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Using QCD light-cone sum rules, the paper predicts the static electromagnetic moments of the three JP=1+ D(*)\bar{K}(*) molecular tetraquark candidates, finding magnetic moments between 1 and 3 nuclear magnetons and quadrupole moments of or

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2026-08-03 01:02 UTC pith:UQXE4OCK

load-bearing objection First LCSR moments for three charm–strange molecules, with a plausible hierarchy—but the flavor table doesn't add up and needs fixing before anyone benchmarks against it. the 3 major comments →

arxiv 2602.10638 v2 pith:UQXE4OCK submitted 2026-02-11 hep-ph hep-exhep-lat

Structural dissection of hadronic molecules: The D^((*))bar{K}^((*)) family under QCD light-cone sum rules

Ula\c{s} \"Ozdem This is my paper
classification hep-ph hep-exhep-lat
keywords hadronic moleculestetraquarksmagnetic momentsquadrupole momentsQCD light-cone sum rulescharm-strange exotic statesD(*)Kbar(*) systemsphoton distribution amplitudes
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 paper aims to establish the first quantitative electromagnetic benchmarks for three charm–strange hadronic-molecule candidates with spin-parity 1+: D\bar{K}*, D*\bar{K}, and D*\bar{K}*. Using QCD light-cone sum rules with color-singlet meson-bilinear interpolating currents, it predicts magnetic moments in the range 1–3 nuclear magnetons (largest for the D*\bar{K} configuration) and electric quadrupole moments about ten times smaller. The key physical message is a hierarchy and a flavor pattern: light quarks dominate the magnetic response, the charm quark is suppressed, and the ordering mu(D*\bar{K}) > mu(D\bar{K}*) ≈ mu(D*\bar{K}*) emerges. If these predictions are correct, they provide discriminants that could distinguish loosely bound molecular states from compact tetraquark alternatives, and guidance for future photoproduction and radiative-decay searches.

Core claim

The central claim is that the static electromagnetic properties of the JP=1+ D(*)\bar{K}(*) molecular tetraquark states can be extracted from light-cone sum rules, and that the resulting moments have a characteristic pattern: the D*\bar{K} state has the largest magnetic moment, about 3.1 nuclear magnetons, while D\bar{K}* and D*\bar{K}* come in near 2 nuclear magnetons; the neutral D\bar{K}* combination has vanishing moments by charge symmetry; and the quadrupole moments are small, of order 10^-3 fm^2. A flavor decomposition shows the light-quark contribution dominates and the charm-quark piece is strongly suppressed, which the author interprets as a natural molecular signature.

What carries the argument

The calculation uses the external-field formulation of QCD light-cone sum rules: a three-point correlation function of the tetraquark interpolating current with the electromagnetic current is evaluated both in hadronic variables (saturated by a single 1+ state with mass m and residue λ) and in QCD via an operator product expansion near the light cone. Photon couplings include both perturbative quark-line insertions and nonperturbative photon distribution amplitudes. The master sum rules (Eqs. 30–32) express each moment as the Borel-transformed spectral integral R_i divided by λ^2 times an exponential factor e^{m^2/M^2}; the magnetic moment is isolated from the coefficient of the antisymmetri

Load-bearing premise

The absolute scale of every predicted moment is set by the masses and residues of three unobserved 1+ states, taken from a single external calculation; because the sum rules divide by the residue squared and exponentiate the mass squared over the Borel mass, any shift in those inputs changes all six central values and can erase the hierarchy.

What would settle it

A lattice QCD computation of the magnetic moments of these 1+ charm–strange systems that yields values outside the quoted ranges (e.g., a D*\bar{K} moment below about 2 nuclear magnetons, or charm-quark contributions comparable to light-quark ones) would falsify the molecular pattern. Alternatively, an independent sum-rule analysis using diquark–antidiquark currents that reproduces the same numbers would weaken the claim that the moments discriminate molecular from compact structures.

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

If this is right

  • If the predictions are right, photon-induced production and radiative M1 transitions of these states should be enhanced for the D*\bar{K} configuration, whose moment is roughly 3 nuclear magnetons.
  • The hierarchy mu(D*\bar{K}) > mu(D\bar{K}*) ≈ mu(D*\bar{K}*) and the strong suppression of the charm-quark contribution give a pattern that experiments and lattice QCD can use to test the molecular interpretation.
  • The vanishing moments of the neutral D\bar{K}* state are a sharp consequence of charge and flavor symmetry within the molecular current.
  • Small quadrupole moments of order 10^-3 fm^2 imply nearly spherical charge distributions, meaning these states are weakly deformed and spatially extended.
  • The results provide the first dedicated LCSR benchmarks for these systems, against which quark-model and effective-field-theory predictions can be compared.

Where Pith is reading between the lines

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

  • A natural extension is to compute the same moments with compact diquark–antidiquark interpolating currents; if the two calculations separate as sharply as the molecular hierarchies suggest, the moments would serve as a direct discrimination tool.
  • The exponential sensitivity to the adopted masses and residues implies that lattice QCD determinations of the 1+ state masses and couplings would tighten or refute these central values.
  • The same framework can be applied to the bottom counterparts (B(*)\bar{K}(*)) to see whether the hierarchy and light-quark dominance persist, which would strengthen the molecular interpretation.
  • A radiative decay measurement (e.g., T* -> T gamma) would give a direct test: the predicted M1 width scales with |mu|^2, so the D*\bar{K} state should be the brightest in photon transitions.

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

3 major / 4 minor

Summary. This paper uses QCD light-cone sum rules in an external electromagnetic field to compute the magnetic dipole and electric quadrupole moments of three JP=1+ charm–strange molecular tetraquark candidates: D K̄*, D* K̄, and D* K̄*, described by color-singlet meson-bilinear interpolating currents. The authors match the hadronic and OPE representations, apply double Borel transformation and continuum subtraction, and obtain the six moment values in Table III (e.g., μ(D*K̄[ūc]) = 3.08 ± 0.77 μN, quadrupole moments of order 10^-3 fm²), a flavor decomposition in Table IV, an uncertainty budget combined in quadrature, and stability diagnostics (PC > 40%, CVG < 0.5% in Table II). The central claims are the 1–3 μN range, the hierarchy μ_D*K̄ > μ_DK̄* ≈ μ_D*K̄*, and light-quark dominance of the magnetic response.

Significance. If correct, this would be the first systematic LCSR determination of electromagnetic moments for these charm–strange molecular systems and would provide quantitative benchmarks for distinguishing molecular from compact tetraquark interpretations. The calculation follows a standard LCSR framework: the master sum rules in Eqs. (30)–(32) are explicit, the pole-dominance and OPE-convergence conditions are imposed, the higher-dimensional terms are checked (CVG below 0.5% in Table II), and the error budget is transparent. The inputs — photon DAs, magnetic susceptibility, and tetraquark masses/residues — are taken from published external sources, and the paper does not fit its outputs to inputs, so the circularity concern is not supported. The main obstacle is an internal numerical inconsistency in the flavor decomposition that must be corrected before the benchmark status is warranted.

major comments (3)
  1. [Table IV (and Table III)] The flavor decomposition in Table IV does not satisfy the relation μ_tot = μu+μs+μc stated in the caption. For D*K̄*[ūc][ūs]: 1.70 − 0.44 − 0.21 = 1.05 μN, not the quoted 1.93 μN. For DK̄*[ūc][ūs]: 1.33 − 0.66 + 0.00 = 0.67 μN, not the quoted 1.99 μN. The other four rows sum correctly. This is not a rounding effect: the discrepancies are 0.88 μN and 1.32 μN, well outside the 0.47 and 0.49 uncertainties in Table III. Because the total moments and the flavor entries derive from the same spectral integrals R_i (Eqs. 35–37), the mismatch signals an error in the numerical evaluation, the decomposition, or the quoted totals. The abstract's claims of a 1–3 μN range and of light-quark dominance rest on these numbers, so the inconsistency must be resolved before the results can serve as benchmarks.
  2. [Abstract and §III.C.1] The abstract states that 'The magnetic moments are found to lie in the range 1–3 nuclear magnetons.' This is not supported by Table III, which contains entries 0.00±0.00 for DK̄*[d̄c][d̄s], −0.62±0.15 for D*K̄*[d̄c][d̄s], and −2.04±0.50 for D*K̄[d̄c][d̄s]. If the statement is intended to refer only to the u-flavor or charged configurations, it should be worded accordingly. The same issue appears in §III.C.1, where 'magnitudes of about 2 μN' is said for the DK̄* and D*K̄* channels, ignoring the −0.62 μN D*K̄* entry. Please revise the abstract and the summary paragraph to match the full table.
  3. [Eqs. (30)–(32) and Table I] The absolute scale of every prediction is set by the masses and residues of three unobserved JP=1+ states, adopted exclusively from Ref. [44]. Because the master formulas contain exp(m²/M²)/λ² and m²/M² ≈ 3.5 in the chosen Borel windows, the moments are exponentially sensitive to these inputs: a 10% shift in m changes the exponential factor by roughly 30–40% before the coupling λ is even considered. The paper propagates the 1σ errors from Table I, but it does not quantify how the hierarchy or the 'molecular fingerprint' would change if the states were not predominantly molecular or if their masses and residues differed by more than the adopted ranges. A focused sensitivity scan over m and λ, or a comparison with an independent determination of these parameters, would substantially strengthen the benchmark claim.
minor comments (4)
  1. [§III.C, first paragraph] 'The resulting central values and uncertainties are summarized in Table II' — the moments are in Table III; Table II lists the parameter windows. Please correct the cross-reference.
  2. [Appendix, Eqs. (35)–(37)] The spectral densities are presented without derivation or a description of how the convolution integrals I_i[A] are evaluated numerically. Since the central results depend on these lengthy expressions, a derivation sketch for at least one channel, or an ancillary file with the algebra and numerical implementation, would improve reproducibility.
  3. [Figure 1] The stability plots are shown only for the D*K̄* channel. Analogous plots for DK̄* and D*K̄ would help the reader verify that the selected Borel windows and thresholds in Table II are representative for all three states.
  4. [Eq. (26)] The equation equates a scalar moment on the left-hand side with a tensor T^QCD_{\mu\nu} on the right-hand side. Stating explicitly which Lorentz coefficient is projected out after the Borel transformation would improve clarity.

Circularity Check

0 steps flagged

No load-bearing circularity: the LCSR moment predictions are self-contained given external masses, residues, and photon-DA inputs.

full rationale

The derivation chain is explicit and non-circular: molecular interpolating currents (Eqs. 4-6) define the correlation function; the OPE side (Eqs. 9-17) is computed with perturbative and nonperturbative photon couplings; the hadronic side (Eqs. 18-25) fixes the Lorentz structures; matching plus Borel transformation yields the master relation (Eq. 26) and finally the sum rules (Eqs. 30-32). The predicted magnetic and quadrupole moments in Tables III-IV are outputs; they are never used as inputs anywhere in the sum rules. The masses and residues m_Tcs and lambda_Tcs in Table I are taken from an external calculation (Ref. [44] by H.-X. Chen), and the photon-DA and magnetic-susceptibility inputs come from Ball-Braun-Kivel and Rohrwild, not from this paper. The self-citations in the method paragraph (Refs. 26, 31-40) advertise prior LCSR applications but are not load-bearing: the actual formalism is anchored in Refs. 28-30, 41, and the numerical results follow from the printed equations, not from those citations. The paper also explicitly disclaims the interpretive leap in Sec. III.C.3: the analysis is 'consistent with, rather than proving, a loosely bound molecular interpretation,' so the molecular-current ansatz is not smuggled in as a derived conclusion. One non-circular numerical issue should be noted: the flavor rows in Table IV for [uc][us] do not sum to the quoted totals (e.g., 1.70-0.44-0.21 = 1.05, not 1.93, for D*Kbar*; and 1.33-0.66+0.00 = 0.67, not 1.99, for DKbar*), while the d-flavor rows do sum correctly. That is an internal arithmetic/consistency problem in the numerical evaluation and a correctness risk, but it is not evidence of circularity because the totals were not constructed from the flavor decomposition. The low score reflects only the non-load-bearing self-citation density in the method section, not a circular derivation.

Axiom & Free-Parameter Ledger

8 free parameters · 6 axioms · 0 invented entities

The computation's only genuinely new content is the spectral-density algebra; everything dimensional is imported. The six observables are normalized by model masses/residues for states that do not exist in the data, and the extraction is bracketed by auxiliary Borel/threshold windows. No new entities are invented; the molecular states are borrowed from prior literature, and the paper concedes it does not prove their existence or composition. The magnetic susceptibility χ and photon DAs are external inputs, not free parameters of this work.

free parameters (8)
  • m_DK̅* = 2.89^{+0.10}_{-0.11} GeV
    Mass of the unobserved JP=1+ D K̅* molecular state, adopted from Ref. [44]; enters the sum rule exponentially via e^{m²/M²} in Eq. (30).
  • λ_DK̅* = 8.6^{+0.19}_{-0.17}×10⁻² GeV⁵
    Current residue from Ref. [44]; enters the sum-rule denominator λ² in Eq. (30).
  • m_D*K̅ = 2.85^{+0.10}_{-0.11} GeV
    Mass of the unobserved JP=1+ D*K̅ molecular state, adopted from Ref. [44]; normalizes Eq. (31).
  • λ_D*K̅ = 0.82^{+0.18}_{-0.17}×10⁻² GeV⁵
    Current residue from Ref. [44]; enters the sum-rule denominator in Eq. (31).
  • m_D*K̅* = 3.13^{+0.12}_{-0.13} GeV
    Mass of the unobserved JP=1+ D*K̅* molecular state, adopted from Ref. [44]; normalizes Eq. (32).
  • λ_D*K̅* = 2.96^{+0.62}_{-0.55}×10⁻² GeV⁵
    Current residue from Ref. [44]; enters the sum-rule denominator in Eq. (32).
  • Continuum thresholds s0 = [11.5,12.9], [11.5,12.9], [13.2,14.6] GeV² per channel
    Auxiliary duality parameter; the chosen windows contribute ~30% of the total uncertainty and bracket the central values.
  • Borel mass windows M² = [1.8,2.4], [2.0,2.8], [2.0,2.8] GeV² per channel
    Auxiliary parameter; fixed by the PC>40% and CVG<5% criteria, with ~8% uncertainty share.
axioms (6)
  • domain assumption Quark–hadron duality: the OPE spectral density equals the physical spectral density above threshold s0 within the triangular region of Eq. (27), reducing the double Borel integral to Eq. (29).
    Standard QCD sum-rule premise; underpins the matching in Sec. II.E.
  • domain assumption The interpolating currents (Eqs. 4–6) couple predominantly to the molecular D(*)K̅(*) JP=1+ ground states.
    Sec. II.B; supported only by threshold-proximity arguments; the 1+ states are not experimentally established.
  • domain assumption Photon interaction is fully captured by perturbative quark-line insertion plus light-quark photon distribution amplitudes; charm-quark photon DAs are neglected as 1/m_c suppressed.
    Sec. II.C; stated truncation, standard for heavy-hadron LCSR but not quantified here.
  • domain assumption OPE truncation at dimension 7 with residual <0.5% (CVG criterion) and a single-pole + continuum hadronic model with PC > 40%.
    Sec. III.B, Eqs. (33)–(34); pole contribution falls to ~40% at the upper Borel edge, so the continuum is comparable.
  • standard math The electromagnetic matrix element of the spin-1 tetraquark obeys the three-form-factor Brodsky–Hiller decomposition (Eq. 21).
    Sec. II.D; general Lorentz decomposition for spin-1 systems, taken from Ref. [48].
  • standard math The free and gluonic quark propagator forms (Eqs. 12–15) with the standard perturbative expansion in the background field.
    Sec. II.C; standard QCD sum-rule technology (refs. [45,46]).

pith-pipeline@v1.3.0-alltime-deepseek · 18519 in / 29992 out tokens · 256015 ms · 2026-08-03T01:02:26.285645+00:00 · methodology

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read the original abstract

We investigate the static electromagnetic properties of three charm--strange molecular tetraquark candidates with quantum numbers $J^{P}=1^{+}$, namely the $D\bar{K}^{\ast}$, $D^{\ast}\bar{K}$, and $D^{\ast}\bar{K}^{\ast}$ systems. The analysis is carried out within the framework of QCD light-cone sum rules, using interpolating currents constructed from colour-singlet meson bilinears to reflect their molecular configurations. Both perturbative and non-perturbative photon contributions are included,and numerical predictions for the magnetic and electric quadrupole moments are obtained. The magnetic moments are found to lie in the range $1$--$3$ nuclear magnetons, with the largest value associated with the $D^{*}\bar{K}$ configuration. The quadrupole moments are an order of magnitude smaller, of order $10^{-3}\,\mathrm{fm}^{2}$, indicating only weak deviations from spherical charge distributions. A flavour decomposition shows that the magnetic response is dominated by the light quarks, while the charm-quark contribution is strongly suppressed, a feature naturally expected for loosely bound hadronic molecules. The present analysis extends QCD light-cone sum-rule studies of exotic hadrons by providing a systematic determination of the electromagnetic moments of the $D^{(\ast)}\bar K^{(\ast)}$ molecular systems. These results provide quantitative benchmarks that may help discriminate between molecular configurations and more compact multiquark interpretations and may offer useful guidance for future experimental studies of electromagnetic signatures of charm--strange exotic states.

Figures

Figures reproduced from arXiv: 2602.10638 by Ula\c{s} \"Ozdem.

Figure 1
Figure 1. Figure 1: FIG. 1. Dependence of the sum-rule diagnostics and the extracted magnetic dipole moment on the Borel mass [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗

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Forward citations

Cited by 1 Pith paper

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

  1. Mass spectra and electromagnetic characteristics of the $K^{(*)}\bar D^{(*)}$ and $K^{(*)}{D}^{(*)}$ molecular tetraquarks from the coupled-channel dynamics

    hep-ph 2026-06 unverdicted novelty 4.0

    Using coupled-channel one-boson-exchange dynamics the authors predict several K(*) bar D(*) and K(*) D(*) molecular tetraquark candidates and their electromagnetic properties.

Reference graph

Works this paper leans on

56 extracted references · 36 linked inside Pith · cited by 1 Pith paper

  1. [1]

    The largest value is obtained for the chargedD∗ ¯Kstate,µ= 3.08±0.77µ N, whereas theD ¯K∗ andD∗ ¯K∗ channels yield smaller but comparable magnitudes of about2µN

    Magnetic moments The extracted magnetic moments display a clear and systematic hierarchy among theD(∗) ¯K(∗) molecular configu- rations. The largest value is obtained for the chargedD∗ ¯Kstate,µ= 3.08±0.77µ N, whereas theD ¯K∗ andD∗ ¯K∗ channels yield smaller but comparable magnitudes of about2µN. This behavior can be traced to the different spin structur...

  2. [2]

    For elastic scattering, the initial and final tetraquark masses are equal, which allows us to symmetrize the Borel parameters by settingM 2 1 = M 2 2 = 2M 2

    = ∫s0 0 dse−s/M2 ˜ρ(s),(29) where the transformed spectral density˜ρ(s)incorporates an integral over the mixing parameteru. For elastic scattering, the initial and final tetraquark masses are equal, which allows us to symmetrize the Borel parameters by settingM 2 1 = M 2 2 = 2M 2. This simplifies the expressions considerably and leads to the final LCSR fo...

  3. [3]

    Quadrupole moments The electric quadrupole moments probe deviations from spherical charge distributions and therefore provide com- plementary information to the magnetic dipole moments about the internal spatial structure of the states. In contrast to the dipole moments, which are controlled mainly by the total spin and flavor content, the quadrupole mome...

  4. [4]

    Consequently, they can lead to potentially observable effects in production mechanisms, radiative transitions, and other electromagnetic probes

    Phenomenological consequences and accessible observables Although the magnetic and quadrupole moments are static quantities, they encode information about the elec- tromagnetic structure of the states and may affect processes involving real or virtual photons. Consequently, they can lead to potentially observable effects in production mechanisms, radiativ...

  5. [5]

    S. K. Choi, et al., Observation of a narrow charmonium-like state in exclusiveB±→K ±π+π−J/ψdecays, Phys. Rev. Lett. 91 (2003) 262001.arXiv:hep-ex/0309032,doi:10.1103/PhysRevLett.91.262001

    Pith/arXiv arXiv 2003

  6. [6]

    Esposito, A

    A. Esposito, A. L. Guerrieri, F. Piccinini, A. Pilloni, A. D. Polosa, Four-Quark Hadrons: an Updated Review, Int. J. Mod. Phys. A 30 (2015) 1530002.arXiv:1411.5997,doi:10.1142/S0217751X15300021

    Pith/arXiv arXiv 2015

  7. [7]

    Esposito, A

    A. Esposito, A. Pilloni, A. D. Polosa, Multiquark Resonances, Phys. Rept. 668 (2017) 1–97.arXiv:1611.07920,doi: 10.1016/j.physrep.2016.11.002

    Pith/arXiv arXiv 2017

  8. [8]

    S. L. Olsen, T. Skwarnicki, D. Zieminska, Nonstandard heavy mesons and baryons: Experimental evidence, Rev. Mod. Phys. 90 (1) (2018) 015003.arXiv:1708.04012,doi:10.1103/RevModPhys.90.015003

    Pith/arXiv arXiv 2018

  9. [9]

    R. F. Lebed, R. E. Mitchell, E. S. Swanson, Heavy-Quark QCD Exotica, Prog. Part. Nucl. Phys. 93 (2017) 143–194. arXiv:1610.04528,doi:10.1016/j.ppnp.2016.11.003

    Pith/arXiv arXiv 2017

  10. [10]

    Nielsen, F

    M. Nielsen, F. S. Navarra, S. H. Lee, New Charmonium States in QCD Sum Rules: A Concise Review, Phys. Rept. 497 (2010) 41–83.arXiv:0911.1958,doi:10.1016/j.physrep.2010.07.005

    Pith/arXiv arXiv 2010

  11. [11]

    Brambilla, S

    N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev, C.-P. Shen, C. E. Thomas, A. Vairo, C.-Z. Yuan, TheXYZstates: experimental and theoretical status and perspectives, Phys. Rept. 873 (2020) 1–154.arXiv:1907.07583,doi:10.1016/j. physrep.2020.05.001

    Pith/arXiv arXiv 2020

  12. [12]

    Agaev, K

    S. Agaev, K. Azizi, H. Sundu, Four-quark exotic mesons, Turk. J. Phys. 44 (2) (2020) 95–173.arXiv:2004.12079, doi:10.3906/fiz-2003-15

    Pith/arXiv arXiv 2020

  13. [13]

    H.-X. Chen, W. Chen, X. Liu, S.-L. Zhu, The hidden-charm pentaquark and tetraquark states, Phys. Rept. 639 (2016) 1–121.arXiv:1601.02092,doi:10.1016/j.physrep.2016.05.004

    Pith/arXiv arXiv 2016

  14. [14]

    A. Ali, J. S. Lange, S. Stone, Exotics: Heavy Pentaquarks and Tetraquarks, Prog. Part. Nucl. Phys. 97 (2017) 123–198. arXiv:1706.00610,doi:10.1016/j.ppnp.2017.08.003

    Pith/arXiv arXiv 2017

  15. [15]

    F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, B.-S. Zou, Hadronic molecules, Rev. Mod. Phys. 90 (1) (2018) 015004, [Erratum: Rev.Mod.Phys. 94, 029901 (2022)].arXiv:1705.00141,doi:10.1103/RevModPhys.90.015004

    Pith/arXiv arXiv 2018

  16. [16]

    Liu, H.-X

    Y.-R. Liu, H.-X. Chen, W. Chen, X. Liu, S.-L. Zhu, Pentaquark and Tetraquark states, Prog. Part. Nucl. Phys. 107 (2019) 237–320.arXiv:1903.11976,doi:10.1016/j.ppnp.2019.04.003

    Pith/arXiv arXiv 2019

  17. [17]

    G. Yang, J. Ping, J. Segovia, Tetra- and penta-quark structures in the constituent quark model, Symmetry 12 (11) (2020) 1869.arXiv:2009.00238,doi:10.3390/sym12111869. 15

    Pith/arXiv arXiv 2020

  18. [18]

    Dong, F.-K

    X.-K. Dong, F.-K. Guo, B.-S. Zou, A survey of heavy-antiheavy hadronic molecules, Progr. Phys. 41 (2021) 65–93.arXiv: 2101.01021,doi:10.13725/j.cnki.pip.2021.02.001

    Pith/arXiv arXiv 2021

  19. [19]

    Dong, F.-K

    X.-K. Dong, F.-K. Guo, B.-S. Zou, A survey of heavy–heavy hadronic molecules, Commun. Theor. Phys. 73 (12) (2021) 125201.arXiv:2108.02673,doi:10.1088/1572-9494/ac27a2

    Pith/arXiv arXiv 2021

  20. [20]

    H.-X. Chen, W. Chen, X. Liu, Y.-R. Liu, S.-L. Zhu, An updated review of the new hadron states, Rept. Prog. Phys. 86 (2) (2023) 026201.arXiv:2204.02649,doi:10.1088/1361-6633/aca3b6

    Pith/arXiv arXiv 2023

  21. [21]

    L. Meng, B. Wang, G.-J. Wang, S.-L. Zhu, Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules, Phys. Rept. 1019 (2023) 1–149.arXiv:2204.08716,doi:10.1016/j.physrep.2023.04.003

    Pith/arXiv arXiv 2023

  22. [22]

    Aaij, et al., Amplitude analysis of theB+→D +D−K+ decay, Phys

    R. Aaij, et al., Amplitude analysis of theB+→D +D−K+ decay, Phys. Rev. D 102 (2020) 112003.arXiv:2009.00026, doi:10.1103/PhysRevD.102.112003

    arXiv 2020

  23. [23]

    Aaij, et al., A model-independent study of resonant structure inB+→D +D−K+ decays, Phys

    R. Aaij, et al., A model-independent study of resonant structure inB+→D +D−K+ decays, Phys. Rev. Lett. 125 (2020) 242001.arXiv:2009.00025,doi:10.1103/PhysRevLett.125.242001

    arXiv 2020

  24. [24]

    Aaij, et al., Amplitude analysis of B0→D¯0Ds+π- and B+→D-Ds+π+ decays, Phys

    R. Aaij, et al., Amplitude analysis of B0→D¯0Ds+π- and B+→D-Ds+π+ decays, Phys. Rev. D 108 (1) (2023) 012017. arXiv:2212.02717,doi:10.1103/PhysRevD.108.012017

    arXiv 2023

  25. [25]

    Aaij, et al., First Observation of a Doubly Charged Tetraquark and Its Neutral Partner, Phys

    R. Aaij, et al., First Observation of a Doubly Charged Tetraquark and Its Neutral Partner, Phys. Rev. Lett. 131 (4) (2023) 041902.arXiv:2212.02716,doi:10.1103/PhysRevLett.131.041902

    arXiv 2023

  26. [26]

    Aaij, et al., Observation of New Charmonium or Charmoniumlike States in B+→D*±D∓K+ Decays, Phys

    R. Aaij, et al., Observation of New Charmonium or Charmoniumlike States in B+→D*±D∓K+ Decays, Phys. Rev. Lett. 133 (13) (2024) 131902.arXiv:2406.03156,doi:10.1103/PhysRevLett.133.131902

    arXiv 2024

  27. [27]

    Molina, E

    R. Molina, E. Oset, Molecular picture for theX0(2866)as aD ∗ ¯K ∗ JP = 0+ state and related1+,2 + states, Phys. Lett. B 811 (2020) 135870, [Erratum: Phys.Lett.B 837, 137645 (2023)].arXiv:2008.11171,doi:10.1016/j.physletb.2020. 135870

    Pith/arXiv arXiv 2020

  28. [28]

    L. R. Dai, R. Molina, E. Oset, The B¯0→D∗+D¯∗0K−reaction to detect theI= 0,JP = 1+ partner of the X0(2866), Phys. Lett. B 832 (2022) 137219.arXiv:2202.00508,doi:10.1016/j.physletb.2022.137219

    Pith/arXiv arXiv 2022

  29. [29]

    Sundu, S

    H. Sundu, S. S. Agaev, K. Azizi, Axial-vector and pseudoscalar tetraquarks[ud][cs], Eur. Phys. J. C 83 (3) (2023) 198. arXiv:2206.05004,doi:10.1140/epjc/s10052-023-11339-8

    Pith/arXiv arXiv 2023

  30. [30]

    Azizi, U

    K. Azizi, U. Özdem, Magnetic dipole moments of the Tcc+ and ZV++ tetraquark states, Phys. Rev. D 104 (11) (2021) 114002.arXiv:2109.02390,doi:10.1103/PhysRevD.104.114002

    Pith/arXiv arXiv 2021

  31. [31]

    S. S. Agaev, K. Azizi, H. Sundu, Doubly charged vector tetraquarkZ ++ V =[cu][¯s¯d], Phys. Lett. B 820 (2021) 136530. arXiv:2105.00081,doi:10.1016/j.physletb.2021.136530

    Pith/arXiv arXiv 2021

  32. [32]

    V. L. Chernyak, I. R. Zhitnitsky, B meson exclusive decays into baryons, Nucl. Phys. B 345 (1990) 137–172.doi: 10.1016/0550-3213(90)90612-H

    doi:10.1016/0550-3213(90)90612-h 1990

  33. [33]

    V. M. Braun, I. E. Filyanov, QCD Sum Rules in Exclusive Kinematics and Pion Wave Function, Z. Phys. C 44 (1989) 157. doi:10.1007/BF01548594

    doi:10.1007/bf01548594 1989

  34. [34]

    I. I. Balitsky, V. M. Braun, A. V. Kolesnichenko, Radiative Decay Sigma+ —>p gamma in Quantum Chromodynamics, Nucl. Phys. B 312 (1989) 509–550.doi:10.1016/0550-3213(89)90570-1

    doi:10.1016/0550-3213(89)90570-1 1989

  35. [35]

    Özdem, Analysis of theΞ∗ c ¯Kmolecular pentaquark state by its electromagnetic properties, Eur

    U. Özdem, Analysis of theΞ∗ c ¯Kmolecular pentaquark state by its electromagnetic properties, Eur. Phys. J. C 84 (7) (2024) 765.arXiv:2407.08635,doi:10.1140/epjc/s10052-024-13134-5

    Pith/arXiv arXiv 2024

  36. [36]

    Özdem, Electromagnetic properties ofΩ 0 c resonances via light-cone QCD, Eur

    U. Özdem, Electromagnetic properties ofΩ 0 c resonances via light-cone QCD, Eur. Phys. J. Plus 139 (11) (2024) 978. arXiv:2402.18901,doi:10.1140/epjp/s13360-024-05779-8

    Pith/arXiv arXiv 2024

  37. [37]

    Özdem, Analysis of theXAV state through its electromagnetic properties, Eur

    U. Özdem, Analysis of theXAV state through its electromagnetic properties, Eur. Phys. J. C 84 (4) (2024) 359.arXiv: 2401.00481,doi:10.1140/epjc/s10052-024-12724-7

    Pith/arXiv arXiv 2024

  38. [38]

    Özdem, Magnetic dipole moments of theΩc(3185)0 andΩc(3327)0 states from molecular perspective, Phys

    U. Özdem, Magnetic dipole moments of theΩc(3185)0 andΩc(3327)0 states from molecular perspective, Phys. Lett. B 849 (2024) 138432.arXiv:2311.02925,doi:10.1016/j.physletb.2023.138432

    Pith/arXiv arXiv 2024

  39. [39]

    Ozdem, Electromagnetic properties of theΣc(2800)+ andΛ c(2940)+ states via light-cone QCD, Eur

    U. Ozdem, Electromagnetic properties of theΣc(2800)+ andΛ c(2940)+ states via light-cone QCD, Eur. Phys. J. C 83 (11) (2023) 1077.arXiv:2309.00959,doi:10.1140/epjc/s10052-023-12251-x

    Pith/arXiv arXiv 2023

  40. [40]

    Özdem, K

    U. Özdem, K. Azizi, Magnetic moment of theX1(2900)state in the diquark–antidiquark picture, Eur. Phys. J. A 58 (9) (2022) 171.arXiv:2202.11466,doi:10.1140/epja/s10050-022-00815-6

    Pith/arXiv arXiv 2022

  41. [41]

    Özdem, Magnetic moment of theΞb(6227)as a molecular pentaquark state, Eur

    U. Özdem, Magnetic moment of theΞb(6227)as a molecular pentaquark state, Eur. Phys. J. Plus 137 (1) (2022) 103. arXiv:2109.09313,doi:10.1140/epjp/s13360-022-02339-w

    Pith/arXiv arXiv 2022

  42. [42]

    Azizi, U.¨

    K. Azizi, U.¨. Özdem, The electromagnetic multipole moments of the possible charm-strange pentaquarks in light-cone QCD, Eur. Phys. J. C 78 (9) (2018) 698.arXiv:1807.06503,doi:10.1140/epjc/s10052-018-6187-0

    Pith/arXiv arXiv 2018

  43. [43]

    Azizi, U

    K. Azizi, U. Özdem, The electromagnetic multipole moments of the charged open-flavorZ¯cqstates, J. Phys. G 45 (5) (2018) 055003.arXiv:1802.07711,doi:10.1088/1361-6471/aab56b

    Pith/arXiv arXiv 2018

  44. [44]

    Özdem, Electromagnetic properties of the Ds1+(2460), Ds1+(2536), and their bottom partners in a molecular config- uration, Phys

    U. Özdem, Electromagnetic properties of the Ds1+(2460), Ds1+(2536), and their bottom partners in a molecular config- uration, Phys. Rev. D 112 (11) (2025) 114013.arXiv:2510.17477,doi:10.1103/y77p-ch1k

    arXiv 2025

  45. [45]

    P. Ball, V. M. Braun, N. Kivel, Photon distribution amplitudes in QCD, Nucl. Phys. B 649 (2003) 263–296.arXiv: hep-ph/0207307,doi:10.1016/S0550-3213(02)01017-9

    Pith/arXiv arXiv 2003

  46. [46]

    V. A. Novikov, M. A. Shifman, A. I. Vainshtein, V. I. Zakharov, Calculations in External Fields in Quantum Chromody- namics. Technical Review, Fortsch. Phys. 32 (1984) 585

    1984

  47. [47]

    B. L. Ioffe, A. V. Smilga, Nucleon Magnetic Moments and Magnetic Properties of Vacuum in QCD, Nucl. Phys. B 232 (1984) 109–142.doi:10.1016/0550-3213(84)90364-X

    doi:10.1016/0550-3213(84)90364-x 1984

  48. [48]

    Chen, Hadronic molecules in B decays, Phys

    H.-X. Chen, Hadronic molecules in B decays, Phys. Rev. D 105 (9) (2022) 094003.arXiv:2103.08586,doi:10.1103/ PhysRevD.105.094003

    Pith/arXiv arXiv 2022

  49. [49]

    I. I. Balitsky, V. M. Braun, Evolution Equations for QCD String Operators, Nucl. Phys. B 311 (1989) 541–584.doi: 16 10.1016/0550-3213(89)90168-5

    doi:10.1016/0550-3213(89)90168-5 1989

  50. [50]

    V. M. Belyaev, B. Y. Blok, CHARMED BARYONS IN QUANTUM CHROMODYNAMICS, Z. Phys. C 30 (1986) 151. doi:10.1007/BF01560689

    doi:10.1007/bf01560689 1986

  51. [51]

    Antonov, J

    D. Antonov, J. E. F. T. Ribeiro, Quark condensate for various heavy flavors, Eur. Phys. J. C 72 (2012) 2179.arXiv: 1209.0408,doi:10.1140/epjc/s10052-012-2179-7

    Pith/arXiv arXiv 2012

  52. [52]

    S. J. Brodsky, J. R. Hiller, Universal properties of the electromagnetic interactions of spin one systems, Phys. Rev. D 46 (1992) 2141–2149.doi:10.1103/PhysRevD.46.2141

    doi:10.1103/physrevd.46.2141 1992

  53. [53]

    Navas, et al., Review of particle physics, Phys

    S. Navas, et al., Review of particle physics, Phys. Rev. D 110 (3) (2024) 030001.doi:10.1103/PhysRevD.110.030001

    doi:10.1103/physrevd.110.030001 2024

  54. [54]

    B. L. Ioffe, QCD at low energies, Prog. Part. Nucl. Phys. 56 (2006) 232–277.arXiv:hep-ph/0502148,doi:10.1016/j. ppnp.2005.05.001

    Pith/arXiv arXiv 2006

  55. [55]

    Narison, mc,b, < αsG2 >andα s from Heavy Quarkonia, Nucl

    S. Narison, mc,b, < αsG2 >andα s from Heavy Quarkonia, Nucl. Part. Phys. Proc. 300-302 (2018) 153–164.doi: 10.1016/j.nuclphysbps.2018.12.026

    doi:10.1016/j.nuclphysbps.2018.12.026 2018

  56. [56]

    J. Rohrwild, Determination of the magnetic susceptibility of the quark condensate using radiative heavy meson decays, JHEP 09 (2007) 073.arXiv:0708.1405,doi:10.1088/1126-6708/2007/09/073

    Pith/arXiv arXiv 2007