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Production of heavy tetraquarks in rare exclusive decays of the Higgs boson

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Pith's one-line read This paper predicts that the Higgs boson, via a quark–gluon mechanism, decays to a fully charmed tetraquark plus a photon with a branching fraction around 2×10⁻⁹, making the state potentially visible at future Higgs factories.

desk verdict New estimate for H -> fully charmed tetraquark + gamma: quark-gluon mechanism dominates at ~2e-9 branching, but the absolute rate inherits order-of-magnitude model dependence from the imported tetraquark wave function. read the letter →

arxiv 2509.08964 v1 pith:62J2KNEQ submitted 2025-09-10 hep-ph

F. A. Martynenko , A. V. Eskin , A. P. Martynenko This is my paper · ORCID
classification hep-ph
keywords fullycharmedtetraquarkHiggsbosondecayrelativisticquarkmodelbranchingfractionquark–gluonmechanismX(6900)variationalwavefunctionexotichadrons
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 asks whether the Higgs boson, decaying in a rare exclusive channel, can serve as a production site for fully charmed tetraquarks: bound states of two charm quarks and two charm antiquarks, such as the X(6900) candidate. Using a relativistic quark model with a four-particle wave function obtained by variational methods, the authors compute branching fractions for H → T + γ through three mechanisms: quark–gluon, ZZ-boson, and quark–gluon loop. Their central result is that the quark–gluon mechanism dominates, with a branching fraction around 2×10⁻⁹ for the vector 1⁺⁻ tetraquark, several orders of magnitude larger than the other two. If these numbers are right, Higgs factories could observe dozens of such events, making the Higgs a new window on the internal structure of exotic multiquark states.

What carries the argument

The central object is the tetraquark quasipotential wave function at zero relative coordinates, Ψ(0,0,0), the probability amplitude for all four constituents to meet at one point; its square sets the overall scale of every S-wave decay width. This wave function is obtained variationally as a Gaussian expansion for a [cc][\bar c\bar c] diquark–antidiquark configuration, yielding Ψ(0,0,0) = 0.10 GeV^{9/2} and mean-square relative momenta ω_p = ω_q = 0.18, ω_t = 0.12. The decay amplitudes are built by convoluting the hard H → c\bar c (+γ) interaction with this wave function, using spin projection operators for spin-1 diquark and antidiquark pairs, Wigner rotations, and relativistic corrections

What would settle it

Search for the exclusive decay H → J/ψ J/ψ γ at a Higgs factory with sensitivity below 10⁻⁹; the model predicts this channel should be fed by the 1⁺⁻ tetraquark at a rate near 2×10⁻⁹, so observing it at a level far below 10⁻¹⁰ would falsify the quark–gluon dominance and the assumed tetraquark wave function.

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Extended reading notes

Core claim

The paper claims that among the mechanisms for exclusive production of a fully charmed vector tetraquark T(cc\bar c\bar c) in the decay H → T + γ, the quark–gluon mechanism dominates. The authors calculate relativistic amplitudes for three production paths—quark–gluon, ZZ-boson, and quark–gluon loop—by convoluting the hard production amplitude with the tetraquark quasipotential wave function, keeping relativistic corrections up to quadratic order in the internal relative momenta. They obtain a branching fraction of 0.21×10⁻⁸ for H → Q\bar Q → T(1⁺⁻) + γ, compared with 0.61×10⁻¹⁴ for the ZZ mechanism and 0.50×10⁻¹¹ for the loop mechanism; an orbital-excitation state T(1⁻⁻) is predicted at 0.8

Load-bearing premise

The calculations assume the fully charmed tetraquark is a compact [cc][\bar c\bar c] diquark–antidiquark state whose S-wave wave function at zero separation is Ψ(0,0,0) = 0.10 GeV^{9/2}; if the physical X(6900) is instead a molecule or has large noncompact components, every predicted branching fraction changes by orders of magnitude.

Editorial extensions

If this is right

  • The quark–gluon mechanism gives a branching fraction around 2.1×10⁻⁹ for H → T(1⁺⁻) + γ, exceeding the ZZ and loop mechanisms by four to five orders of magnitude.
  • Because the decay width scales as |Ψ(0,0,0)|², any refinement of the four-quark wave function directly rescales all predicted rates.
  • The predicted event yield at a 100 TeV Higgs factory is roughly 60 tetraquarks per year at 30 ab⁻¹, making the decay a plausible discovery channel.
  • The T(1⁻⁻) orbital-excitation state has a branching fraction near 0.88×10⁻¹⁰, smaller than the ground-state vector but still larger than the ZZ-mediated S-wave rate.
  • The quark–gluon channel is an order of magnitude more probable than the previously studied H → J/ψ J/ψ decay, so tetraquark final states may be a better probe of the Higgs–charm coupling.

Reading between the lines

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

  • If a compact [cc][\bar c\bar c] tetraquark exists, the same wave-function machinery could be applied to other Higgs exclusive decays, such as H → T(0⁺⁺) + γ or H → T + Z, testing whether the 1⁺⁻ dominance is a physical pattern or a model artifact.
  • The extreme sensitivity to |Ψ(0,0,0)|² suggests a clean cross-check: a lattice QCD computation of the four-quark distribution at zero separation for the fully charmed system would either confirm or rule out the diquark–antidiquark assumption underpinning the rate.
  • Measuring the invariant-mass shape of the cc\bar c\bar c system in Higgs decays would help distinguish a compact tetraquark from a J/ψ J/ψ threshold enhancement: the model predicts a narrow resonance, whereas a molecular picture would produce a broader, shifted distribution.
  • The predicted dominance of the quark–gluon mechanism implies that tetraquark searches at Higgs factories should trigger on charmed final states with an associated photon rather than on Z/Z-associated channels, which are heavily suppressed.
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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

5 major / 5 minor

Summary. The paper estimates branching fractions for the exclusive Higgs decay H -> (cc cbar cbar) + gamma in a relativistic quark model. It considers three S-wave mechanisms for the 1+- tetraquark (ZZ-boson, quark-gluon, and quark-gluon loop) and one P-wave mechanism for the 1-- state. The main numerical result is that the quark-gluon mechanism dominates, with Br ~ 0.21 x 10^-8, while the ZZ and loop mechanisms are suppressed by several orders of magnitude. The authors also translate this branching fraction into an estimate of about 60 events at FCC-hh. Relativistic corrections in the amplitudes are retained to second order in internal momenta, with the required momentum moments taken from a companion variational calculation.

Significance. If correct, the paper provides a concrete, testable prediction for a rare exclusive Higgs decay and identifies the dominant production mechanism. Its strengths are the explicit construction of multiple production amplitudes and the clear separation between mechanisms. Importantly, the conclusion that the quark-gluon mechanism dominates among the S-wave channels is robust, because all S-wave widths share the same factor |Psi(0,0,0)|^2. However, the absolute branching fractions depend on a short-distance four-quark wave function whose uncertainty is not quantified, and one of the loop formulas requires a specified analytic continuation. The numerical predictions should therefore be regarded as estimates unless the model dependence is quantified.

major comments (5)
  1. [Sec. II, Eq. (49) and Table I] All S-wave widths, Eqs. (29), (54), (64), are proportional to |Psi(0,0,0)|^2. The value Psi(0,0,0)=0.10 GeV^{9/2} is taken from companion paper [36], but neither its uncertainty nor the variational parameters are given. The text after Eqs. (46)-(48) itself admits that the wave function is poorly known at relativistic momenta; since Psi(0,0,0) is a short-distance quantity, this uncertainty feeds directly into the headline branching 0.21 x 10^-8 and the ~60-event estimate. Please provide an uncertainty estimate or a sensitivity scan, e.g. +/-50% in Psi(0,0,0). The relative ordering of the S-wave mechanisms is unaffected.
  2. [Sec. II, Eqs. (62) and (64)] The loop structure function A_Q(tau) is written in terms of ArcSin(sqrt(tau)), while for the physical b- and t-quark loops tau = M_H^2/(4m_Q^2) > 1. In this regime the expression is complex unless a specific analytic continuation is specified; Eq. (64) then takes an absolute value of the expression. The dispersion representation (60) is the correct route, but the final formula must be given in a manifestly real form, or with an explicit continuation, before the Table I loop entry can be verified.
  3. [Sec. II, Eqs. (46)-(48)] The relativistic parameters omega_p, omega_q, omega_t are obtained with a hard cutoff at |p|=m because, as stated in the text, the wave function is unreliable at relativistic momenta. These parameters are numerically significant: they change the quark-gluon branching from 0.15 x 10^-8 to 0.21 x 10^-8 in Table I. The cutoff prescription and the neglect of mixed moments <pt>, <qt>, <pq> need a sensitivity study (e.g. varying the cutoff between m/2 and 2m) before the error on the central value can be assessed.
  4. [Sec. II, color structure after Eq. (30)] The calculation assumes a compact diquark-antidiquark [cc][cbar cbar] configuration with each pair in a color antitriplet and spin 1. If the physical X(6900) has a large molecular or six-quark component, Psi(0,0,0) is not the relevant production quantity and the absolute rates can change by orders of magnitude. This is a legitimate model choice, but it should be explicitly stated as a limitation and, if possible, calibrated against alternative wave-function models.
  5. [Table I] No uncertainties are propagated into Table I. The only error estimate given in the text is 'not less than 30 percent' for R'(0,0,0) in the 1-- case, but this is not reflected in the table. Since the paper ends with an event-rate estimate for FCC-hh, an error budget for all rows is needed.
minor comments (5)
  1. [Eq. (9)] The entry |2++> is labeled J_T=0; it should be J_T=2.
  2. [Eqs. (17) and (54)] Notation such as 'sin2 theta MZ' should read 'sin 2 theta_W M_Z', and similar missing/faulty subscripts occur in several amplitudes.
  3. [Appendix A, Eq. (A7)] There is an apparent typesetting artifact: 'gamma^omega hat r - (3/4 hat T - hat p + ...)' should be cleaned up.
  4. [Eq. (45)] The phrase 'determined by first half of terms in matrix elements Q' is unclear; please define the tilde-Q elements in this context.
  5. [Table I and conclusion] The event-rate estimate 'about 60' at FCC-hh assumes a specific integrated luminosity and should also state assumptions about reconstruction efficiency and acceptance.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular reduction: the predicted branching fractions are model-dependent outputs of an independently calibrated variational wave function, not quantities defined by the fit itself.

full rationale

The paper's derivation chain is a standard model-calculation chain rather than a circular one. All three S-wave Higgs-decay widths in Eqs. (29), (54), and (64) are proportional to |Ψ(0,0,0)|^2, and the numerical value Ψ(0,0,0)=0.10 GeV^{9/2} is taken from the authors' companion variational calculation [36]. This is a model input, not a fitted output of the present paper: the companion paper fixes its potential parameters from meson and baryon spectra, not from the Higgs-decay branching fractions or from any data on H -> T + γ. The present paper does not fit any parameter to the quantity it claims to predict. The dominance of the quark-gluon mechanism is also unaffected by the value of Ψ(0,0,0) because the same factor multiplies all three S-wave widths, so the qualitative conclusion has independent content. The admitted limitations—the uncertainty in the short-distance wave function, the cutoff at relativistic momentum m in Eqs. (46)–(48), and the ≥30% uncertainty on R'(0,0,0)—are model-dependence and robustness concerns, not circularity. The self-citations to [28], [29], and [36] are prior applications of the same formalism or separate model calculations; they do not define the predicted quantity in terms of itself. Because no equation reduces to an input by construction and no fitted parameter is renamed as a prediction, the correct circularity score is 0.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

No new particles or forces are introduced. The main external dependency is the tetraquark wave function from the authors' companion paper [36]; its parameters are effective and fitted to hadron spectra, so the branching fractions are model outputs rather than first-principle predictions.

free parameters (6)
  • Charm quark mass m = not stated in this paper, taken from [36]
    Enters the H to c bar c vertex (Eq. 3) and all relativistic expansions in omega_p, omega_q, omega_t; value inherited from the potential model.
  • Pairwise strong couplings alpha_s,ij = not stated, from [36]
    Coulomb part of the tetraquark potential (Eq. 32); chosen to reproduce meson/baryon spectra.
  • Confinement parameters A, B = not stated, from [36]
    Linear confinement potential (Eq. 33); fitted to hadron spectra.
  • Wave function at zero Psi(0,0,0) = 0.10 GeV^{9/2}
    Central input from companion paper [36]; all S-wave widths scale as its square.
  • Relativistic moment ratios omega_p, omega_q, omega_t = 0.18, 0.18, 0.12
    Averages of p^2/m^2 etc. evaluated with the model wave function (Eq. 49).
  • P-wave derivative R'(0,0,0) = 0.02 GeV^{11/2}
    Input for the 1-- width (Eq. 67); admitted error is at least 30%.
assumptions (6)
  • standard math Quasipotential reduction of the Bethe-Salpeter amplitude is valid for a four-particle bound state (Eq. 11).
    Generalization of Refs. [37-40]; no proof given here.
  • domain assumption The tetraquark is a compact [cc]_anti-triplet [bar c bar c]_triplet state with each pair in spin-1 S-wave; the Pauli principle forces spin-1 diquarks.
    Section II: the model configuration is stated, not derived. Alternative meson-meson or higher Fock components are neglected.
  • domain assumption The quark interaction is a sum of pairwise Coulomb and linear confinement potentials (Eqs. 31-33) with parameters from meson/baryon fits.
    Potential model assumption; central to computing Psi(0,0,0) in Ref. [36].
  • domain assumption The divergent quark-loop integral in Fig. 2(b) can be evaluated with dispersion relations, keeping only the structure function A_Q(tau) (Eqs. 58-62).
    Standard technique, but the analytic continuation of the closed-form A_Q(tau) for tau > 1 is not specified.
  • ad hoc to paper The integral for <p^2/m^2> is cut off at |p| = m because the wave function is unreliable at relativistic momenta.
    Explicitly stated before Eq. (49); affects the size of relativistic corrections.
  • domain assumption For the L=1 state only orbital excitation L_sigma=1 is included (Appendix B).
    Other orbital excitations (L_rho, L_lambda) are neglected.

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Pith. "Pith review of Production of heavy tetraquarks in rare exclusive decays of the Higgs boson." pith.science (2026). https://pith.science/paper/62J2KNEQ

@misc{pith2026250908964,
  author       = {Pith},
  title        = {Pith review of: Production of heavy tetraquarks in rare exclusive decays of the Higgs boson},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/62J2KNEQ}},
  note         = {Machine review of arXiv:2509.08964}
}
abstract

The relativistic quark model is used to study the processes of heavy tetraquark $(cc\bar{c}\bar{c})$ production in the Higgs boson decay. We consider quark-gluon, ZZ-boson, and quark-gluon loop decay mechanisms with the production of a fully charmed tetraquark. Relativistic interaction amplitudes are constructed and decay widths are calculated taking into account relativistic corrections in the decay amplitude connected with the relative motion of quarks and antiquarks.

Figures

Figures reproduced from arXiv: 2509.08964 by the authors.

Figure 1
Figure 1. FIG. 1: Quark-gluon and [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Quark-gluon loop mechanism of heavy tetraquark prod [PITH_FULL_IMAGE:figures/full_fig_p005_2.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. Full citation record

  1. Heavy tetraquarks in the hyperspherical approach

    hep-ph 2025-09 conditional novelty 5.0 of 10

    Ground-state masses of fully heavy tetraquarks are predicted with the hyperspherical hyperradial approximation, yielding e.g. 5.86 GeV for the lightest all-charm state.

Reference graph

Works this paper leans on

56 extracted references · 10 canonical work pages · cited by 1 Pith paper

  1. [28]

    Qin, J.-L

    Q. Qin, J.-L. Qiu, Fu-Sh. Yu, Diagrammatic analysis of h idden- and open-charm tetraquark production in B decays, Eur. Phys. J. C 83, 227 (2023); https://doi.org/10.1140/epjc/s10052- 023-11375-4

    doi:10.1140/epjc/s10052- 2023

  2. [36]

    Wu, Y.-R

    J. Wu, Y.-R. Liu, K. Chen, X. Liu, and Sh.-L. Zhu, Heavy-fl avored tetraquark states with the QQ ¯Q ¯Q configuration, Phys. Rev. D 97, 094015 (2018); https://doi.org/10.1103/PhysRevD.97.094015

    doi:10.1103/physrevd.97.094015 2018

  3. [1]

    The color part of amplitudes (17)-(20) is allocated as a product o f color factors describing pairs of quarks and antiquarks in an antisymmetric state: 1√ 2εijk 1√ 2εijl = δkl. Leaving in the numerator of amplitudes the quadratic terms in relativ e momenta ωp = p2/m2, ωq = q2/m2, ωt = t2/m2, we obtain the following expression for the numerator of total am...

  4. [2]

    − m) 2m + (ˆp − ˆt 2) 2m ] , (23) where εi (i=1,2) are polarization vectors describing pairs of quarks and antiq uarks with spin

  5. [3]

    One of parameters that enters (29) is the value of the tetraquar k wave function at zero coordinate values Ψ(0 , 0, 0)

    − r2 1r2 3]2 × (29) [ 3N 2 2 + 2N 2 3 (vvγ)2 − N 2 1 (vvγ)2] , (vvγ) = (r2 2 − r2 3) 2r2 3 . One of parameters that enters (29) is the value of the tetraquar k wave function at zero coordinate values Ψ(0 , 0, 0). This parameter can be found by solving the eigenvalue problem for the Hamiltonian of four-particle system. As discussed above, t otal tetraquark...

    2003

  6. [4]

    R. N. Faustov, V. O. Galkin and E. M. Savchenko, Heavy tetr aquarks in the relativistic quark model, Universe 7, 94 (2021), https://doi.org/10.3390/universe7040094

    doi:10.3390/universe7040094 2021

  7. [5]

    R. N. Faustov, V. O. Galkin and E. M. Savchenko, Masses of t he QQ ¯Q ¯Q tetraquarks in the relativistic diquark-antidiquark picture, Phys. Re v. D 102, 114030 (2020), https://doi:10.1103/PhysRevD.102.114030

    doi:10.1103/physrevd.102.114030 2020

  8. [6]

    Similarly, in a qu ark-antiquark pair, the attractive force arises in the color singlet state, and in the color oc tet state, the repulsive force arises

    Pairs of quarks in the color antitriplet state are attracted to eac h other, 4 and in the color sextet state they repel each other. Similarly, in a qu ark-antiquark pair, the attractive force arises in the color singlet state, and in the color oc tet state, the repulsive force arises. Thus, various configurations of four quarks are possible, which lead to ...

Show all 56 references
  1. [7]

    + 2B12B13B22B23 − B2 13B2 22 ] , < 1 λ >= K∑ I,J =1 CICJ 8π3 (det B)2(B22B33 − B2 23)3/2 [ 3B11B22(B11B33 − B2 13)− (B10) B2 12(3B11B33 − 2B2

  2. [8]

    − 3B33(B11 + B22) ] + 2B12(B13 − B23) [ B11(4B22 + B23) − B13B22 ] + 6B11B12B22B33 + B11B22(−3B2 13 + 8B13B22− 4B13B23 + 3B22B33 − 3B2

  3. [9]

    + 8B4 12 + B3 12(−8B13 + 8B23 − 6B33) − B2 13B2 22 } , where auxiliary functions are introduced: F1 = B11 + 1 4 B33 + B13, (B12) F2 = B22 + 1 4 B33 − B23, (B13) 22 F3 = B12 + 1 2 B23 − 1 4B33 − 1 2 B13. (B14) The matrix elements < 1 |r1−r4| >, < 1 |r2−r3| >, < 1 |r2−r4| > are ...

  4. [10]

    − 2B12B13B22B23 + B2 13B2 22 ] , < λ > = K∑ I,J =1 CICJ 16π3 (det B)3 √ (B11B33 − B2 13) [ B2 12(4B2 13 − 3B11B33)− (B16) 2B11B12B13B23 + B2 11(3B22B33 + B2

  5. [11]

    − 3B11B22B2 13 ] , < |r1 − r3| >= K∑ I,J =1 CICJ 4π3 (det B)3 √ (F1F2 − F 2 3 ) { B2 11(16B2 22 − 16B22B23 + 3B22B33 + B2 23)+ (B17) B2 12 [ 4(−8B11B22 + 4B11B23 + B2 13 + B13(B23 − 4B22) + B2

  6. [12]

    − 3B33(B11 + B22) ] + 2B12(B13 −B23)(8B11B22 −B11B23 +B13B22)+6 B11B12B22B33 +B11B22(−3B2 13 +16B13B22− 8B13B23 + 3B22B33 − 3B2

  7. [13]

    + 2B11B12B13B23 − B2 11B2 23 ] , < 1 |r1 − r3| >= K∑ I,J =1 CICJ 2π3 (det B)2(F1F2 − F 2 3 )3/2 { B2 11(8B2 22 − 8B22B23 + 3B22B33 − B2 23)+ (B11) B2 12 [ 2(4B23(B11 + B13) − 8B11B22 + B2 13 − 4B13B22 + B2

  8. [14]

    + 16B4 12 − 2B3 12(8B13 − 8B23 + 3B33) + B2 13B2 22 } . The matrix elements < |r1 − r4| >, < |r2 − r3| >, < |r2 − r4| > are obtained from (B17) using the substitutions: B12 → − B12, B23 → − B23; B12 → − B12, B13 → − B13; B13 → −B13, B23 → −B23

  9. [15]

    S. K. Choi, S. L. Olsen, K. Abe, T. Abe, et al. (Belle Collab oration), Observation of a narrow charmoniumlike state in exclusive B± → K ±π+π−J/Ψ decays, Phys. Rev. Lett. 91, 262001 (2003), https://doi.org/10.1103/PhysRevLett.91.262001

    2003 doi

  10. [16]

    Aaij, et al

    R. Aaij, et al. (LHCb Collaboration), Observation of str ucture in the J/Ψ-pair mass spectrum, Sci. Bull. 65, 1983 (2020), https://doi.org/10.1016/j.scib.2020.08. 032

    1983 doi

  11. [17]

    The CMS Collaboration, Observation of a family of all-ch arm tetraquark candidates at the LHC, CMS PAS BPH-24-003; https://cds.cern.ch/record/292 9472/files/BPH-24-003-pas.pdf 23

  12. [18]

    Liang, J

    X. Liang, J. Jiang, S.-Y. Li, Y.-R. Liu, and Z.-G. Si, The exclusive production of a fully heavy tetraquark and a photon in electron-positron collisi on, arXiv:2502.16777 [hep-ph]; https://doi.org/10.48550/arXiv.2502.16777

    doi

  13. [19]

    V. O. Galkin and E. M. Savchenko, Masses of Ground States o f Triply Heavy Tetraquarks, Phys. Part. Nuclei 56, 330 (2025), https://doi.org/10.1134/S106377962470159 4

    2025 doi

  14. [20]

    H. X. Chen, W. Chen, X. Liu, S. L. Zhu, The hidden-charm pen taquark and tetraquark states, Phys. Rep. 639, 1-121 (2016), https://doi.org/10.1016/j.physrep.2016 .05.004

    2016 doi

  15. [21]

    H.-X. Chen, W. Chen, X. Liu, Y.-R. Liu and Sh.-L. Zhu, An up dated review of the new hadron states, Rep. Prog. Phys. 86, 026201 (2023), https://doi.org/10.1088/1361-6633/aca 3b6

    2023 doi

  16. [22]

    S. L. Olsen, T. Skwarnicki, D. Zieminska, Nonstandard he avy mesons and baryons: experimental evidence, Rev. Mod. Phys. 90, 015003 (2018), https://doi.org/10.1103/RevModPhys.90.015003

    2018 doi

  17. [23]

    + B2 12(5B2 23 − 3B22B33)− 4B12B13B22B23 + 2B2 13B2 22 ] + 2AI 13AI 23 [ −B12(3B11B22B33 + 2B11B2 23 + 2B2 13B22) + 3B3 12B33+ 5B11B13B22B23 − B2 12B13B23 ] + 10AI 13AI 33 [ (B13B22 − B12B23)(B2 12 − B11B22) ] − 2AI 13(B13B22 − B12B23) [ B11(B2 23 − B22B33) + B2 12B33 − 2B12B1...

  18. [24]

    S. Pal, B. Chakrabarti, A. Bhattacharya, A theoretical investigation on the spectroscopy and structure of the exotic tetraquark states, Nuclear Phys ics A 1029, 122559 (2023), https://doi.org/10.1016/j.nuclphysa.2022.122559

    2023

  19. [25]

    Szczurek, W

    A. Szczurek, W. Sch¨ afer, R. Maciula, Mechanisms of ful ly heavy tetraquark produc- tion in proton-proton collisions, Acta Phys. Polonica B Pro c. Suppl. 16, 5-A24 (2023), https://www.actaphys.uj.edu.pl/S/16/5-A24/pdf

    2023

  20. [26]

    S. J. Brodsky, D. S. Hwang and R. F. Lebed, Dynamical Pict ure for the Forma- tion and Decay of the Exotic XYZ Mesons, Phys. Rev. Lett. 113, 112001, (2014); http://dx.doi.org/10.1103/PhysRevLett.113.112001

    2014 doi

  21. [27]

    V. P. Goncalves, B. D. Moreira, Fully -heavy tetraquark production by γγ in- teractions in hadronic collisions at the LHC, Phys. Lett. B 816, 136249 (2021), https://doi.org/10.1016/j.physletb.2021.136249

    2021

  22. [29]

    Niu and H.-H

    J.-J. Niu and H.-H. Ma, Photoproduction of doubly charm ed tetraquark Tcc via photon-gluon fusion at ILC and CLIC, arXiv:2506.16721 [hep-ph]; https:/ /arxiv.org/abs/2506.16721v1. 24

    arXiv

  23. [30]

    F. Feng, Y. Huang, Y. Jia, W.-L. Sang, De-Sh. Yang, and J. -Y. Zhang, Inclusive pro- duction of fully charmed tetraquarks at the LHC, Phys. Rev. D 108, L051501 (2023); https://doi.org/10.1103/PhysRevD.108.L051501

    2023 doi

  24. [31]

    F. Feng, Y. Huang, Y. Jia, W.-L. Sang, X. Xiong, and J.-Y. Zhang, Fragmentation production of fully-charmed tetraquarks at the LHC, Phys. R ev. D 106, 114029 (2022); https://doi.org/10.1103/PhysRevD.106.114029

    2022 doi

  25. [32]

    A. Ali, L. Maiani, A. Parkhomenko and W. Wang, Tetraquar k Interpretation and Production Mechanism of the Belle Yb(10750)-Resonance, PoS(ICHEP2020)493; https://pos.sissa.it/390/493

  26. [33]

    A. V. Berezhnoy, A. K. Likhoded, A. V. Luchinsky, and A. A . Novoselov, Production of J/Ψ-meson pairs and 4 c tetraquark at the LHC, Phys. Rev. D 84, 094023 (2011); http://dx.doi.org/10.1103/PhysRevD.84.094023

    2011 doi

  27. [34]

    A. V. Berezhnoy, A. V. Luchinsky, and A. A. Novoselov, He avy tetraquarks production at the LHC, Phys. Rev. D 86, 034004 (2012); http://dx.doi.org/10.1103/PhysRevD.86 .034004

    2012 doi

  28. [35]

    V. R. Debastiani and F. S. Navarra, A non-relativistic m odel for the [ cc][¯c¯c] tetraquark, Chinese Physics C 43, 1, 013105 (2019); https://iopscience.iop.org/article/ 10.1088/1674- 1137/43/1/013105/pdf

    2019 doi

  29. [37]

    Ablikim, M

    M. Ablikim, M. N. Achasov, P. Adlarson, S. Ahmed, M. Albr echt, R. Aliberti, A. Amoroso, Q. An, Anita et al. (BESIII Collaboration), Observation of a Near-Threshold Structure in the K + Recoil-Mass Spectra in e+e− → K +D− s D∗0 + D∗− s D0; Phys. Rev. Lett. 126, 102001 (2021); ...

    2021 doi

  30. [38]

    Z. G. Wang, Analysis of the X(6600), X(6900), X(7300) an d related tetraquark states with the QCD sum rules, Nucl. Phys. B 985, 115983 (2022); https://doi.org/10.1016/j.nuclphysb.2022.115983

    2022

  31. [39]

    G. L. Yu, Z. Y. Li, Z. G. Wang, L. Jie, and Y. Meng, The S- and P-wave fully 25 charmed tetraquark states and their radial excitations, Eu r. Phys. J. C (2023) 83:416; https://doi.org/10.1140/epjc/s10052-023-11445-7

    2023 doi

  32. [40]

    W. C. Dong and Z. G. Wang, Going in quest of potential tetr aquark interpretations for the newly observed Tψψ states in light of the diquark-antidiquark scenarios, Phys . Rev. D 107, 074010 (2023); https://doi.org/10.1103/PhysRevD.107.0 74010

    2023 doi

  33. [41]

    R. N. Faustov, A. P. Martynenko, F. A. Martynenko, Relat ivistic corrections to paired produc- tion of charmonium and bottomonium in decays of the Higgs bos on, Phys.Rev.D 107 (2023) 5, 056002, https://doi.org/10.1103/PhysRevD.107.05600 2

    2023 doi

  34. [42]

    R. N. Faustov, F. A. Martynenko, A. P. Martynenko, Higgs boson decay to the pair of S- and P-wave Bc mesons, Eur. Phys. J. A 58, 4 (2022), https://doi.org/10.1140/epja/s10050-021- 00660-z

    2022 doi

  35. [43]

    F. A. Martynenko, A. P. Martynenko and A. V. Eskin, Produ ction of dilep- tonic bound states in the Higgs boson decay, Phys. Rev. D 110, 056016 (2024); https://doi.org/10.1103/PhysRevD.110.056016

    2024 doi

  36. [44]

    V. I. Borodulin, R. N. Rogalev and S. R. Slabospitsky, CO RE: COmpendium of RElations: Version 3.1, e-Print: arXiv:1702.08246v2 [hep-ph]

    arXiv

  37. [45]

    D. M. Brink and Fl. Stancu, Tetraquarks with heavy flavor s, Phys. Rev. D 57, 6778 (1998)

    1998

  38. [46]

    Buccella, H

    F. Buccella, H. Hogaasen, J.-M. Richard, and P. Sorba, T etraquarks with heavy flavors, Eur. Phys. J. C 49, 743 (2007); DOI 10.1140/epjc/s10052-006-0142-1

    2007 doi

  39. [47]

    Maiani, F

    L. Maiani, F. Piccinini, A. D. Polosa, and V. Riquer, Z(4 430) and a new paradigm for spin interactions in tetraquarks, Phys. Rev. D 89, 114010 (2014); http://dx.doi.org/10.1103/PhysRevD.89.114010

    2014 doi

  40. [48]

    Park and S

    W. Park and S. H. Lee, Color spin wavefunctions of heavy t etraquark states, Nucl. Phys. A 925, 161 (2014); http://dx.doi.org/10.1016/j.nuclphysa.20 14.02.008

    2014 doi

  41. [49]

    A. V. Eskin, A. P. Martynenko and F. A. Martynenko, Mass s pectrum of heavy tetraquarks in variational approach, arXiv:2505.05993 [hep-ph]; https: //doi.org/10.48550/arXiv.2505.05993

    doi arXiv

  42. [50]

    Ebert and A

    D. Ebert and A. P. Martynenko, Relativistic effects in the production of pseudoscalar and vector doubly heavy mesons from e+e− annihilation, Phys. Rev. D 74, 054008 (2006); https://doi.org/10.1103/PhysRevD.74.054008

    2006 doi

  43. [51]

    A. P. Martynenko and F. A. Martynenko, Relativistic Cor rections to the Higgs Boson Decay into a Pair of Vector Quarkonia, Symmetry 15, 448 (2023); 26 https://doi.org/10.3390/sym15020448

    2023 doi

  44. [52]

    S. J. Brodsky and J. R. Primack, The electromagnetic int eractions of composite systems, Ann. Phys. 52, 315 (1969); https://doi.org/10.1016/0003-4916(69)902 64-4

    1969 doi

  45. [53]

    R. N. Faustov, Relativistic wavefunction and form fact ors of the bound system, Ann. Phys. 78, 176 (1973); https://doi.org/10.1016/0003-4916(73)900 07-9

    1973 doi

  46. [54]

    d’Enterria and D

    D. d’Enterria and D. V. Le, Rare and exclusive few-body d ecays of the Higgs, Z, W bosons, and the top quark, J. Phys. G: Nucl. Part. Phys. 52, 053001 (2025); https://doi.org/10.1088/1361- 6471/ad3c59

    2025 doi

  47. [55]

    Brau et al

    J. Brau et al. [ILC], ILC Reference Design Report Volume 1 - Executive Summary, [arXiv:0712.1950 [physics.acc-ph]]

    1950 arXiv

  48. [56]

    Brunner et al., The CLIC project, arXiv:2203.09186 [ physics.acc-ph]

    O. Brunner et al., The CLIC project, arXiv:2203.09186 [ physics.acc-ph]

    arXiv

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