charm and/or strangeness

A. Mart\'inez Torres , Breno Agat\~ao , Pedro Brand\~ao , K. P. Khemchandani , Luciano M. Abreu , E. Oset This is my paper
classification hep-ph nucl-th
keywords exotic hadronshadronic moleculesD1(2420)D_s1(2460)D_s1(2536)three-body statescorrelation functionss-wave dynamics
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

This paper argues that the axial mesons D1(2420), D_s1(2460), and D_s1(2536) are not ordinary quark-antiquark states but emerge from s-wave interactions between pseudoscalar and vector mesons. It shows that a coupled-channel two-body calculation reproduces the D*π invariant mass distribution seen in B decays, supporting a molecular interpretation of D1(2420). It further predicts that a neutron interacting with an anti-D_s1(2460) cluster forms a three-body state with a mass of about 3265 MeV and a width of about 90 MeV, and it gives the corresponding correlation function. A reader would care because, if correct, the result turns these mesons into predictable consequences of hadron–hadron dynamics and opens a new class of three-body states with charm and strangeness.

Core claim

In the paper's own terms, the key claim is that s-wave pseudoscalar–vector dynamics generate the axial mesons. Solving the coupled-channel two-body equations with channels such as D*π, Dρ, and D_s K* gives a pole near 2428 MeV with a width of about 33 MeV, identified with D1(2420), and the same amplitude reproduces the measured D*π invariant mass distribution in B decays within the model's bands. When a nucleon is added, the fixed-center approximation to the three-body problem, using the same two-body t-matrices and molecular form factors, yields a T-matrix pole at about 3265 MeV with a width of about 90 MeV in the n anti-D_s1(2460) system; the analogous calculation for anti-D_s1(2536) gives

What carries the argument

The central machinery is a coupled-channel, s-wave two-hadron scattering amplitude, generated from pseudoscalar–vector dynamics, that produces the axial-meson poles as molecular states. This same amplitude is then inserted into a fixed-center approximation to the three-body equations: the nucleon rescatters successively off the two constituents of an assumed anti-D_s1(2460) or anti-D_s1(2536) cluster, and the resulting amplitudes are iterated with cluster form factors. The predicted three-body T-matrix pole is the new state. Correlation functions are obtained from the same amplitudes through the standard source-averaged wave-function formula, with a Gaussian source of variable size R.

Load-bearing premise

The calculation assumes that the anti-D_s1(2460) and anti-D_s1(2536) mesons are tightly bound two-hadron clusters and that the fixed-center approximation to the three-body equations is reliable for a nucleon hitting such a cluster; if the cluster is not predominantly molecular or the approximation is too crude, the 3265 MeV prediction and the associated correlation functions do not follow.

What would settle it

A full three-body calculation of the n anti-D_s1(2460) system without the fixed-center approximation, or a high-statistics measurement of the n anti-D_s1(2460) correlation function, would settle the claim: the predicted pole would appear as a distinct low-momentum suppression with source-size dependence, while its absence would indicate the molecular-cluster assumption is wrong.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • If D1(2420) is indeed generated from s-wave pseudoscalar–vector dynamics, then its production in B decays is a rescattering effect, and the observed invariant mass distribution follows from the two-body amplitude without invoking a quark-antiquark seed.
  • The D*π and Dρ correlation functions are sensitive to the assumed scattering length; future correlation measurements can therefore distinguish between different theoretical extractions.
  • A new three-body state in the n anti-D_s1(2460) system should exist at about 3265 MeV with a width of about 90 MeV, and its correlation function should show a low-momentum depletion that strengthens as the source size increases.
  • The analogous calculation for n anti-D_s1(2536) gives similar three-body behavior, so the prediction is a small family of states rather than an isolated one.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If confirmed, the 3265 MeV state would be a baryonic hadronic molecule—a neutron bound to a charmed-strange meson—outside the usual three-quark classification of baryons.
  • The same fixed-center scheme could be applied to other molecular clusters, such as a nucleon bound to other heavy-light mesons, to produce a spectroscopy of three-body states; this goes beyond the paper's explicit examples.
  • The correlation-function differences identified for D*π suggest that high-statistics heavy-ion data, which measure correlation functions directly, could provide a more model-independent determination of the D*π scattering length than invariant-mass fits alone.
  • Since the three-body prediction depends on the fixed-center approximation, a full three-body calculation or a lattice study of the n anti-D_s1 system would be a sharper test than the paper's current comparison.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. This proceedings contribution summarizes a coupled-channel study in which the axial charm-strange states are generated from s-wave pseudoscalar-vector dynamics. Section 2 presents D* pi and D rho correlation functions and the D*+ pi- invariant mass distribution from B decays, comparing with LHCb data to argue that D1(2420) is dynamically generated. Section 3 extends the formalism to three-body systems using the fixed-center approximation to the Faddeev equations, claiming a state in the n \bar D_s1(2460) system with mass ~3265 MeV and width ~90 MeV, together with the corresponding correlation function.

Significance. If the results are correct, the paper provides complementary evidence from correlation functions and invariant mass distributions for the molecular interpretation of D1(2420), and it makes a sharp, falsifiable prediction of a three-body state in n \bar D_s1(2460). The underlying coupled-channel and fixed-center methods are established in the authors' previous work, and comparison with LHCb data is valuable. However, the numerical claims are not reproducible from this manuscript: the printed Lippmann-Schwinger equation is tautological, key inputs are fitted to the very states being described, and the central three-body result is delegated to Ref. [20] without convergence checks.

major comments (4)
  1. [Sec. 3, Eq. (3.2)] The equation T = T + T G T as printed is not a meaningful Lippmann-Schwinger equation; it is algebraically tautological and cannot be solved to produce the pole in Fig. 5. Presumably the intended form is T = V + V G T with V built from the T_{ij} amplitudes of Eq. (3.1), but this is never stated. As written, the central three-body prediction at ~3265 MeV with ~90 MeV width is not reproducible.
  2. [Sec. 3, after Eq. (3.1)] The cluster form factors and the propagators g and G^(i) are essential inputs to the fixed-center calculation, yet the manuscript only says 'We refer the reader to Ref. [20] for more details.' No explicit expressions are provided, and no convergence check against a full three-body Faddeev/AGS calculation or variation of the cluster form factor is reported. The predicted pole and the n \bar D_s1 correlation function in Figs. 5-6 therefore cannot be independently assessed from this paper.
  3. [Secs. 2.1-2.2] The 'explanation' of D1(2420) is not parameter-free: in Sec. 2.1 the bare q\bar q pole mass and coupling are varied to reproduce the mass and width of D1(2430), and in Sec. 2.2 an arbitrary normalization constant is fixed to reproduce 100% (or 85%) of the LHCb area. The conclusion that the model 'can explain quite well' the LHCb behavior is therefore a shape test after fitting to the state itself, not a parameter-free prediction. The sensitivity of the correlation functions and the invariant mass distribution to these fitted parameters should be quantified.
  4. [Sec. 2, Eqs. (2.3)-(2.4)] The momentum cutoff q_max appears as a regularization parameter set to ~1000 MeV, but no values are specified for the results in Figs. 1 and 3, and no cutoff dependence is shown. Since the coupled-channel amplitude and the correlation function depend on this cutoff, the robustness of the comparison with LHCb and ALICE data is not established.
minor comments (5)
  1. [Abstract] The abstract is truncated at 'obtained from n\bar'; the sentence is incomplete.
  2. [Eq. (2.3)] The notation for the integral is confusing: the upper limit 'infinity' appears before the integrand, and the q_max Heaviside factor is not reflected in the displayed limits. Please rewrite the integration limits cleanly.
  3. [Fig. 3 caption] The caption reads 'mD*- pi+' but should likely be 'm_{D^{*+}\pi^-}' to match the text.
  4. [Sec. 3, Eq. (3.1)] The index structure in T_{ij} = t_i \delta_{ij} + t_i g T_{kj} is not fully defined, especially the range of the free index and the meaning of k. A clear definition of the coupled-channel rows and columns would improve reproducibility.
  5. [Sec. 3, after Eq. (3.4)] The statement that the T-matrix 'satisfies elastic two-body unitarity' is unclear because T is a sum of four components, not a single elastic amplitude. Please clarify what unitarity condition is meant.

Circularity Check

1 steps flagged

Three-body prediction rests on a self-referential equation as printed; two-body sections are not circular.

specific steps
  1. self definitional [Section 3, Eq. (3.2)]
    "The amplitudes Tij are then used as a kernel in a Lippmann-Schwinger type equation to implement the particle-cluster propagation in each of the contributions considered in Eq. (3.1): T=T+TGT, where T= ( T11 T12 ; T21 T22 ), G= ( G(1) 0 ; 0 G(2) )."

    As printed, the unknown T-matrix appears on both sides with no distinct kernel: T = T + T G T. Rearranged, this only enforces T G T = 0, so the equation does not determine a nontrivial particle-cluster amplitude from the stated two-body inputs t_i and propagators. The claimed ~3265 MeV state in Fig. 5 is presented as the output of solving this equation, so on the written derivation the central three-body prediction reduces to a self-referential identity rather than following from the input dynamics. The surrounding text suggests the Eq. (3.1) amplitudes were meant to serve as a separate kernel, but the manuscript's explicit equation is tautological.

full rationale

The two-body sections are not significantly circular. In Sec. 2.1 the bare-pole parameters are varied to reproduce D1(2430), but the correlation functions are displayed as subsequent outputs, not as the fitted quantities. In Sec. 2.2 the arbitrary constant is explicitly stated to fix only the total area, so the shape comparison with LHCb data is not statistically forced by that normalization. The reliance on Refs. [15,18,20] is a normal citation of prior published calculations, not a uniqueness argument or a self-citation chain that forbids alternatives. The genuine circularity is localized in Eq. (3.2): as written, the fixed-center Faddeev equation defines T in terms of itself. If the intended Lippmann-Schwinger form with a separate kernel (e.g., T = V + V G T, with V from Eq. 3.1) is restored, the three-body prediction would be a legitimate, if model-dependent, derivation. But the printed derivation makes the sharpest new claim—the n\bar D_s1(2460) bound state—depend on a tautological equation, warranting a partial circularity score rather than a no-circularity finding.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 2 invented entities

The calculation leans on several fitted or hand-chosen inputs. Most consequential: the D1(2430)-pole parameters are fitted to the state they are used to describe (§2.1), the B-decay amplitude is normalized to the experimental area (§2.2), and the three-body result depends on the validity of the fixed-center approximation and on two-body t-matrices from previous coupled-channel fits. The existence of these tuned inputs is the main reason the 'predictions' are only partially independent.

free parameters (5)
  • Bare q\bar q pole mass and coupling in the D*pi amplitude = not given (varied to reproduce D1(2430) mass/width)
    Sec. 2.1: 'the coupling constant and mass of this pole are varied to try to reproduce the mass and width of D1(2430)'—direct fitting of the model to the state it later claims to describe.
  • Overall normalization constant in B^- -> D_s^- D^*+ pi^- invariant mass amplitude = fixed to reproduce 100% or 85% of the experimental area
    Sec. 2.2: constant fixed by normalizing to the LHCb distribution, so the shape agreement is not a parameter-free prediction.
  • Momentum cutoff q_max in loop/correlation functions = ~1000 MeV
    Eq. (2.4) and text: q_max is a cutoff 'needed to regularize the integral when r -> 0'; results depend on its value.
  • Gaussian source size R = 1 fm (Fig. 1); varied in Fig. 6
    Eq. (2.2) and Fig. 1 caption: source size chosen as R=1 fm; correlation function magnitude depends on R (Fig. 6).
  • Cluster form-factor parameters in three-body propagator = not specified here; from Refs. [18,20]
    Eqs. (3.2)-(3.3) and text: G^(i) 'depends on a form-factor related to the molecular nature of the cluster'; no parameters or functional forms are given in this manuscript.
axioms (4)
  • domain assumption Bethe-Salpeter coupled-channel equations with s-wave pseudoscalar-vector interactions generate D1(2420), D_s1(2460), D_s1(2536) poles
    Sec. 2, 3: the whole analysis assumes these states are dynamically generated by two-hadron channels rather than predominantly q\bar q; Refs. [15-19] are cited but no independent check is given in this manuscript.
  • ad hoc to paper Fixed-center approximation (FCA) to Faddeev equations is valid for N \bar D^* \bar K (N \bar D \bar K^*) scattering
    Sec. 3, Eq. (3.1): uses FCA 'where the interaction of the three-particles resembles that of a particle with a fixed scattering center'; no convergence tests or comparison with a full Faddeev solution are provided.
  • standard math Koonin-Pratt formula Eq. (2.1)-(2.3) with a static Gaussian source and spherical Bessel projection is the correct description of the measured correlation functions
    Sec. 2.1: standard femtoscopy formalism [26-28]; assumed, not derived.
  • domain assumption The hadronization of q\bar q pairs in B decays produces tree-level amplitudes with only the relative strength between final states fixed
    Sec. 2.2: 'the hadronization procedure considered fixes only the relative strength between different final states', leaving an arbitrary overall constant that must be fitted.
invented entities (2)
  • Bare q\bar q pole in the D*pi amplitude no independent evidence
    purpose: Introduced to reproduce D1(2430) mass/width and a lattice/ALICE-compatible D*pi scattering length while keeping D1(2420) from Drho dynamics (Sec. 2.1).
    This is an unobserved ad hoc component; its mass/coupling are fitted to input observables, and it has no independent falsifiable handle in this manuscript.
  • Predicted three-body state in n \bar D_s1(2460) independent evidence
    purpose: Emerges from the fixed-center Faddeev calculation as a resonance with mass ~3265 MeV and width ~90 MeV (Sec. 3, Fig. 5).
    It is a falsifiable prediction: the mass/width and depletion in the n\bar D_s1 correlation function (Fig. 6) can be tested in future measurements, so this is a genuine predicted entity rather than an ad hoc fit.

reviewed 2026-08-02 · how reviews work

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Cite this review

Pith. "Pith review of Exotic states with charm and/or strangeness." pith.science (2026). https://pith.science/paper/YVJX2BTA

@misc{pith2026260714389,
  author       = {Pith},
  title        = {Pith review of: Exotic states with charm and/or strangeness},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YVJX2BTA}},
  note         = {Machine review of arXiv:2607.14389}
}
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abstract

In this talk, I will discuss the properties of several exotic states with charm and/or strangeness. These states can be interpreted either as being generated from two- or three-hadron dynamics. In particular, I will focus on $D_1(2420)$ and some predictions of three-body states obtained from $n\bar

discussion (0)

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Reference graph

Works this paper leans on

34 extracted references · 3 linked inside Pith

  1. [1]

    Acharyaet al.[ALICE], Phys

    S. Acharyaet al.[ALICE], Phys. Lett. B844(2023), 137223

    2023

  2. [2]

    Fabbietti, V

    L. Fabbietti, V . Mantovani Sarti and O. Vazquez Doce, Ann. Rev. Nucl. Part. Sci.71(2021), 377-402

    2021

  3. [3]

    K. P . Khemchandani, L. M. Abreu, A. Martinez Torres and F. S. Navarra, Phys. Rev. D110(2024) no.3, 036008

    2024

  4. [4]

    Albaladejo, A

    M. Albaladejo, A. Feijoo, J. Nieves, E. Oset and I. Vidaña, Phys. Rev. D110(2024) no.11, 114052

    2024

  5. [5]

    L. M. Abreu, P . Gubler, K. P . Khemchandani, A. Martinez Torres and A. Hosaka, Phys. Lett. B860(2025), 139175

    2025

  6. [6]

    Brandão, B

    P . Brandão, B. Agatão, L. M. Abreu, K. P . Khemchandani and A. Martínez Torres, [arXiv:2512.24370 [hep-ph]]

    Pith/arXiv arXiv

  7. [7]

    Acharyaet al.[ALICE], Phys

    S. Acharyaet al.[ALICE], Phys. Rev. X14(2024) no.3, 031051

    2024

  8. [8]

    M. Z. Liu, Y. W. Pan, Z. W. Liu, T. W. Wu, J. X. Lu and L. S. Geng, Phys. Rept.1108(2025), 1-108

    2025

  9. [9]

    W. T. Lyu, L. R. Dai and E. Oset, [arXiv:2603.16640 [hep-ph]]

    Pith/arXiv arXiv

  10. [10]

    W. H. Jia, J. Song, W. H. Liang and E. Oset, [arXiv:2602.16683 [hep-ph]]

    Pith/arXiv arXiv

  11. [11]

    B. B. Malabarba, X. L. Ren, K. P . Khemchandani and A. Martinez Torres, Phys. Rev. D103(2021) no.1, 016018

    2021

  12. [12]

    B. B. Malabarba, K. P . Khemchandani and A. Martinez Torres, Phys. Rev. D108(2023) no.3, 036010

    2023

  13. [13]

    X. L. Ren, B. B. Malabarba, K. P . Khemchandani and A. Martinez Torres, JHEP05(2019), 103

    2019

  14. [14]

    X. L. Ren, K. P . Khemchandani and A. Martinez Torres, Phys. Rev. D102(2020) no.1, 016005

    2020

  15. [15]

    B. B. Malabarba, K. P . Khemchandani, A. Martinez Torres and E. Oset, Phys. Rev. D107(2023) no.3, 036016

    2023

  16. [16]

    E. E. Kolomeitsev and M. F. M. Lutz, Phys. Lett. B582(2004), 39-48

    2004

  17. [17]

    Hofmann and M

    J. Hofmann and M. F. M. Lutz, Nucl. Phys. A733(2004), 142-152

    2004

  18. [18]

    Gamermann and E

    D. Gamermann and E. Oset, Eur. Phys. J. A33(2007), 119-131

    2007

  19. [19]

    Cleven, F

    M. Cleven, F. K. Guo, C. Hanhart and U. G. Meissner, Eur. Phys. J. A47(2011), 19

    2011

  20. [20]

    Agatão, P

    B. Agatão, P . Brandão, A. Martínez Torres, K. P . Khemchandani, L. M. Abreu and E. Oset, Eur. Phys. J. C 85(2025) no.10, 1136

    2025

  21. [21]

    Mohler, S

    D. Mohler, S. Prelovsek and R. M. Woloshyn, Phys. Rev. D87(2013) no.3, 034501

    2013

  22. [22]

    Z. H. Guo, L. Liu, U. G. Meißner, J. A. Oller and A. Rusetsky, Eur. Phys. J. C79(2019) no.1, 13

    2019

  23. [23]

    F. K. Guo, C. Hanhart and U. G. Meissner, Eur. Phys. J. A40(2009), 171-179

    2009

  24. [24]

    M. L. Du, M. Albaladejo, P . Fernández-Soler, F. K. Guo, C. Hanhart, U. G. Meißner, J. Nieves and D. L. Yao, Phys. Rev. D98(2018) no.9, 094018

    2018

  25. [25]

    Acharyaet al.[ALICE], Phys

    S. Acharyaet al.[ALICE], Phys. Rev. D110(2024) no.3, 032004

    2024

  26. [26]

    S. E. Koonin, Phys. Lett. B70(1977), 43-47

    1977

  27. [27]

    Pratt, Phys

    S. Pratt, Phys. Rev. D33(1986), 1314-1327

    1986

  28. [28]

    Vidana, A

    I. Vidana, A. Feijoo, M. Albaladejo, J. Nieves and E. Oset, Phys. Lett. B846(2023), 138201

    2023

  29. [29]

    Aaijet al.[LHCb], JHEP08(2024), 165

    R. Aaijet al.[LHCb], JHEP08(2024), 165

    2024

  30. [30]

    Aaijet al.[LHCb], Phys

    R. Aaijet al.[LHCb], Phys. Rev. D101(2020) no.3, 032005

    2020

  31. [31]

    Kaiser, P

    N. Kaiser, P . B. Siegel and W. Weise, Nucl. Phys. A594(1995), 325-345

    1995

  32. [32]

    Oset and A

    E. Oset and A. Ramos, Nucl. Phys. A635(1998), 99-120

    1998

  33. [33]

    E. J. Garzon and E. Oset, Eur. Phys. J. A48(2012), 5

    2012

  34. [34]

    Martinez Torres, K

    A. Martinez Torres, K. P . Khemchandani, L. Roca and E. Oset, Few Body Syst.61(2020) no.4, 35

    2020

This paper was first reviewed by deepseek-v4-flash on August 2, 2026.