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REVIEW 3 major objections 4 minor 80 references

A short review on the compositeness of the $X(3872)$

T0 review · 3 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read This paper argues that the X(3872) is not a shallow D D* molecule: its measured radiative decay ratio is about forty times the molecular prediction, and the LHCb lineshape fit does not test partial compositeness.

desk verdict A thoughtful review with a correct and useful point about Flatte lineshapes testing only the compact limit, but the radiative-decay exclusion of the molecule is softer than the conclusions admit. read the letter →

arxiv 2502.02505 v2 pith:MVUXM5JQ submitted 2025-02-04 hep-ph

Angelo Esposito , Alfredo Glioti , Davide Germani , Antonio D. Polosa This is my paper · ORCID
classification hep-ph
keywords X(3872)hadronicmoleculecompacttetraquarkcompositenessradiativedecaysFlattelineshapeeffectiverangeWeinbergcriterion
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

This paper argues that the $X(3872)$ is not a shallow $\bar D D^*$ molecule, the way the deuteron is a shallow proton-neutron molecule. The measured branching ratio $\mathrm{Br}(X\to\psi'\gamma)/\mathrm{Br}(X\to\psi\gamma)\simeq 1.67$ is roughly forty times the molecular prediction of about $0.034$, which pion corrections raise only to $0.043$. The paper also argues that the LHCb lineshape analysis, often quoted as evidence for partial compositeness, is built on an effective theory with no $\bar D D^*$ bound state and therefore tests only the compact hypothesis. If these arguments hold, the $X(3872)$ is at least as elementary as ordinary open-charm mesons, and its large prompt production at the LHC is naturally explained by a compact component.

What carries the argument

The argument is carried by three instruments. First, the universal shallow-bound-state wavefunction $\Psi_{\rm mol}(r)\propto e^{-r/a_s}/r$, whose only input is the binding energy and which fixes the molecular prediction for the radiative ratio through the factorized amplitude of Eq. (12.3), in which the molecular wavefunction multiplies the internal wavefunctions of the $D$ and $D^*$ mesons. Second, the distinction between two effective theories for the lineshape: the molecular amplitude (Eq. (11.33)) contains the quartic meson-meson interaction that can bind $\bar D D^*$, whereas the Flatt\'e amplitude (Eq. (11.46)) contains only the $X\bar D D^*$ trilinear coupling and hence no bound state. Third, Weinberg's effective-range relation $r_0 = -Z R_0/(1-Z)$, which the paper shows cannot be applied to the Flatt\'e parameters, because the negative $r_0$ of the Flatt\'e amplitude is a kinematic property of the charged threshold, not a sign of compactness.

What would settle it

Measure the light-quark charge radius of the D and D* mesons (for example from semileptonic form factors) and recompute the molecular radiative ratio using the same universal wavefunction and factorization: a radius of about 0.9 fm or larger would lift the prediction from roughly 0.04 toward the measured 1.67 and remove the paper's main exclusion.

Watch

Extended reading notes

Core claim

The authors' central claim is that the composite (molecular) interpretation of the $X(3872)$ is excluded by data, while the compact (elementary tetraquark) hypothesis is the one being tested by the currently available LHCb lineshape fit. Using the universal wavefunction of a shallow bound state, they compute the radiative decays into $\psi'\gamma$ and $\psi\gamma$ and obtain a ratio $R\simeq 0.034$ (or $0.043$ after including pion corrections), against the LHCb measurement $R=1.67\pm 0.21\pm 0.12\pm 0.04$. They further show that the Flatt\'e amplitude used by LHCb follows from a Lagrangian containing only the trilinear $X\bar D D^*$ coupling, with no quartic $(\bar D D^*)^2$ interaction, so no molecular bound state exists in that effective theory; consequently the $Z$ values extracted from that fit are not a measure of partial compositeness. Under the purely compact hypothesis the coupling extracted from the lineshape reproduces the measured $X\to \bar D D\pi$ rate when the $D^{*0}$ width is around $100$ keV, close to the charged $D^{*\pm}$ width. The conclusion is that the $X(3872)$ is not less elementary than the open-charm mesons.

Load-bearing premise

The radiative-decay exclusion of the molecule depends on assuming the D and D* mesons are about 0.68 fm in size and that the molecular wavefunction factorizes from their internal wavefunctions; if the mesons are actually as big as about 0.9 fm, the molecular prediction can reach the measured ratio.

Editorial extensions

If this is right

  • If the $X(3872)$ is mostly compact, its large prompt production cross section at high $p_T$ stops being a puzzle: the compact component can be produced and then decay into $\bar D D^*$.
  • The $Z$ values quoted from the LHCb Flatt\'e fit should not be cited as measurements of partial compositeness; a molecular fit using Eq. (11.33) is needed to compare the two hypotheses on the same data.
  • Under the compact hypothesis the $D^{*0}$ width is predicted near $100$ keV, consistent with the measured charged $D^{*\pm}$ width, which is a testable cross-check.
  • The effective range $r_0$, after subtracting the charged-threshold contribution, becomes the practical discriminant: positive $r_0$ would favor a molecule, a large negative value would favor a compact state.

Reading between the lines

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

  • A direct measurement of the $D$/$D^*$ light-quark radius would settle the radiative-decay argument: if the radius is near $0.9$ fm or larger, the molecular prediction could reach the observed ratio, as the paper itself concedes.
  • The same universal-wavefunction test could be applied to other near-threshold exotics such as $T_{cc}^+$, where radiative or hidden-flavor decay ratios might discriminate molecules from compact states more sharply than line shapes.
  • The paper's distinction between the Flatt\'e and molecular amplitudes implies that reinterpreting existing LHCb data with the molecular amplitude, or fitting Weinberg's pole formula directly to the few near-threshold points, is the most direct next step and may require no new data, only new fits.
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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 paper reviews the compositeness of the X(3872), contrasting a shallow D0 Dbar*0 molecule, a compact tetraquark, and a partially composite state. It re-derives the universal scattering amplitude and Weinberg's elementariness parameter Z, then builds a nonrelativistic effective field theory in which the D Dbar* scattering amplitude can include quartic meson couplings (molecular case) or an elementary X field (Flatte case). A central claim is that the LHCb Flatte analysis uses only the latter, so the Z values sometimes extracted from it are not meaningful for partial compositeness; the paper proposes a fit to the purely molecular amplitude instead. It then uses the LHCb coupling to predict Gamma(X -> D Dbar pi) and finds agreement for Gamma_D*0 ~ 105 +/- 70 keV. Finally, the measured ratio R = Br(X -> psi' gamma)/Br(X -> psi gamma) = 1.67 is compared with the molecular prediction R ~ 0.034 (0.043 after pion corrections), leading to the conclusion that a pure molecule is excluded and that the X is not less elementary than open-charm mesons.

Significance. If the radiative-decay modeling is correct, the paper provides a clean, falsifiable discriminator between the molecular and compact hypotheses for the X(3872), with a numerical gap of nearly two orders of magnitude between prediction and experiment. The EFT derivation is transparent and checkable, and the explicit demonstration that the LHCb Flatte parametrization is a Lambda = 0 limit with no quartic interaction is a useful contribution. The paper also gives a concrete strategy for extracting r0 from the universal amplitude and for testing the molecular lineshape. The significance is reduced, however, because the main exclusion of Z = 0 rests on the 0.68 fm D-meson size from Ref. [49] and on an unproven factorization at short distances; the manuscript itself identifies the parameter range that would remove the conflict. With a quantified sensitivity analysis the conclusion could be made solid; as written it is conditional.

major comments (3)
  1. [Sec. 12 (Eqs. 12.3, 12.8-12.10, 12.32)] The conclusion in Section 13 that the X(3872) is 'not less elementary than open-charm mesons' rests on the radiative ratio R. The predicted values R = 0.034 and R = 0.043 are obtained with the Gaussian light-quark wavefunction of Eq. (12.8) with sqrt(<r^2>) ~ 0.68 fm from Ref. [49]. The manuscript itself concedes in Section 12, item 1, that D-meson sizes of about 0.9 fm or more would reconcile the molecular prediction with the measured R = 1.67. Because the discrepancy is a factor of roughly 40 and depends on a single most important adopted parameter, the authors should either provide a quantitative R(b) scan with a critical value or soften the Section 13 conclusion. As written, the central exclusion of Z = 0 is not robust to this modeling assumption.
  2. [Sec. 12 (Eq. 12.3 and discussion after Eq. 12.10)] The factorization Psi_mol(R) Xi_D Xi_D* in Eq. (12.3) assumes that the universal shallow-bound-state wavefunction can be evaluated at the short distances probed by c-cbar annihilation. The universal wavefunction (12.1) is only justified at separations larger than the range of the binding potential, while Eq. (12.3) samples separations of the order of the D-meson size, where the effective-range description and the factorization from the internal meson wavefunctions are not controlled. The one-pion correction computed in Eqs. (12.14)-(12.32) tests only one short-distance modification and leaves the factor-of-roughly-40 gap. Without an estimate of other short-distance uncertainties, such as finite charmonium size, form factors, or coupled-channel effects, the radiative-decay exclusion is not decisive.
  3. [Secs. 11.1.2 and 13] The lineshape analysis in Section 11.1.2 properly supports the statement that the LHCb Flatte fit is consistent with a purely compact description, but it does not exclude partially composite scenarios, because the fitted amplitude contains no quartic DD* interaction and therefore no molecular component by construction. The conclusion in Section 13 combines this with the radiative-decay argument, yet no quantitative bound on Z is obtained from the lineshape alone. The authors should make explicit that the 'not less elementary' conclusion is driven by the radiative-ratio modeling, and that the lineshape evidence is only a consistency test of one extreme hypothesis.
minor comments (4)
  1. [Sec. 5 (Eq. 5.10) and Sec. 11.1.2 (Eq. 11.54)] The central value Z = 0.1 +/- 0.4 is obtained with Gamma_D*0 ~ 2 MeV, while Eq. (11.54) later estimates Gamma_D*0 ~ 105 +/- 70 keV; since Fig. 1 shows the allowed region depends strongly on Gamma_D*0, the text should use a consistent value or explicitly state that the earlier value is a conservative upper-bound choice.
  2. [References] References [6] and [7] are identical (both Artoisenet, Braaten, Kang, 'Using Line Shapes to Discriminate between Binding Mechanisms for the X(3872)'); one of them should be removed or replaced with the intended citation.
  3. [Sec. 11.1.3 (Eq. 11.67)] The wrong-sign kinetic term for the auxiliary field X_m is introduced abruptly; a sentence explaining that this is an auxiliary-field representation of a contact interaction and does not imply a propagating ghost would prevent confusion.
  4. [Sec. 10 (Eq. 10.31 and footnote 23)] The isospin-subtraction recipe is applied to obtain r'_0 = -3.78 fm and Z ~ 0.11, but footnote 23 states that no rigorous proof of the recipe is known; the text should label this value as illustrative, especially because the following section argues that the Z extraction from the Flatte fit is not meaningful.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular reduction: the radiative-ratio exclusion and the Flatte critique are self-contained derivations benchmarked against external LHCb and PDG data; the paper's self-citations are not load-bearing.

full rationale

The central exclusions are not constructed from their conclusions. Section 12 computes R = 0.034 from the universal wavefunction (12.1), the factorization (12.3)/(12.5), and the 1989 quark-model Gaussian size (12.8)-(12.9); no parameter is fitted to the measured ratio (12.2), and the pion-corrected value R = 0.043 in (12.32) is obtained by an explicit renormalized perturbative computation rather than by imposing Rexp. The paper's own caveat that D-meson sizes of 0.9 fm or more would reconcile the prediction (Section 12, item 1) is a modeling-sensitivity limitation, not a circular identity. Similarly, the lineshape argument in Sections 10 and 11.1.2 shows that the Flatte amplitude is derived by setting Lambda = 0, i.e. by excluding the quartic meson-meson interaction; the statement that Z extracted from such a fit is meaningless is a structural consequence of the effective theory, not a prediction reduced to its input. The X -> D Dbar pi consistency check in Section 11.1.2 uses g_LHCb from the 2020 LHCb lineshape and compares the resulting width with the PDG branching fraction, which is an external benchmark. Refs [34] and [42] are self-citations, but the load-bearing computations are reproduced in Sections 9 and 12 with explicit equations and fixed external constants; they are not black-box uniqueness theorems. No fitted parameter is renamed as a prediction, and no known empirical pattern is merely relabeled. Hence no circular step is present, and the derivation is self-contained against external data.

Assumptions & free parameters 7 free parameters · 8 assumptions · 1 invented entities

The central claims rest on measured inputs (binding energy, Flatte parameters, D-meson width, D-meson size from quark model) and on modeling choices (universal shallow-bound-state wavefunction, origin annihilation, isospin-singlet X). The only invented object is the wrong-sign auxiliary field X_m, which is a mathematical device with no independent evidence.

free parameters (7)
  • Binding energy B = 0 to 0.3 MeV; central about 100 keV; also B = 3 +/- 192 keV from [77]
    Input from PDG mass measurements; controls all shallow-bound-state formulas (g_Z, R0, universal wavefunction).
  • Z (elementariness probability) = 0.1 +/- 0.4 from X -> D Dbar pi in Section 5
    The paper constrains Z from decay data and uses it in Weinberg formulas; central claim is that Z from Flatte fits is meaningless.
  • Gamma_D*0 (D*0 total width) = 105 +/- 70 keV derived; 2 MeV upper bound used in Section 5
    In Section 5 it is an input at the PDG upper bound; in Section 11.1.2 it is inferred by matching computed and measured Gamma(X to D Dbar pi).
  • g_LHCb (Flatte width parameter) = 0.108 +/- 0.003 from LHCb fit
    Fitted to lineshape data; converted to gc = (1.87 +/- 0.03) x 10^-2 MeV^-1/2; used in the X to D Dbar pi cross-check.
  • m_F (Flatte mass parameter relative to threshold) = -7.18 MeV from LHCb fit
    Fitted parameter in Flatte amplitude; enters a_F and r_F^0.
  • lambda_S and lambda_T (quartic meson couplings) = not yet fitted; expected order 1/Lambda^2 with Lambda about 1 GeV
    Parameters of the molecular model (11.14); the paper proposes a future fit, so no numerical values are given.
  • b (light-quark wavefunction size in D mesons) = b such that sqrt(r^2) about 0.68 fm from [49]
    Controls the radiative decay ratio; if D mesons are 0.9 fm or larger, the molecular prediction changes and the main argument against the molecule weakens.
assumptions (8)
  • standard math The S-wave low-energy scattering amplitude for a shallow bound state is universal and takes the form f(E) = -sqrt(2B/m)/(E+B) (Eq. 2.16).
    Basis for the Landau-Weinberg coupling formulas and Weinberg's criterion; derived in Section 2 from Schrodinger matching.
  • domain assumption The Kallen-Lehmann spectral representation and the Lehman sum rule 1 = Z + integral sigma(mu^2) d(mu^2) hold, and the continuum can be truncated to a single delta-function bound state at mass mD + mD* - B (Eqs. 3.14, 3.25).
    This truncation is what converts the field-theory amplitude into the Landau-Weinberg g_Z formula (3.24); it assumes no other multiparticle states contribute.
  • domain assumption The short-range (D Dbar*) squared interaction can be modeled as a renormalized Dirac-delta potential, yielding the universal bound-state wavefunction Psi(r) proportional to exp(-r sqrt(2mB))/r.
    Used for molecular radiative decays (Section 12) and for r0 and pion corrections (Sections 8 and 9).
  • domain assumption The X is treated as an isospin singlet; only neutral and charged D D* channels are included, with charged-neutral mass difference Delta about 8 MeV.
    Section 11 states this is pedagogical and a full EFT should include an isotriplet; the molecular amplitude (11.33) is restricted to this case.
  • domain assumption One-pion exchange in the u channel does not bind; its non-relativistic potential is V_w(r) = -alpha e^{i mu r}/r with alpha = 5 x 10^-4 and mu = 43 MeV (Eq. 8.4).
    Taken from the authors' prior work [34]; used for r0 corrections and for the perturbative wavefunction correction in Section 12.
  • domain assumption Radiative decays X to psi(') gamma are dominated by light-quark annihilation at the origin, with factorized charmonium and open-charm wavefunctions (Eq. 12.3).
    The whole radiative-decay argument rests on this factorization and on the D-meson size parameter b from the quark model [49].
  • ad hoc to paper The isospin subtraction recipe of Baru et al. [10] for removing coupled-channel effects before applying Weinberg's formula is valid.
    Invoked in Sections 10 and 11.1.1 to reinterpret r0, but footnote 23 concedes no rigorous proof is found; the paper's central conclusion does not depend on it.
  • ad hoc to paper An auxiliary molecular field X_m with wrong-sign kinetic term (11.67) correctly represents short-range molecular interactions.
    Used in Section 11.1.3 to show the sign of r0 distinguishes compact vs molecular; it is a formal device from Kaplan [51], with no independent evidence.
invented entities (1)
  • Auxiliary molecular field X_m with wrong-sign kinetic term
    purpose: Formal bookkeeping device to reproduce a molecular scattering amplitude with a trilinear coupling in Section 11.1.3
    It is introduced ad hoc to invert the sign of r0 in the compact vs molecular comparison; it is not a new physical particle, has no predicted observable of its own, and is not needed for the main radiative-decay argument.

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Pith. "Pith review of A short review on the compositeness of the $X(3872)$." pith.science (2026). https://pith.science/paper/MVUXM5JQ

@misc{pith2026250202505,
  author       = {Pith},
  title        = {Pith review of: A short review on the compositeness of the $X(3872)$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MVUXM5JQ}},
  note         = {Machine review of arXiv:2502.02505}
}
abstract

The $X(3872)$ could be a shallow $D\bar D^*$ bound state, a compact four-quark state, or a partially composite particle, i.e. a superposition of the two. We will review how these hypotheses could be tested experimentally, examining especially the cases in which the $X$ is a pure bound state or a pure compact tetraquark. Data on $X\to D\bar D\pi$ decays are compared with the analysis of the $X$ lineshape. The pure bound state hypothesis corresponds to a well-defined region in parameter space defined by the width of the $D^*$ versus the binding energy of the $X$. As for the $X$ lineshape, we observe that the currently available experimental analysis tests the compatibility with the compact hypothesis for the $X$. We propose how to extend the analysis to examine the molecular or the partially composite hypotheses. We also review the analysis on the radiative decays of the $X$ including pion corrections confirming some conclusions reached in the literature on the use of the universal wave function description for the molecular $X$.

Figures

Figures reproduced from arXiv: 2502.02505 by the authors.

Figure 1
Figure 1. Using g 2 X ≃ g 2 Z as in (4.17). The shadowed region represents Z > 0 values in the g 2 Z formula for the partially composite X. On the x axis the total D∗ width. On the y axis the binding energy B. Uncertainties reported on the PDG [68] have been taken into account. The pure molecule case corresponds only to the Z = 0 blue line. The unshadowed areas require sizeable values of the gc coupling. Assuming that the X i… view at source ↗
Figure 2
Figure 2. Diagrammatic representation of the Schwinger-Dyson equation for the complete resummed [PITH_FULL_IMAGE:figures/full_fig_p034_2.png] view at source ↗
Figure 3
Figure 3. The black solid line represents the central value of Γ( [PITH_FULL_IMAGE:figures/full_fig_p039_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Defining ψ(|R|) as the wave function of the final charmonium, as a function of the distance between the cc¯ pair, R, the transition amplitude A in the rest frame of the X, at a fixed photon three-momentum k, is given by [42]31 A  X → ψ (′) γ  = F Z R,ξ e −ik·(ξ− R 2 …
Figure 4
Figure 4. Figure 4: Scheme of the dominant process for the radiative decay [PITH_FULL_IMAGE:figures/full_fig_p047_4.png]

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Works this paper leans on

80 extracted references · 26 canonical work pages

  1. [49]

    Isgur, N., Scora, D., Grinstein, B., and Wise, M. B. Semileptonic B and D Decays in the Quark Model. Phys. Rev. D 39 (1989), 799–818

    work page 1989

  2. [1]

    Observation of the resonant character of the Z(4430)− state

    Aaij, R., et al. Observation of the resonant character of the Z(4430)− state. Phys. Rev. Lett. 112, 22 (2014), 222002, 1404.1903

    arXiv 2014

  3. [2]

    Study of the lineshape of the χc1(3872) state

    Aaij, R., et al. Study of the lineshape of the χc1(3872) state. Phys. Rev. D 102 , 9 (2020), 092005, 2005.13419

    arXiv 2020

  4. [3]

    Observation of Multiplicity Dependent Prompt χc1(3872) and ψ(2S) Production in pp Collisions

    Aaij, R., et al. Observation of Multiplicity Dependent Prompt χc1(3872) and ψ(2S) Production in pp Collisions. Phys. Rev. Lett. 126 , 9 (2021), 092001, 2009.06619

    arXiv 2021

  5. [4]

    Tetraquarks at large M and large N

    Allaman, H., Ekhterachian, M., Nardi, F., Rattazzi, R., and Stelzl, S. Tetraquarks at large M and large N. JHEP 11 (2024), 034, 2407.18298

    arXiv 2024

  6. [5]

    Production of the X(3872) at the Tevatron and the LHC

    Artoisenet, P., and Braaten, E. Production of the X(3872) at the Tevatron and the LHC. Phys. Rev. D 81 (2010), 114018, 0911.2016

    arXiv 2010

  7. [7]

    Using Line Shapes to Discriminate between Binding Mechanisms for the X(3872)

    Artoisenet, P., Braaten, E., and Kang, D. Using Line Shapes to Discriminate between Binding Mechanisms for the X(3872). Phys. Rev. D 82 (2010), 014013, 1005.2167

    arXiv 2010

  8. [8]

    The ratio of decay widths of X(3872) to $ \psi^{\prime}\gamma $ and $ J/\psi\gamma$ as a test of the X(3872) dynamical structure

    Badalian, A. M., Orlovsky, V. D., Simonov, Y. A., and Bakker, B. L. G. The ratio of decay widths of X(3872) to ψ′γ and J/ψγ as a test of the X(3872) dynamical structure. Phys. Rev. D 85 (2012), 114002, 1202.4882

    work page Pith review arXiv 2012

Show all 80 references
  1. [9]

    Charmonium options for the X(3872)

    Barnes, T., and Godfrey, S. Charmonium options for the X(3872). Phys. Rev. D 69 (2004), 054008, hep-ph/0311162

    2004 arXiv

  2. [10]

    Effective range expansion for narrow near-threshold resonances

    Baru, V., Dong, X.-K., Du, M.-L., Filin, A., Guo, F.-K., Hanhart, C., Nefediev, A., Nieves, J., and W ang, Q. Effective range expansion for narrow near-threshold resonances. Phys. Lett. B 833 (2022), 137290, 2110.07484

    2022 arXiv

  3. [11]

    A., Guo, F

    Baru, V., Epelbaum, E., Filin, A. A., Guo, F. K., Hammer, H. W., Hanhart, C., Meißner, U. G., and Nefediev, A. V. Remarks on study of X(3872) from effective field theory with pion-exchange interaction. Phys. Rev. D 91 , 3 (2015), 034002, 1501.02924

    2015 arXiv

  4. [12]

    D* —> D pi and D* — > D gamma decays: Axial coupling and Magnetic moment of D* meson

    Becirevic, D., and Haas, B. D* —> D pi and D* — > D gamma decays: Axial coupling and Magnetic moment of D* meson. Eur. Phys. J. C 71 (2011), 1734, 0903.2407. 51

    2011 arXiv

  5. [13]

    Hybrids, tetraquarks, pentaquarks, doubly heavy baryons, and quarkonia in Born-Oppenheimer effective theory

    Berwein, M., Brambilla, N., Mohapatra, A., and V airo, A. Hybrids, tetraquarks, pentaquarks, doubly heavy baryons, and quarkonia in Born-Oppenheimer effective theory. Phys. Rev. D 110 , 9 (2024), 094040, 2408.04719

    2024 arXiv

  6. [14]

    Bethe, H. A. Theory of the Effective Range in Nuclear Scattering. Phys.Rev. 76 (1949), 38

    1949

  7. [15]

    Probing the nature of the χc1(3872) state using radiative decays

    Bezshyiko, I., et al. Probing the nature of the χc1(3872) state using radiative decays. JHEP 11 (2024), 121, 2406.17006

    2024

  8. [16]

    Tetraquarks and pentaquarks in lattice QCD with light and heavy quarks

    Bicudo, P. Tetraquarks and pentaquarks in lattice QCD with light and heavy quarks. Phys. Rept. 1039 (2023), 1–49, 2212.07793

    2023 arXiv

  9. [17]

    D., and Sabelli, C

    Bignamini, C., Grinstein, B., Piccinini, F., Polosa, A. D., and Sabelli, C. Is the X(3872) Production Cross Section at Tevatron Compatible with a Hadron Molecule Interpretation? Phys. Rev. Lett. 103 (2009), 162001, 0906.0882

    2009 arXiv

  10. [18]

    Galilean-invariant effective field theory for the X(3872)

    Braaten, E. Galilean-invariant effective field theory for the X(3872). Phys. Rev. D 91 , 11 (2015), 114007, 1503.04791

    2015 arXiv

  11. [19]

    Exotic Hidden-heavy Hadrons and Where to Find Them

    Braaten, E., and Bruschini, R. Exotic Hidden-heavy Hadrons and Where to Find Them. 2409.08002

    arXiv

  12. [20]

    Galilean-invariant effective field theory for the X(3872) at next-to-leading order

    Braaten, E., He, L.-P., and Jiang, J. Galilean-invariant effective field theory for the X(3872) at next-to-leading order. Phys. Rev. D 103 , 3 (2021), 036014, 2010.05801

    2021 arXiv

  13. [21]

    Low-energy universality and the new charmonium resonance at 3870-MeV

    Braaten, E., and Kusunoki, M. Low-energy universality and the new charmonium resonance at 3870-MeV. Phys. Rev. D 69 (2004), 074005, hep-ph/0311147

    2004 arXiv

  14. [22]

    Production of the X(3870) in B meson decay by the coalescence of charm mesons

    Braaten, E., Kusunoki, M., and Nussinov, S. Production of the X(3870) in B meson decay by the coalescence of charm mesons. Phys. Rev. Lett. 93 (2004), 162001, hep-ph/0404161

    2004 arXiv

  15. [23]

    E., V airo, A., and Yuan, C.-Z

    Brambilla, N., Eidelman, S., Hanhart, C., Nefediev, A., Shen, C.-P., Thomas, C. E., V airo, A., and Yuan, C.-Z. The XY Zstates: experimental and theoretical status and perspectives. Phys. Rept. 873 (2020), 1–154, 1907.07583

    2020 arXiv

  16. [25]

    The nature of χc1 (3872) and T + cc (3875)

    Brambilla, N., Mohapatra, A., Scirpa, T., and V airo, A. The nature of χc1 (3872) and T + cc (3875). 2411.14306

  17. [26]

    Measurement of the X(3872) Production Cross Section Via Decays to J/ψπ +π− in pp collisions at √s = 7 TeV

    Chatrchyan, S., et al. Measurement of the X(3872) Production Cross Section Via Decays to J/ψπ +π− in pp collisions at √s = 7 TeV. JHEP 04 (2013), 154, 1302.3968

    2013 arXiv

  18. [27]

    K., et al

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

    2003 arXiv

  19. [28]

    D., Gelman, B

    Cohen, T. D., Gelman, B. A., and van Kolck, U. An Effective field theory for coupled channel scattering. Phys. Lett. B 588 (2004), 57–66, nucl-th/0402054. 52

    2004 arXiv

  20. [29]

    2501.15888

    Colangelo, P., De F azio, F., and Roselli, G.The charming case of X(3872) and χc1(2P ). 2501.15888

    arXiv

  21. [30]

    Toward the quark mass dependence of Tcc+ from lattice QCD

    Collins, S., Nefediev, A., Padmanath, M., and Prelovsek, S. Toward the quark mass dependence of Tcc+ from lattice QCD. Phys. Rev. D 109 , 9 (2024), 094509, 2402.14715

    2024 arXiv

  22. [31]

    Radiative transitions of heavy quarkonium states

    De F azio, F. Radiative transitions of heavy quarkonium states. Phys. Rev. D 83 (2011), 099901, 0812.0716

    2011 arXiv

  23. [32]

    Dong, X. K. Precise determination of the X(3872) properties. https://indico.cern.ch/event/1423686/contributions/6139373/ (2024)

    2024

  24. [33]

    G., Pilloni, A., Polosa, A

    Esposito, A., Ferreiro, E. G., Pilloni, A., Polosa, A. D., and Salgado, C. A. The nature of X(3872) from high-multiplicity pp collisions. Eur. Phys. J. C 81 , 7 (2021), 669, 2006.15044

    2021 arXiv

  25. [34]

    D., Rattazzi, R., and Tarquini, M

    Esposito, A., Germani, D., Glioti, A., Polosa, A. D., Rattazzi, R., and Tarquini, M. The role of the pion in the lineshape of the X(3872). Phys. Lett. B 847 (2023), 138285, 2307.11400

    2023 arXiv

  26. [35]

    L., Maiani, L., Piccinini, F., Pilloni, A., Polosa, A

    Esposito, A., Guerrieri, A. L., Maiani, L., Piccinini, F., Pilloni, A., Polosa, A. D., and Riquer, V. Observation of light nuclei at ALICE and the X(3872) conundrum. Phys. Rev. D 92 , 3 (2015), 034028, 1508.00295

    2015 arXiv

  27. [36]

    D., and Riquer, V

    Esposito, A., Maiani, L., Pilloni, A., Polosa, A. D., and Riquer, V. From the line shape of the X(3872) to its structure. Phys. Rev. D 105 , 3 (2022), L031503, 2108.11413

    2022 arXiv

  28. [37]

    Esposito, A., Piccinini, F., Pilloni, A., and Polosa, A. D. A Mechanism for Hadron Molecule Production in p pbar(p) Collisions. J. Mod. Phys. 4 (2013), 1569–1573, 1305.0527

    2013 arXiv

  29. [38]

    Esposito, A., Pilloni, A., and Polosa, A. D. Hybridized Tetraquarks. Phys. Lett. B 758 (2016), 292–295, 1603.07667

    2016 arXiv

  30. [39]

    Esposito, A., Pilloni, A., and Polosa, A. D. Multiquark Resonances. Phys. Rept. 668 (2017), 1–97, 1611.07920

    2017 arXiv

  31. [40]

    Flatte, S. M. Coupled - Channel Analysis of the pi eta and K anti-K Systems Near K anti-K Threshold. Phys. Lett. B 63 (1976), 224–227

    1976

  32. [41]

    Germani, D., Grinstein, B., and Polosa, A. D. Tetraquarks in the Born-Oppenheimer approximation. 2501.13249

    arXiv

  33. [42]

    Grinstein, B., Maiani, L., and Polosa, A. D. Radiative decays of X(3872) discriminate between the molecular and compact interpretations. Phys. Rev. D 109 , 7 (2024), 074009, 2401.11623

    2024 arXiv

  34. [43]

    L., Piccinini, F., Pilloni, A., and Polosa, A

    Guerrieri, A. L., Piccinini, F., Pilloni, A., and Polosa, A. D. Production of Tetraquarks at the LHC. Phys. Rev. D 90 , 3 (2014), 034003, 1405.7929. 53

    2014 arXiv

  35. [44]

    S., Meißner, U.-G., and Nefediev, A

    Guo, F.-K., Hanhart, C., Kalashnikova, Y. S., Meißner, U.-G., and Nefediev, A. V. What can radiative decays of the X(3872) teach us about its nature? Phys. Lett. B 742 (2015), 394–398, 1410.6712

    2015 arXiv

  36. [45]

    Production of the X(3872) in charmonia radiative decays

    Guo, F.-K., Hanhart, C., Meißner, U.-G., W ang, Q., and Zhao, Q. Production of the X(3872) in charmonia radiative decays. Phys. Lett. B 725 (2013), 127–133, 1306.3096

    2013 arXiv

  37. [47]

    Hadronic molecules

    Guo, F.-K., Hanhart, C., Meißner, U.-G., W ang, Q., Zhao, Q., and Zou, B.- S. Hadronic molecules. Rev. Mod. Phys. 90 , 1 (2018), 015004, 1705.00141. [Erratum: Rev.Mod.Phys. 94, 029901 (2022)]

    2018 arXiv

  38. [48]

    Hackenburg, R. W. Neutron-proton effective range parameters and zero-energy shape dependence. Phys. Rev. C 73 (2006), 044002

    2006

  39. [50]

    Delta function potentials in two-dimensional and three-dimensional quantum mechanics

    Jackiw, R. Delta function potentials in two-dimensional and three-dimensional quantum mechanics. 35–53

  40. [51]

    Kaplan, D. B. More effective field theory for nonrelativistic scattering. Nucl. Phys. B 494 (1997), 471–484, nucl-th/9610052

    1997 arXiv

  41. [52]

    B., and Steele, J

    Kaplan, D. B., and Steele, J. V. The Long and short of nuclear effective field theory expansions. Phys. Rev. C 60 (1999), 064002, nucl-th/9905027

    1999 arXiv

  42. [53]

    Landau, L. D. JETP 39 (1960), 1865

    1960

  43. [54]

    D., and Lifshitz, E

    Landau, L. D., and Lifshitz, E. M. Quantum Mechanichs, Vol. 3 . Butterworth, 2003

    2003

  44. [55]

    F., and Martinez, S

    Lebed, R. F., and Martinez, S. R. Diabatic representation of exotic hadrons in the dynamical diquark model. Phys. Rev. D 106 , 7 (2022), 074007, 2207.01101

    2022 arXiv

  45. [56]

    F., Mitchell, R

    Lebed, R. F., Mitchell, R. E., and Swanson, E. S. Heavy-Quark QCD Exotica. Prog. Part. Nucl. Phys. 93 (2017), 143–194, 1610.04528

    2017 arXiv

  46. [57]

    W., F aessler, A., Gutsche, T., and Lyubovitskij, V

    Lee, I. W., F aessler, A., Gutsche, T., and Lyubovitskij, V. E. X(3872) as a molecular DD* state in a potential model. Phys. Rev. D 80 (2009), 094005, 0910.1009

    2009 arXiv

  47. [58]

    D., and Riquer, V

    Maiani, L., Piccinini, F., Polosa, A. D., and Riquer, V. Diquark-antidiquarks with hidden or open charm and the nature of X(3872). Phys. Rev. D 71 (2005), 014028, hep- ph/0412098

    2005

  48. [59]

    D., and Riquer, V

    Maiani, L., Piccinini, F., Polosa, A. D., and Riquer, V. The Z(4430) and a New Paradigm for Spin Interactions in Tetraquarks. Phys. Rev. D 89 (2014), 114010, 1405.1551. 54

    2014 arXiv

  49. [60]

    D., and Riquer, V

    Maiani, L., Pilloni, A., Polosa, A. D., and Riquer, V. Doubly heavy tetraquarks in the Born-Oppenheimer approximation. Phys. Lett. B 836 (2023), 137624, 2208.02730

    2023 arXiv

  50. [61]

    D., and Riquer, V

    Maiani, L., Polosa, A. D., and Riquer, V. The charged Z(4430) in the diquark-antidiquark picture. New J. Phys. 10 (2008), 073004

    2008

  51. [62]

    D., and Riquer, V

    Maiani, L., Polosa, A. D., and Riquer, V. A Theory of X and Z Multiquark Resonances. Phys. Lett. B 778 (2018), 247–251, 1712.05296

    2018 arXiv

  52. [63]

    D., and Riquer, V

    Maiani, L., Polosa, A. D., and Riquer, V. Hydrogen bond of QCD. Phys. Rev. D 100 , 1 (2019), 014002, 1903.10253

    2019 arXiv

  53. [64]

    D., and Riquer, V

    Maiani, L., Polosa, A. D., and Riquer, V. Hydrogen bond of QCD in doubly heavy baryons and tetraquarks. Phys. Rev. D 100 , 7 (2019), 074002, 1908.03244

    2019 arXiv

  54. [65]

    X(3872) and its production at hadron colliders

    Meng, C., Han, H., and Chao, K.-T. X(3872) and its production at hadron colliders. Phys. Rev. D 96 , 7 (2017), 074014, 1304.6710

    2017 arXiv

  55. [66]

    Doubly charm tetraquark channel with isospin 1 from lattice QCD

    Meng, L., Ortiz-Pacheco, E., Baru, V., Epelbaum, E., Padmanath, M., and Prelovsek, S. Doubly charm tetraquark channel with isospin 1 from lattice QCD. 2411.06266

    arXiv

  56. [67]

    Effective-range expansion of the T + cc state at the complex D∗+D0 threshold

    Mikhasenko, M. Effective-range expansion of the T + cc state at the complex D∗+D0 threshold. 2203.04622

    arXiv

  57. [68]

    Review of particle physics

    Navas, S., et al. Review of particle physics. Phys. Rev. D 110 , 3 (2024), 030001

    2024

  58. [69]

    E., and Schroeder, D

    Peskin, M. E., and Schroeder, D. V. An Introduction to quantum field theory . Addison- Wesley, Reading, USA, 1995

    1995

  59. [70]

    J., and Smith, H

    Pethick, C. J., and Smith, H. Bose–Einstein condensation in dilute gases . Cambridge University press, 2008

    2008

  60. [71]

    Polosa, A. D. Constraints from precision measurements on the hadron-molecule interpretation of X , Y , Z resonances. Phys. Lett. B 746 (2015), 248–250, 1505.03083

    2015 arXiv

  61. [72]

    Radiative decays of heavy-light mesons and the f (T ) H,H ∗,H1 decay constants

    Pullin, B., and Zwicky, R. Radiative decays of heavy-light mesons and the f (T ) H,H ∗,H1 decay constants. JHEP 09 (2021), 023, 2106.13617

    2021 arXiv

  62. [73]

    Charmoniumlike Channels 1 + with Isospin 1 from Lattice and Effective Field Theory

    Sadl, M., Collins, S., Guo, Z.-H., Padmanath, M., Prelovsek, S., and Yan, L.- W. Charmoniumlike Channels 1 + with Isospin 1 from Lattice and Effective Field Theory. 2406.09842

    arXiv

  63. [74]

    M., et al

    Sirunyan, A. M., et al. Evidence for X(3872) in Pb-Pb Collisions and Studies of its Prompt Production at √sN N=5.02 TeV. Phys. Rev. Lett. 128 , 3 (2022), 032001, 2102.13048

    2022 arXiv

  64. [75]

    Smorodinsky, Y. A. Normalization of the deuteron wave function. Dokl.Akad.Nauk SSSR. 60 (1948), 217

    1948

  65. [76]

    Swanson, E. S. Diagnostic decays of the X(3872). Phys. Lett. B 598 (2004), 197–202, hep-ph/0406080. 55

    2004 arXiv

  66. [77]

    Tomaradze, A., Dobbs, S., Xiao, T., and Seth, K. K. Precision Measurement of the Mass of the D∗0 Meson and the Binding Energy of the X(3872) Meson as a D0D∗0 Molecule. Phys. Rev. D 91 , 1 (2015), 011102, 1501.01658

    2015 arXiv

  67. [78]

    A., Santorelli, P., and Vo, Q.-C

    Tran, C.-T., Ivanov, M. A., Santorelli, P., and Vo, Q.-C. Radiative decays D∗ (s) → D(s)γ in covariant confined quark model. Chin. Phys. C 48 , 2 (2024), 023103, 2311.15248

    2024 arXiv

  68. [79]

    Evidence That the Deuteron Is Not an Elementary Particle

    Weinberg, S. Evidence That the Deuteron Is Not an Elementary Particle. Phys. Rev. 137 (1965), B672–B678

    1965

  69. [80]

    The Quantum theory of fields

    Weinberg, S. The Quantum theory of fields. Vol. 1: Foundations . Cambridge University Press, 6 2005

    2005

  70. [81]

    Lectures on quantum mechanics

    Weinberg, S. Lectures on quantum mechanics . Cambridge University Press, 2015

    2015

  71. [82]

    Wu, C.-t., She, Z.-L., Peng, X.-Y., Kang, X.-L., Zhou, H.-G. X. D.-M., Chen, G., and Sa, B.-H. Study on the structure of exotic states χc1(3872) via beauty-hadron decays in pp collisions at s=8 TeV. Phys. Rev. D 107 , 11 (2023), 114022, 2303.03696

    2023 arXiv

  72. [83]

    Predicting isovector charmonium-like states from X(3872) properties

    Zhang, Z.-H., Ji, T., Dong, X.-K., Guo, F.-K., Hanhart, C., Meißner, U.-G., and Rusetsky, A. Predicting isovector charmonium-like states from X(3872) properties. JHEP 08 (2024), 130, 2404.11215. 56

    2024 arXiv

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Reviewed August 9, 2026 · model on record in the stance chip above.