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Electromagnetic Form Factors and Structure of the Tbb Tetraquark from Lattice QCD

Ivan Vujmilovic1,2,*, Sara Collins3,†, Luka Leskovec1,2,‡, and Sasa Prelovsek1,2,§

  • *Contact author: ivan.vujmilovic@ijs.si
  • Contact author: sara.collins@ur.de
  • Contact author: luka.leskovec@ijs.si
  • §Contact author: sasa.prelovsek@ijs.si

Phys. Rev. Lett. 136, 161901 – Published 23 April, 2026

DOI: https://doi.org/10.1103/jnsy-5nhj

Abstract

We present the first lattice QCD determination of the electromagnetic form factors of the exotic tetraquark Tbb(bbu¯d¯) with quantum numbers I(JP)=0(1+). The extracted form factors encode information about its internal structure, including the charge distribution and the magnetic dipole moments, determined separately for the light and heavy quarks. Our results provide evidence in favor of it being a bound state consisting of a compact heavy diquark [bb] in a color-antitriplet with spin one and a light antidiquark [u¯d¯] in a color-triplet with spin zero. The charge radius of Tbb is found to be significantly smaller than the combined charge radii of B and B* mesons. These two comprise the lowest-lying threshold BB* in the channel that we are considering, and their electric charge form factors are also determined. The computations were performed on a single ensemble, generated by the Coordinated Lattice Simulations effort, with Nf=2+1 dynamical quarks and a lattice spacing of approximately a0.064fm at the pion mass mπ290MeV.

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References (105)

  1. M. Gell-Mann, A schematic model of baryons and mesons, Phys. Lett. 8, 214 (1964).
  2. G. Zweig, An SU(3) Model for Strong Interaction Symmetry and Its Breaking. Version 2 (Hadronic Press; Nonantum, 1964) pp. 22–101.
  3. R. L. Jaffe, Exotica, Phys. Rep. 409, 1 (2005).
  4. R. F. Lebed, R. E. Mitchell, and E. S. Swanson, Heavy-quark QCD exotica, Prog. Part. Nucl. Phys. 93, 143 (2017).
  5. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  6. S. K. Choi et al. (Belle Collaboration), Observation of a narrow charmonium-like state in exclusive B±K±π+πJ/ψ decays, Phys. Rev. Lett. 91, 262001 (2003).
  7. S. K. Choi et al. (Belle Collaboration), Observation of a resonance-like structure in the π±ψ mass distribution in exclusive BKπ±ψ decays, Phys. Rev. Lett. 100, 142001 (2008).
  8. M. Ablikim et al. (BESIII Collaboration), Observation of a charged charmoniumlike structure in e+eπ+πJ/ψ at s=4.26GeV, Phys. Rev. Lett. 110, 252001 (2013).
  9. B. Aubert et al. (BABAR Collaboration), Observation of a broad structure in the π+πJ/ψ mass spectrum around 4.26GeV/c2, Phys. Rev. Lett. 95, 142001 (2005).
  10. R. Aaij et al. (LHCb Collaboration), Observation of J/ψp resonances consistent with pentaquark States in Λb0J/ψKp decays, Phys. Rev. Lett. 115, 072001 (2015).
  11. R. Aaij et al. (LHCb Collaboration), Observation of a narrow pentaquark state, Pc(4312)+, and of two-peak structure of the Pc(4450)+, Phys. Rev. Lett. 122, 222001 (2019).
  12. T. Aaltonen et al. (CDF Collaboration), Evidence for a narrow near-threshold structure in the J/ψϕ mass spectrum in B+J/ψϕK+ decays, Phys. Rev. Lett. 102, 242002 (2009).
  13. R. Aaij et al. (LHCb Collaboration), Observation of J/ψϕ structures consistent with exotic states from amplitude analysis of B+J/ψϕK+ decays, Phys. Rev. Lett. 118, 022003 (2017).
  14. R. Aaij et al. (LHCb Collaboration), Observation of an exotic narrow doubly charmed tetraquark, Nat. Phys. 18, 751 (2022).
  15. P. Bicudo, Tetraquarks and pentaquarks in lattice QCD with light and heavy quarks, Phys. Rep. 1039, 1 (2023).
  16. A. Francis, Lattice perspectives on doubly heavy tetraquarks, Prog. Part. Nucl. Phys. 140, 104143 (2025).
  17. N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev, C.-P. Shen, C. E. Thomas, A. Vairo, and C.-Z. Yuan, The XYZ states: Experimental and theoretical status and perspectives, Phys. Rep. 873, 1 (2020).
  18. J. Bulava et al., Hadron spectroscopy with Lattice QCD, in Snowmass 2021 (2022).
  19. E. J. Eichten and C. Quigg, Heavy-quark symmetry implies stable heavy tetraquark mesons QiQjq¯kq¯l, Phys. Rev. Lett. 119, 202002 (2017).
  20. P. Bicudo and M. Wagner (European Twisted Mass Collaboration), Lattice QCD signal for a bottom-bottom tetraquark, Phys. Rev. D 87, 114511 (2013).
  21. M. Karliner and J. L. Rosner, Discovery of the doubly charmed Ξcc baryon implies a stable bbu¯d¯ tetraquark, Phys. Rev. Lett. 119, 202001 (2017).
  22. J. Vijande, A. Valcarce, and N. Barnea, Exotic meson-meson molecules and compact four-quark states, Phys. Rev. D 79, 074010 (2009).
  23. N. Brambilla, A. Mohapatra, T. Scirpa, and A. Vairo, Nature of χc1(3872) and Tcc+(3875), Phys. Rev. Lett. 135, 131902 (2025).
  24. J. Hoffer, G. Eichmann, and C. S. Fischer, Structure of open-flavor four-quark states in the charm and bottom region, Phys. Rev. D 111, 054028 (2025).
  25. D. Janc and M. Rosina, The Tcc=DD* molecular state, Few-Body Syst. 35, 175 (2004).
  26. L. Maiani, A. Pilloni, A. D. Polosa, and V. Riquer, Doubly heavy tetraquarks in the Born-Oppenheimer approximation, Phys. Lett. B 836, 137624 (2023).
  27. R. J. Hudspith and D. Mohler, Exotic tetraquark states with two b¯ quarks and JP=0+ and 1+ Bs states in a nonperturbatively tuned lattice NRQCD setup, Phys. Rev. D 107, 114510 (2023).
  28. L. Leskovec, S. Meinel, M. Pflaumer, and M. Wagner, Lattice qcd investigation of a doubly-bottom b¯b¯ud tetraquark with quantum numbers i(JP)=0(1+), Phys. Rev. D 100, 014503 (2019).
  29. B. Colquhoun, A. Francis, R. J. Hudspith, R. Lewis, K. Maltman, and W. G. Parrott, Improved analysis of strong-interaction-stable doubly bottom tetraquarks on the lattice, Phys. Rev. D 110, 094503 (2024).
  30. C. Alexandrou, J. Finkenrath, T. Leontiou, S. Meinel, M. Pflaumer, and M. Wagner, b¯b¯ud and b¯b¯us tetraquarks from lattice QCD using symmetric correlation matrices with both local and scattering interpolating operators, Phys. Rev. D 110, 054510 (2024).
  31. T. Aoki, S. Aoki, and T. Inoue, Lattice study on a tetraquark state Tbb in the HAL QCD method, Phys. Rev. D 108, 054502 (2023).
  32. P. Junnarkar, N. Mathur, and M. Padmanath, Study of doubly heavy tetraquarks in lattice QCD, Phys. Rev. D 99, 034507 (2019).
  33. S. Prelovsek, E. Ortiz-Pacheco, S. Collins, L. Leskovec, M. Padmanath, and I. Vujmilovic, Doubly heavy tetraquarks from lattice QCD: Incorporating diquark-antidiquark operators and the left-hand cut, Phys. Rev. D 112, 014507 (2025).
  34. B. S. Tripathy, N. Mathur, and M. Padmanath, bbud and bsud tetraquarks from lattice QCD using two-meson and diquark-antidiquark variational basis, Phys. Rev. D 111, 114504 (2025).
  35. A. Ali, Q. Qin, and W. Wang, Discovery potential of stable and near-threshold doubly heavy tetraquarks at the LHC, Phys. Lett. B 785, 605 (2018).
  36. Ivan Polyakov, LHCb mini-workshop: Tbc (2023).
  37. C. Alexandrou, J. Finkenrath, T. Leontiou, S. Meinel, M. Pflaumer, and M. Wagner, Shallow bound states and hints for broad resonances with quark content bcud in BD and B*D scattering from lattice QCD, Phys. Rev. Lett. 132, 151902 (2024).
  38. A. Radhakrishnan, M. Padmanath, and N. Mathur, Study of the isoscalar scalar bcud tetraquark Tbc with lattice QCD, Phys. Rev. D 110, 034506 (2024).
  39. M. Padmanath, A. Radhakrishnan, and N. Mathur, Bound isoscalar axial-vector bcud tetraquark Tbc from lattice QCD using two-meson and diquark-antidiquark variational basis, Phys. Rev. Lett. 132, 201902 (2024).
  40. T. Gershon and A. Poluektov, Displaced Bc mesons as an inclusive signature of weakly decaying double beauty hadrons, J. High Energy Phys. 01 (2019) 019.
  41. V. Tadevosyan et al. (Jefferson Lab F(pi) Collaboration), Determination of the pion charge form-factor for Q2=0.601.60GeV2, Phys. Rev. C 75, 055205 (2007).
  42. G. M. Huber et al. (Jefferson Lab Collaboration), Charged pion form-factor between Q2=0.60 and 2.45GeV2. II. Determination of, and results for, the pion form-factor, Phys. Rev. C 78, 045203 (2008).
  43. X. Gao, N. Karthik, S. Mukherjee, P. Petreczky, S. Syritsyn, and Y. Zhao, Pion form factor and charge radius from lattice QCD at the physical point, Phys. Rev. D 104, 114515 (2021).
  44. C. Alexandrou, S. Bacchio, I. Cloët, M. Constantinou, J. Delmar, K. Hadjiyiannakou, G. Koutsou, C. Lauer, and A. Vaquero (ETM Collaboration), Scalar, vector, and tensor form factors for the pion and kaon from lattice QCD, Phys. Rev. D 105, 054502 (2022).
  45. F. V. Ignatov et al. (CMD-3 Collaboration), Measurement of the pion form factor with CMD-3 detector and its implication to the hadronic contribution to muon (g-2), Phys. Rev. Lett. 132, 231903 (2024).
  46. F. G. Ortega-Gama, J. J. Dudek, and R. G. Edwards (for the Hadron Spectrum Collaboration), Timelike meson form factors beyond the elastic region from lattice QCD, Phys. Rev. D 110, 094505 (2024).
  47. C. Alexandrou, S. Bacchio, M. Constantinou, J. Finkenrath, K. Hadjiyiannakou, K. Jansen, G. Koutsou, and A. V. Aviles-Casco, Proton and neutron electromagnetic form factors from lattice QCD, Phys. Rev. D 100, 014509 (2019).
  48. D. Djukanovic, G. von Hippel, H. B. Meyer, K. Ottnad, M. Salg, and H. Wittig, Electromagnetic form factors of the nucleon from Nf=2+1 lattice QCD, Phys. Rev. D 109, 094510 (2024).
  49. S. Park, R. Gupta, B. Yoon, S. Mondal, T. Bhattacharya, Y.-C. Jang, B. Joó, and F. Winter (Nucleon Matrix Elements (NME) Collaboration), Precision nucleon charges and form factors using (2+1)-flavor lattice QCD, Phys. Rev. D 105, 054505 (2022).
  50. C. Chen, C. S. Fischer, C. D. Roberts, and J. Segovia, Nucleon axial-vector and pseudoscalar form factors and PCAC relations, Phys. Rev. D 105, 094022 (2022).
  51. M. K. Jones et al. (Jefferson Lab Hall A Collaboration), GEp/GMp ratio by polarization transfer in epep, Phys. Rev. Lett. 84, 1398 (2000).
  52. S. N. Santiesteban et al. (Jefferson Lab Hall A Collaboration), Novel measurement of the neutron magnetic form factor from A=3 mirror nuclei, Phys. Rev. Lett. 132, 162501 (2024).
  53. M. Carmignotto et al., Separated kaon electroproduction cross section and the kaon form factor from 6 GeV JLab data, Phys. Rev. C 97, 025204 (2018).
  54. C. Alexandrou, G. Koutsou, H. Neff, J. W. Negele, W. Schroers, and A. Tsapalis, Nucleon to delta electromagnetic transition form factors in lattice QCD, Phys. Rev. D 77, 085012 (2008).
  55. D. C. Hackett, D. A. Pefkou, and P. E. Shanahan, Gravitational form factors of the proton from lattice QCD, Phys. Rev. Lett. 132, 251904 (2024).
  56. J. Delaney, C. E. Thomas, and S. M. Ryan (Hadron Spectrum Collaboration), Radiative transitions in charmonium from lattice QCD, J. High Energy Phys. 05 (2024) 230.
  57. J. J. Dudek, R. G. Edwards, and D. G. Richards, Radiative transitions in charmonium from lattice QCD, Phys. Rev. D 73, 074507 (2006).
  58. R. Abbott, D. C. Hackett, D. A. Pefkou, F. Romero-López, and P. E. Shanahan, Lattice evidence that scalar glueballs are small, arXiv:2508.21821.
  59. G. Ramalho, Electromagnetic form factors of the Ω baryon in the spacelike and timelike regions, Phys. Rev. D 103, 074018 (2021).
  60. A. J. Buchmann, E. Hernández, and A. Faessler, Electromagnetic properties of the Δ(1232), Phys. Rev. C 55, 448 (1997).
  61. L. Leskovec, S. Meinel, M. Petschlies, J. Negele, S. Paul, and A. Pochinsky, bρν¯ resonance form factors from bππν¯ in lattice QCD, Phys. Rev. Lett. 134, 161901 (2025).
  62. Y. Tan, X. Liu, X. Chen, Y. Wu, H. Huang, and J. Ping, Equivalence among color-singlet, color-octet, and diquark structures in a chiral quark model, Phys. Rev. D 109, 076026 (2024).
  63. M. Padmanath, C. B. Lang, and S. Prelovsek, x(3872) and y(4140) using diquark-antidiquark operators with lattice QCD, Phys. Rev. D 92, 034501 (2015).
  64. R. A. Briceño and M. T. Hansen, Relativistic, model-independent, multichannel 22 transition amplitudes in a finite volume, Phys. Rev. D 94, 013008 (2016).
  65. A. Baroni, R. A. Briceño, M. T. Hansen, and F. G. Ortega-Gama, Form factors of two-hadron states from a covariant finite-volume formalism, Phys. Rev. D 100, 034511 (2019).
  66. L. Durand, P. C. DeCelles, and R. B. Marr, Lorentz invariance and the kinematic structure of vertex functions, Phys. Rev. 126, 1882 (1962).
  67. A. Khodjamirian, Hadron Form Factors (CRC Press, Boca Raton, 2020).
  68. R. G. Arnold, C. E. Carlson, and F. Gross, Polarization transfer in elastic electron scattering from nucleons and deuterons, Phys. Rev. C 23, 363 (1981).
  69. F. Gross, Relativistic calculation of the deuteron electromagnetic form factor. II, Phys. Rev. 136, B140 (1964).
  70. H. Haberzettl, Model-independent form-factor constraints for electromagnetic spin-1 currents, Phys. Rev. D 100, 036008 (2019).
  71. C. Lorce, Electromagnetic properties for arbitrary spin particles. Part 1. Electromagnetic current and multipole decomposition, arXiv:0901.4199.
  72. G. S. Bali, S. Collins, P. Georg, D. Jenkins, P. Korcyl, A. Schäfer, E. E. Scholz, J. Simeth, W. Söldner, and S. Weishäupl (RQCD Collaboration), Scale setting and the light baryon spectrum in Nf=2+1 QCD with Wilson fermions, J. High Energy Phys. 05 (2023) 035.
  73. M. Bruno et al., Simulation of QCD with Nf=2+1 flavors of non-perturbatively improved Wilson fermions, J. High Energy Phys. 02 (2015) 043.
  74. P. Chen, Heavy quarks on anisotropic lattices: The charmonium spectrum, Phys. Rev. D 64, 034509 (2001).
  75. See Supplemental Material at http://link.aps.org/supplemental/10.1103/jnsy-5nhj for more details about the lattice setup and subsequent analysis of the spectrum and matrix elements. Refs. [76–80] are additionally cited in the Supplemental Material.
  76. J. J. Dudek, R. G. Edwards, M. J. Peardon, D. G. Richards, and C. E. Thomas, Toward the excited meson spectrum of dynamical QCD, Phys. Rev. D 82, 034508 (2010).
  77. V. Bernard, M. Lage, U.-G. Meissner, and A. Rusetsky, Resonance properties from the finite-volume energy spectrum, J. High Energy Phys. 08 (2008) 024.
  78. M. Albanese et al. (APE Collaboration), Glueball masses and string tension in lattice QCD, Phys. Lett. B 192, 163 (1987).
  79. C. Morningstar and M. Peardon, Analytic smearing of SU(3) link variables in lattice QCD, Phys. Rev. D 69, 054501 (2004).
  80. A. X. El-Khadra, A. S. Kronfeld, and P. B. Mackenzie, Massive fermions in lattice gauge theory, Phys. Rev. D 55, 3933 (1997).
  81. C. Alexandrou, M. Constantinou, K. Hadjiyiannakou et al., Strange nucleon electromagnetic form factors from lattice QCD, Phys. Rev. D 97, 094504 (2018).
  82. C. G. Boyd, B. Grinstein, and R. F. Lebed, Constraints on form-factors for exclusive semileptonic heavy to light meson decays, Phys. Rev. Lett. 74, 4603 (1995).
  83. C. G. Boyd and M. J. Savage, Analyticity, shapes of semileptonic form-factors, and anti-B> pi lepton anti-neutrino, Phys. Rev. D 56, 303 (1997).
  84. C. Bourrely, I. Caprini, and L. Lellouch, Model-independent description of B> pi l nu decays and a determination of V(ub), Phys. Rev. D 79, 013008 (2009); 82, 099902(E) (2010).
  85. K.-K. Zhang, W.-X. Zhang, and D. Jia, Systematics of doubly heavy strange and nonstrange tetraquarks, Phys. Rev. D 112, 054008 (2025).
  86. J.-B. Cheng, S.-Y. Li, Y.-R. Liu, Z.-G. Si, and T. Yao, Double-heavy tetraquark states with heavy diquark-antiquark symmetry, Chin. Phys. C 45, 043102 (2021).
  87. S. H. Lee and S. Yasui, Stable multiquark states with heavy quarks in a diquark model, Eur. Phys. J. C 64, 283 (2009).
  88. C.-W. Hwang, Charge radii of light and heavy mesons, Eur. Phys. J. C 23, 585 (2002).
  89. A. S. Miramontes, J. Papavassiliou, and J. M. Pawlowski, Electromagnetic properties of heavy-light mesons, Eur. Phys. J. C 85, 1390 (2025).
  90. D. Becirevic, E. Chang, and A. Le Yaouanc, On internal structure of the heavy-light mesons, Phys. Rev. D 80, 034504 (2009).
  91. A. M. Green, J. Koponen, P. Pennanen, and C. Michael (UKQCD Collaboration), Charge and matter radial distributions of heavy-light mesons calculated on a lattice, Phys. Rev. D 65, 014512 (2001).
  92. J. Koponen, A. M. Green, C. Michael, and P. Pennanen (UKQCD Collaboration), The radial distributions of a heavy light meson on a lattice, Nucl. Phys. B, Proc. Suppl. 119, 638 (2003).
  93. E. Santopinto and G. Galatà, Spectroscopy of tetraquark states, Phys. Rev. C 75, 045206 (2007).
  94. S.-Q. Luo, K. Chen, X. Liu, Y.-R. Liu, and S.-L. Zhu, Exotic tetraquark states with the qqQ¯Q¯ configuration, Eur. Phys. J. C 77, 709 (2017).
  95. G. Yang, J. Ping, and J. Segovia, Double-heavy tetraquarks, Phys. Rev. D 101, 014001 (2020).
  96. R. D. Amado, The deuteron D state revisited, Comments Nucl. Part. Phys. 10, 131 (1981).
  97. M. Bashkanov, D. P. Watts, and A. Pastore, Electromagnetic properties of the d*(2380) hexaquark, Phys. Rev. C 100, 012201 (2019).
  98. A. Francis, P. de Forcrand, R. Lewis, and K. Maltman, Diquark properties from full QCD lattice simulations, J. High Energy Phys. 05 (2022) 062.
  99. F. T. Winter, QDP-JIT/PTX: A QDP ++ Implementation for CUDA-Enabled GPUs, Proc. Sci. LATTICE2013 (2014) 042.
  100. R. G. Edwards and B. Joo (SciDAC, LHPC, and UKQCD Collaborations), The chroma software system for lattice QCD, Nucl. Phys. B, Proc. Suppl. 140, 832 (2005).
  101. M. A. Clark, R. Babich, K. Barros, R. C. Brower, and C. Rebbi (QUDA Collaboration), Solving Lattice QCD systems of equations using mixed precision solvers on GPUs, Comput. Phys. Commun. 181, 1517 (2010).
  102. https://www.hpc-rivr.si.
  103. https://eurohpc-ju.europa.eu.
  104. https://www.izum.si/en/home.
  105. Central values and the covariance matrices of form factors shown in this work can be found at http://www-f1.ijs.si/ sasa/available-lattice-data/form-factors-Tbb.txt.

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