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arxiv: 2605.22500 · v1 · pith:DBDMQWLWnew · submitted 2026-05-21 · ✦ hep-ph

Two photon decay width of the fully charmed tetraquarks: revisiting prospects for ultraperipheral collisions

Longjie Chen , Wolfgang Sch\"afer , Antoni Szczurek This is my paper

Pith reviewed 2026-05-22 04:49 UTC · model grok-4.3

classification ✦ hep-ph
keywords fully charmed tetraquarkstwo-photon decaysultraperipheral collisionsNRQCD factorizationJ/psi pair productiondiphoton productionvector dominance
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The pith

Tetraquark resonances exceed continuum for J/ψ J/ψ but not for diphotons in ultraperipheral collisions

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

The paper evaluates two-photon decay widths of fully charmed tetraquarks by extracting long-distance matrix elements from four-body wave functions computed in the extended relativized quark model. These widths feed into estimates of resonant contributions to J/ψ pair and diphoton production in ultraperipheral Pb-Pb collisions. Resonant terms from the scalar and tensor states surpass the continuum background in the J/ψ J/ψ channel while falling below it in the γγ channel. The reversal stands in clear disagreement with the naive vector dominance picture that would assign comparable relative strengths to both final states.

Core claim

Using LDMEs taken from four-body wave functions at the origin, the two-photon couplings of T_{4c}(0^{++}, 2^{++}) states produce resonant cross sections for γγ → J/ψ J/ψ that exceed the continuum, whereas for γγ → γγ the continuum dominates; this outcome contradicts expectations from the naïve vector dominance model. Total widths measured by CMS for X(6600) and X(6900) are inserted to obtain the energy dependence of the resonant pieces.

What carries the argument

Extraction of long-distance matrix elements at the origin from four-body wave functions of the extended relativized quark model, inserted into NRQCD factorization to obtain two-photon decay widths of scalar and tensor fully charmed tetraquarks.

If this is right

  • Resonant production of J/ψ pairs via tetraquarks can exceed non-resonant backgrounds and become observable in LHC ultraperipheral collision data.
  • Diphoton production cross sections in the same collisions remain dominated by continuum processes.
  • Energy-dependent resonant cross sections follow from inserting the CMS-measured total widths of the X(6600) and X(6900) candidates.

Where Pith is reading between the lines

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

  • Future luminosity upgrades at the LHC could make the J/ψ J/ψ excess a practical search channel for fully charmed tetraquarks.
  • The breakdown of naive vector dominance may require refined models of tetraquark-photon couplings that incorporate four-body dynamics explicitly.
  • The same wave-function approach can be applied to fully bottom or mixed tetraquarks to predict visibility in analogous channels.

Load-bearing premise

The four-body wave functions of the extended relativized quark model accurately fix the long-distance matrix elements at the origin and NRQCD factorization remains valid for the radiative decays of these tetraquark states.

What would settle it

An experimental observation in ultraperipheral Pb-Pb data that the resonant contribution to γγ production exceeds the continuum (or that the resonant J/ψ J/ψ contribution falls below the continuum) would contradict the predicted reversal.

Figures

Figures reproduced from arXiv: 2605.22500 by Antoni Szczurek, Longjie Chen, Wolfgang Sch\"afer.

Figure 1
Figure 1. Figure 1: FIG. 1. Some of the 40 Feynman diagrams for the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Invariant-mass (left) and rapidity (right) distributions of [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Invariant-mass distribution of the diphoton system produced in [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
read the original abstract

We discuss the role of fully heavy tetraquarks in ultraperipheral collisions $AA\to AA\, J/\psi J/\psi$ and $AA \to AA\, \gamma \gamma$. Two-photon couplings to scalar and tensor tetraquarks are considered. We use relatively recent results of four-body calculation of fully heavy tetraquark wave function within the extended relativized quark model. The corresponding radiative decay widths for different tetraquark states are evaluated using NRQCD factorisation, with LDMEs extracted from the four-body wave functions at the origin. The results are collected in tables. The cross sections for production of pairs of $J/\psi$ mesons and diphotons in UPC of $^{208}Pb + {^{208}Pb}$ collisions are presented. While the couplings for $T_{4c}\left(0^{++}, 2^{++}\right) \to \gamma \gamma$ are calculated based on the model wave functions, simplified couplings are used for $T_{4c}\left(0^{++}, 2^{++}\right) \to J/\psi J/\psi$. When calculating the energy dependence of the resonant $\gamma \gamma \to J/\psi J/\psi$ and $\gamma \gamma \to \gamma \gamma$ cross section, we employ the total decay widths measured at $\Gamma_{\rm{tot}}=0.446\,\rm{GeV}$ for $X(6600)$ while $\Gamma_{\rm{tot}}=0.135\,\rm{GeV}$ for $X(6900)$ in latest CMS data. The resonant terms are compared with continuum contributions for both considered channels. While for the $J/\psi J/\psi$ channel the resonant contributions are larger than continuum ones, for the $\gamma \gamma$ channels the situation is reversed. The latter result is in clear disagreement with the result obtained from the n\"aive use of vector dominance picture.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 1 minor

Summary. The manuscript computes two-photon decay widths of fully charmed tetraquarks T_{4c}(0^{++},2^{++}) via NRQCD factorization, extracting LDMEs from four-body wave functions at the origin in the extended relativized quark model. It then evaluates resonant cross sections for γγ → J/ψ J/ψ and γγ → γγ in ultraperipheral ^{208}Pb+^{208}Pb collisions at the LHC, using CMS-measured total widths (0.446 GeV for X(6600), 0.135 GeV for X(6900)), and compares them to continuum contributions. The central claim is that resonant terms exceed continuum for the J/ψ J/ψ channel while continuum dominates for γγ, in disagreement with naive vector dominance.

Significance. If the results hold, the work supplies concrete, falsifiable predictions for tetraquark signals in UPCs, demonstrating how model wave functions and experimental total widths can be combined to distinguish resonant from continuum processes in heavy-ion collisions. The explicit contrast between channels and the use of recent CMS data add phenomenological value for LHC analyses.

major comments (2)
  1. Abstract: simplified couplings are adopted for T_{4c}(0^{++},2^{++}) → J/ψ J/ψ while model wave functions determine the γγ couplings. Because the resonant cross section is proportional to the product of the two partial widths (normalized by the measured Γ_tot), the claim that resonant exceeds continuum in the J/ψ J/ψ channel but not in γγ rests on the accuracy of this simplification rather than a uniform calculation.
  2. LDME extraction (wave-function section): the radiative widths and cross sections are obtained from a single relativized quark-model wave function without reported variations over model parameters or propagation of uncertainties; this directly affects the numerical values used in the resonant-versus-continuum comparison.
minor comments (1)
  1. The experimental labels X(6600) and X(6900) should be explicitly linked to the theoretical T_{4c}(0^{++},2^{++}) states for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of the significance of our work and for the constructive major comments. We address each point below and indicate the revisions planned for the next version of the manuscript.

read point-by-point responses

  1. Referee: Abstract: simplified couplings are adopted for T_{4c}(0^{++},2^{++}) → J/ψ J/ψ while model wave functions determine the γγ couplings. Because the resonant cross section is proportional to the product of the two partial widths (normalized by the measured Γ_tot), the claim that resonant exceeds continuum in the J/ψ J/ψ channel but not in γγ rests on the accuracy of this simplification rather than a uniform calculation.

    Authors: We acknowledge that the J/ψ J/ψ couplings rely on a simplified ansatz while the γγ couplings are computed directly from the four-body wave functions. This choice follows standard practice in the literature when full overlap integrals for the J/ψ J/ψ channel are not available within the same framework. The qualitative contrast between the two channels is driven primarily by the much larger measured total width of X(6600) compared with X(6900) and by the different phase-space factors; the simplification affects the absolute normalization but does not reverse the relative ordering. In the revised manuscript we will expand the abstract and add a dedicated paragraph in Section 3 explaining the approximation, its expected accuracy, and a brief sensitivity estimate. revision: partial

  2. Referee: LDME extraction (wave-function section): the radiative widths and cross sections are obtained from a single relativized quark-model wave function without reported variations over model parameters or propagation of uncertainties; this directly affects the numerical values used in the resonant-versus-continuum comparison.

    Authors: The LDMEs are taken at face value from the published four-body wave functions of the extended relativized quark model. A systematic variation of all model parameters would require regenerating the entire set of wave functions, which lies outside the scope of the present phenomenological study. In the revised version we will add a short discussion citing the parameter ranges explored in the original wave-function paper and will quote a conservative uncertainty band (approximately 20–30 %) on the two-photon widths; this band will be propagated into the resonant cross-section comparison to illustrate the robustness of the channel-dependent conclusion. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper computes two-photon couplings from four-body wave functions of the extended relativized quark model via NRQCD LDMEs extracted at the origin; this is a direct model evaluation, not a fit to the target cross sections or a self-definition. Simplified couplings are explicitly adopted for the J/ψ J/ψ channel and total widths are taken from external CMS measurements. The resonant-versus-continuum comparison follows from these independent inputs without any reduction of the claimed predictions to the inputs by construction. No self-citation load-bearing steps, uniqueness theorems, or ansatz smuggling are invoked for the central results. The derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The calculation rests on the prior four-body wave functions (treated as input), NRQCD factorization, and experimental total widths; free parameters are inherited from the quark model rather than refitted here.

free parameters (2)
  • relativized quark model parameters
    Quark masses, string tension, and smearing parameters in the extended relativized quark model that determine the tetraquark wave functions.
  • LDME extraction scale
    Choice of origin value and normalization convention when converting wave-function amplitude to long-distance matrix element.
axioms (2)
  • domain assumption NRQCD factorization applies to tetraquark two-photon decays
    Invoked to relate LDMEs extracted from wave functions at the origin to the radiative decay widths.
  • domain assumption The candidate states X(6600) and X(6900) correspond to the calculated T_{4c}(0^{++},2^{++}) tetraquarks
    Used when assigning the measured total widths to the resonant contributions.
invented entities (1)
  • fully charmed tetraquark T_{4c} no independent evidence
    purpose: Bound state of four charm quarks invoked to explain possible exotic resonances
    The central object whose wave function and couplings are computed; no independent collider evidence is provided within the paper.

pith-pipeline@v0.9.0 · 5901 in / 1767 out tokens · 81647 ms · 2026-05-22T04:49:17.651193+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

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    Relation between the paper passage and the cited Recognition theorem.

    We use relatively recent results of four-body calculation of fully heavy tetraquark wave function within the extended relativized quark model. The corresponding radiative decay widths ... are evaluated using NRQCD factorisation, with LDMEs extracted from the four-body wave functions at the origin.

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Reference graph

Works this paper leans on

45 extracted references · 45 canonical work pages · 9 internal anchors

  1. [1]

    Only a spin-0 tetraquark is considered, and values of Γ(X(6900)→γγ)∼ 45÷67 keV, about two orders of magnitude larger than our results, are obtained from a fit to LbL data

    with theoretical predictions by exhausting the missing cross section with a tetraquark contribution. Only a spin-0 tetraquark is considered, and values of Γ(X(6900)→γγ)∼ 45÷67 keV, about two orders of magnitude larger than our results, are obtained from a fit to LbL data. These authors also quoteγγbranching fractions obtained from a VDM ansatz, Br(X(6900)...

    work page 2015

  2. [2]

    Observation of structure in theJ/ψ-pair mass spectrum,

    Roel Aaijet al.(LHCb), “Observation of structure in theJ/ψ-pair mass spectrum,” Sci. Bull. 65, 1983–1993 (2020), arXiv:2006.16957 [hep-ex]

    work page arXiv 1983

  3. [3]

    Observation of an Excess of Dicharmonium Events in the Four-Muon Final State with the ATLAS Detector,

    Georges Aadet al.(ATLAS), “Observation of an Excess of Dicharmonium Events in the Four-Muon Final State with the ATLAS Detector,” Phys. Rev. Lett.131, 151902 (2023), arXiv:2304.08962 [hep-ex]

    work page arXiv 2023

  4. [4]

    Observation of structures in theJ/ψ+ψ(2S) mass spectrum with the ATLAS detector,

    Georges Aadet al.(ATLAS), “Observation of structures in theJ/ψ+ψ(2S) mass spectrum with the ATLAS detector,” (2025), arXiv:2509.13101 [hep-ex]

    work page arXiv 2025

  5. [5]

    New Structures in the J/ψJ/ψMass Spectrum in Proton- Proton Collisions at s=13 TeV,

    Aram Hayrapetyanet al.(CMS), “New Structures in the J/ψJ/ψMass Spectrum in Proton- Proton Collisions at s=13 TeV,” Phys. Rev. Lett.132, 111901 (2024), arXiv:2306.07164 [hep- ex]

    work page arXiv 2024

  6. [6]

    Determination of the spin and parity of all-charm tetraquarks,

    Aram Hayrapetyanet al.(CMS), “Determination of the spin and parity of all-charm tetraquarks,” Nature648, 58–63 (2025), arXiv:2506.07944 [hep-ex]. 16

    work page arXiv 2025

  7. [7]

    Observation of a family of all-charm tetraquarks,

    Aram Hayrapetyanet al.(CMS), “Observation of a family of all-charm tetraquarks,” (2026), arXiv:2602.02252 [hep-ex]

    work page arXiv 2026

  8. [8]

    Double J/psi-meson Production at LHC and 4c-tetraquark state

    A. V. Berezhnoy, A. K. Likhoded, A. V. Luchinsky, and A. A. Novoselov, “Double J/psi-meson Production at LHC and 4c-tetraquark state,” Phys. Rev. D84, 094023 (2011), arXiv:1101.5881 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  9. [9]

    On the mechanism ofT 4c(6900) tetraquark production,

    Rafa l Maciu la, Wolfgang Sch¨ afer, and Antoni Szczurek, “On the mechanism ofT 4c(6900) tetraquark production,” Phys. Lett. B812, 136010 (2021), arXiv:2009.02100 [hep-ph]

    work page arXiv 2021

  10. [10]

    Fragmentation production of fully-charmed tetraquarks at the LHC,

    Feng Feng, Yingsheng Huang, Yu Jia, Wen-Long Sang, Xiaonu Xiong, and Jia-Yue Zhang, “Fragmentation production of fully-charmed tetraquarks at the LHC,” Phys. Rev. D106, 114029 (2022), arXiv:2009.08450 [hep-ph]

    work page arXiv 2022

  11. [11]

    Fully-heavy tetraquark spectra and production at hadron colliders,

    Ruilin Zhu, “Fully-heavy tetraquark spectra and production at hadron colliders,” Nucl. Phys. B966, 115393 (2021), arXiv:2010.09082 [hep-ph]

    work page arXiv 2021

  12. [12]

    Inclusive production of fully charmed tetraquarks at the LHC,

    Feng Feng, Yingsheng Huang, Yu Jia, Wen-Long Sang, De-Shan Yang, and Jia-Yue Zhang, “Inclusive production of fully charmed tetraquarks at the LHC,” Phys. Rev. D108, L051501 (2023), arXiv:2304.11142 [hep-ph]

    work page arXiv 2023

  13. [13]

    Fully charmed tetraquarks from LHC to FCC: natural stability from fragmentation,

    Francesco Giovanni Celiberto, Gabriele Gatto, and Alessandro Papa, “Fully charmed tetraquarks from LHC to FCC: natural stability from fragmentation,” Eur. Phys. J. C84, 1071 (2024), arXiv:2405.14773 [hep-ph]

    work page arXiv 2024

  14. [14]

    Fully charmed tetraquark production at the LHC experiments,

    Ilia Belov, Alessandro Giachino, and Elena Santopinto, “Fully charmed tetraquark production at the LHC experiments,” JHEP01, 093 (2025), arXiv:2409.12070 [hep-ph]

    work page arXiv 2025

  15. [15]

    Fragmentation of fully heavy tetraquarks: The TQ4Q1.1 func- tions as a case study,

    Francesco Giovanni Celiberto, “Fragmentation of fully heavy tetraquarks: The TQ4Q1.1 func- tions as a case study,” Phys. Rev. D112, 074041 (2025), arXiv:2507.09744 [hep-ph]

    work page arXiv 2025

  16. [16]

    Fully charm tetraquark production at hadronic collisions with gluon radiation effects

    Yefan Wang and Ruilin Zhu, “Fully charm tetraquark production at hadronic collisions with gluon radiation effects,” (2025), arXiv:2510.02085 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  17. [17]

    Fully charmed tetraquark production in forward rapidity pp collisions at LHC and FCC energies,

    Francesco G. Celiberto, Andr´ e V. Giannini, Victor P. Gon¸ calves, and Yuri N. Lima, “Fully charmed tetraquark production in forward rapidity pp collisions at LHC and FCC energies,” Phys. Rev. D113, 054014 (2026), arXiv:2511.18984 [hep-ph]

    work page arXiv 2026

  18. [18]

    The $\gamma \gamma \to J/\psi J/\psi$ reaction and the $J/\psi J/\psi$ pair production in exclusive ultraperipheral ultrarelativistic heavy ion collisions

    Sergey Baranov, Anna Cisek, Mariola K lusek-Gawenda, Wolfgang Sch¨ afer, and Antoni Szczurek, “Theγγ→J/ψJ/ψreaction and theJ/ψJ/ψpair production in exclusive ultrape- ripheral ultrarelativistic heavy ion collisions,” Eur. Phys. J. C73, 2335 (2013), arXiv:1208.5917 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  19. [19]

    Charmonium pair production in ultraperiph- eral collision,

    Hao Yang, Zi-Qiang Chen, and Bingwei Long, “Charmonium pair production in ultraperiph- eral collision,” Eur. Phys. J. C85, 802 (2025), arXiv:2504.14850 [hep-ph]

    work page arXiv 2025

  20. [20]

    Fully - heavy tetraquark production byγγinter- actions in hadronic collisions at the LHC,

    Victor P. Gon¸ calves and Bruno D. Moreira, “Fully - heavy tetraquark production byγγinter- actions in hadronic collisions at the LHC,” Phys. Lett. B816, 136249 (2021), arXiv:2101.03798 [hep-ph]

    work page arXiv 2021

  21. [21]

    Hunting for tetraquarks in ultraperipheral heavy ion collisions,

    Angelo Esposito, Claudio Andrea Manzari, Alessandro Pilloni, and Antonio Davide Polosa, “Hunting for tetraquarks in ultraperipheral heavy ion collisions,” Phys. Rev. D104, 114029 (2021), arXiv:2109.10359 [hep-ph]

    work page arXiv 2021

  22. [22]

    Two-photon decay of X(6900) from light-by-light scattering at the LHC,

    Volodymyr Biloshytskyi, Vladimir Pascalutsa, Lucian Harland-Lang, Bogdan Malaescu, Kristof Schmieden, and Matthias Schott, “Two-photon decay of X(6900) from light-by-light scattering at the LHC,” Phys. Rev. D106, L111902 (2022), arXiv:2207.13623 [hep-ph]

    work page arXiv 2022

  23. [23]

    Exclusive photon-fusion production of even-spin reso- nances and exotic QED atoms in high-energy hadron collisions,

    David d’Enterria and Karen Kang, “Exclusive photon-fusion production of even-spin reso- nances and exotic QED atoms in high-energy hadron collisions,” Phys. Rev. D112, 116022 (2025), arXiv:2503.10952 [hep-ph]. 17

    work page arXiv 2025

  24. [24]

    Electromagnetic and hadronic decay of fully heavy tetraquarks,

    Wen-Long Sang, Tao Wang, Yu-Dong Zhang, and Feng Feng, “Electromagnetic and hadronic decay of fully heavy tetraquarks,” Phys. Rev. D109, 056016 (2024), arXiv:2307.16150 [hep- ph]

    work page arXiv 2024

  25. [25]

    All-charm tetraquark and its contribution to two-photon processes,

    Panagiotis Kalamidas and Marc Vanderhaeghen, “All-charm tetraquark and its contribution to two-photon processes,” Phys. Rev. D111, 094033 (2025), arXiv:2501.06034 [hep-ph]

    work page arXiv 2025

  26. [26]

    A study ofcc¯c¯c tetraquark decays in 4 muons and inD (∗) ¯D(∗) at LHC,

    C. Becchi, J. Ferretti, A. Giachino, L. Maiani, and E. Santopinto, “A study ofcc¯c¯c tetraquark decays in 4 muons and inD (∗) ¯D(∗) at LHC,” Phys. Lett. B811, 135952 (2020), arXiv:2006.14388 [hep-ph]

    work page arXiv 2020

  27. [27]

    Hadronic decay of exotic mesons consisting of four charm quarks,

    Hong-Fei Zhang, Xue-Mei Mo, and Yu-Peng Yan, “Hadronic decay of exotic mesons consisting of four charm quarks,” Phys. Rev. D110, 096021 (2024), arXiv:2312.10850 [hep-ph]

    work page arXiv 2024

  28. [28]

    Exclusive Hadron Production in Two Photon Reactions,

    M. Poppe, “Exclusive Hadron Production in Two Photon Reactions,” Int. J. Mod. Phys. A 1, 545–668 (1986)

    work page 1986

  29. [29]

    The Two photon particle production mechanism. Physical problems. Applications. Equivalent photon approximation,

    V. M. Budnev, I. F. Ginzburg, G. V. Meledin, and V. G. Serbo, “The Two photon particle production mechanism. Physical problems. Applications. Equivalent photon approximation,” Phys. Rept.15, 181–281 (1975)

    work page 1975

  30. [30]

    Rigorous QCD Analysis of Inclusive Annihilation and Production of Heavy Quarkonium

    Geoffrey T. Bodwin, Eric Braaten, and G. Peter Lepage, “Rigorous QCD analysis of inclu- sive annihilation and production of heavy quarkonium,” Phys. Rev. D51, 1125–1171 (1995), [Erratum: Phys.Rev.D 55, 5853 (1997)], arXiv:hep-ph/9407339

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  31. [31]

    FeynCalc 10: Do multi- loop integrals dream of computer codes?

    Vladyslav Shtabovenko, Rolf Mertig, and Frederik Orellana, “FeynCalc 10: Do multi- loop integrals dream of computer codes?” Comput. Phys. Commun.306, 109357 (2025), arXiv:2312.14089 [hep-ph]

    work page arXiv 2025

  32. [32]

    Masses of fully heavy tetraquarksQQ¯Q ¯Q in an extended relativized quark model,

    Qi-Fang L¨ u, Dian-Yong Chen, and Yu-Bing Dong, “Masses of fully heavy tetraquarksQQ¯Q ¯Q in an extended relativized quark model,” Eur. Phys. J. C80, 871 (2020), arXiv:2006.14445 [hep-ph]

    work page arXiv 2020

  33. [33]

    Fully heavy tetraquark states and their evidences in LHC observations,

    Ming-Sheng liu, Feng-Xiao Liu, Xian-Hui Zhong, and Qiang Zhao, “Fully heavy tetraquark states and their evidences in LHC observations,” Phys. Rev. D109, 076017 (2024), arXiv:2006.11952 [hep-ph]

    work page arXiv 2024

  34. [34]

    Gaussian expansion method for few-body systems,

    E. Hiyama, Y. Kino, and M. Kamimura, “Gaussian expansion method for few-body systems,” Prog. Part. Nucl. Phys.51, 223–307 (2003)

    work page 2003

  35. [35]

    RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses

    K. G. Chetyrkin, Johann H. Kuhn, and M. Steinhauser, “RunDec: A Mathematica package for running and decoupling of the strong coupling and quark masses,” Comput. Phys. Commun. 133, 43–65 (2000), arXiv:hep-ph/0004189

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  36. [36]

    Four quark states in the heavy quark system,

    A. M. Badalian, B. L. Ioffe, and Andrei V. Smilga, “Four quark states in the heavy quark system,” Nucl. Phys. B281, 85 (1987)

    work page 1987

  37. [37]

    Next-to-leading order QCD corrections to elec- tromagnetic production and decay of fully charm tetraquarks,

    Xinran Liu, Yefan Wang, and Ruilin Zhu, “Next-to-leading order QCD corrections to elec- tromagnetic production and decay of fully charm tetraquarks,” (2025), arXiv:2512.22070 [hep-ph]

    work page arXiv 2025

  38. [38]

    Measurement of light-by-light scattering and search for axion- like particles with 2.2 nb−1 of Pb+Pb data with the ATLAS detector,

    Georges Aadet al.(ATLAS), “Measurement of light-by-light scattering and search for axion- like particles with 2.2 nb−1 of Pb+Pb data with the ATLAS detector,” JHEP03, 243 (2021), [Erratum: JHEP 11, 050 (2021)], arXiv:2008.05355 [hep-ex]

    work page arXiv 2021

  39. [39]

    A non-relativistic model for the $[cc][\bar{c}\bar{c}]$ tetraquark

    V. R. Debastiani and F. S. Navarra, “A non-relativistic model for the [cc][¯c¯c] tetraquark,” Chin. Phys. C43, 013105 (2019), arXiv:1706.07553 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  40. [40]

    Coherent gamma-gamma and gamma-A interactions in very peripheral collisions at relativistic ion colliders

    Gerhard Baur, Kai Hencken, Dirk Trautmann, Serguei Sadovsky, and Yuri Kharlov, “Coher- ent gamma gamma and gamma-A interactions in very peripheral collisions at relativistic ion colliders,” Phys. Rept.364, 359–450 (2002), arXiv:hep-ph/0112211. 18

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  41. [41]

    Photon induced processes: from ultraperipheral to semicentral heavy ion collisions,

    Wolfgang Sch¨ afer, “Photon induced processes: from ultraperipheral to semicentral heavy ion collisions,” Eur. Phys. J. A56, 231 (2020)

    work page 2020

  42. [42]

    Investigating the internal structure ofX(6900) in the 2J/ψdecay channel,

    Duo-Duo Lu and Shao-Zhou Jiang, “Investigating the internal structure ofX(6900) in the 2J/ψdecay channel,” (2025), arXiv:2512.18569 [hep-ph]

    work page arXiv 2025

  43. [43]

    Evidence for light-by-light scattering in heavy-ion collisions with the ATLAS detector at the LHC

    Morad Aaboudet al.(ATLAS), “Evidence for light-by-light scattering in heavy-ion collisions with the ATLAS detector at the LHC,” Nature Phys.13, 852–858 (2017), arXiv:1702.01625 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  44. [44]

    Light- by-light scattering at next-to-leading order in QCD and QED,

    Ajjath A H, Ekta Chaubey, Mathijs Fraaije, Valentin Hirschi, and Hua-Sheng Shao, “Light- by-light scattering at next-to-leading order in QCD and QED,” Phys. Lett. B851, 138555 (2024), arXiv:2312.16956 [hep-ph]

    work page arXiv 2024

  45. [45]

    QCD and QED Corrections to Light-by-Light Scattering

    Z. Bern, A. De Freitas, Lance J. Dixon, A. Ghinculov, and H. L. Wong, “QCD and QED corrections to light by light scattering,” JHEP11, 031 (2001), arXiv:hep-ph/0109079. 19

    work page internal anchor Pith review Pith/arXiv arXiv 2001