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Relativistic description of asymmetric fully heavy tetraquarks in the diquark–antidiquark model

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Abstract

Masses of the ground, orbitally and radially excited states of the asymmetric fully heavy tetraquarks, composed of charm (\(\mathrm c\)) and bottom (\(\mathrm b\)) quarks and antiquarks are calculated in the relativistic diquark–antidiquark picture. The relativistic quark model based on the quasipotential approach and quantum chromodynamics is used to construct the quasipotentials of the quark–quark and diquark–antidiquark interactions. These quasipotentials consist of the short-range one-gluon exchange and long-distance linear confinement interactions. Relativistic effects are consistently taken into account. A tetraquark is considered as a bound state of a diquark and an antidiquark which are treated as a spatially extended colored objects and interact as a whole. It is shown that most of the investigated tetraquarks states (including all ground states) lie above the fall-apart strong decay thresholds into a meson pair. As a result they could be observed as wide resonances. Nevertheless, several orbitally excited states lie slightly above or even below these fall-apart thresholds, thus they could be narrow states.

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Data availibility statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is a theoretical study and no experimental data.] Code availability statementThis manuscript has no associated code/software. [Author’s comment: Not applicable.]

Code availability statement

This manuscript has no associated code/software. [Author’s comment: Not applicable.]

References

  1. M. Gell-Mann, A schematic model of baryons and mesons. Phys. Lett. 8, 214 (1964). https://doi.org/10.1016/S0031-9163(64)92001-3

    Article  ADS  Google Scholar 

  2. G. Zweig, An SU(3) model for strong interaction symmetry and its breaking. version 2. In Developments in the Quark Theory of Hadrons, vol. 1. 1964–1978, ed. by D.B. Lichtenberg, S.P. Rosen, pp. 22–101(1964). https://doi.org/10.17181/CERN-TH-412

  3. A. Ali, J.S. Lange, S. Stone, Exotics: heavy pentaquarks and tetraquarks. Prog. Part. Nucl. Phys. 97, 123 (2017). https://doi.org/10.1016/j.ppnp.2017.08.003

    Article  ADS  Google Scholar 

  4. Y.-R. Liu, H.-X. Chen, W. Chen, X. Liu, S.-L. Zhu, Pentaquark and tetraquark states. Prog. Part. Nucl. Phys. 107, 237 (2019). https://doi.org/10.1016/j.ppnp.2019.04.003

    Article  ADS  Google Scholar 

  5. N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev, C.-P. Shen, C.E. Thomas, A. Vairo, C.-Z. Yuan, The XYZ states: experimental and theoretical status and perspectives. Phys. Rep. 873, 1 (2020). https://doi.org/10.1016/j.physrep.2020.05.001

    Article  ADS  Google Scholar 

  6. R. Aaij et al., (LHCb Collaboration), Amplitude analysis of the \({B^{+} \rightarrow D^{+}D^{-}K^{+}}\) decay. Phys. Rev. D 102, 112003 (2020). https://doi.org/10.1103/physrevd.102.112003. arXiv:2009.00026 [hep-ex]

  7. R. Aaij et al., (LHCb Collaboration), First observation of a doubly charged tetraquark and its neutral partner. Phys. Rev. Lett. 131, 041902 (2023). https://doi.org/10.1103/PhysRevLett.131.041902. arXiv:2212.02716 [hep-ex]

  8. R. Aaij et al., (LHCb Collaboration), Observation of an exotic narrow doubly charmed tetraquark. Nat. Phys. 18, 751 (2022). https://doi.org/10.1038/s41567-022-01614-y. arXiv:2109.01038 [hep-ex]

  9. R. Aaij et al., (LHCb Collaboration), Observation of new resonances decaying to \({J/\psi K^{+}}\) and \({J/\psi \phi }\). Phys. Rev. Lett. 127, 082001 (2021). https://doi.org/10.1103/physrevlett.127.082001. arXiv:2103.01803 [hep-ex]

  10. R. Aaij et al., (LHCb Collaboration), Evidence of a \({J/\psi K_{S}^{0}}\) structure in \({B^{0} \rightarrow J/\psi \phi K_{S}^{0}}\) decays. Phys. Rev. Lett. 131, 131901 (2023). https://doi.org/10.1103/PhysRevLett.131.131901. arXiv:2301.04899 [hep-ex]

  11. S. Chatrchyan et al., (CMS Collaboration), Observation of a peaking structure in the \({J/\psi \phi }\) mass spectrum from \({B^{\pm } \rightarrow J/\psi \phi K^{\pm }}\) decays. Phys. Lett. B 734, 261 (2014). https://doi.org/10.1016/j.physletb.2014.05.055. arXiv:1309.6920 [hep-ex]

  12. R. Aaij et al., (LHCb Collaboration), Observation of \({J/\psi \phi }\) structures consistent with exotic states from amplitude analysis of \({B^{+} \rightarrow J/\psi \phi K^{+}}\) decays. Phys. Rev. Lett. 118, 022003 (2017). https://doi.org/10.1103/PhysRevLett.118.022003

  13. R. Aaij et al., (LHCb Collaboration), Observation of a resonant structure near the \({D_{s}^{+}D_{s}^{-}}\) threshold in the \({B^{+} \rightarrow D_{s}^{+}D_{s}^{-}K^{+}}\) decay. Phys. Rev. Lett. 131, 071901 (2023). https://doi.org/10.1103/PhysRevLett.131.071901. arXiv:2210.15153 [hep-ex]

  14. R. Aaij et al., (LHCb Collaboration), Observation of structure in the \({J/\psi }\)-pair mass spectrum. Sci. Bull. 65, 1983 (2020). https://doi.org/10.1016/j.scib.2020.08.032

  15. G. Aad et al., (ATLAS Collaboration), Observation of an excess of di-charmonium events in the four-muon final state with the ATLAS detector. Phys. Rev. Lett. 131, 151902 (2023). https://doi.org/10.1103/PhysRevLett.131.151902. arXiv:2304.08962 [hep-ex]

  16. CMS Collaboration (CMS Collaboration), Observation of new structure in the \({J/\psi J/\psi }\) mass spectrum in proton–proton collisions at \(\sqrt{s}=13\) TeV (2023). https://doi.org/10.48550/ARXIV.2306.07164. arXiv:2306.07164 [hep-ex]

  17. R. Aaij et al., ( LHCb Collaboration), Observation of \({J/\psi p}\) resonances consistent with pentaquark states in \({{\Lambda _b^0} \rightarrow {J/\psi } K^- p}\) decays. Phys. Rev. Lett. 115, 072001 (2015). https://doi.org/10.1103/PhysRevLett.115.072001. arXiv:1507.03414 [hep-ex]

  18. R. Aaij et al., (LHCb Collaboration), Observation of a narrow pentaquark state, \({P_{c}(4312)^{+}}\), and of two-peak structure of the \({P_{c}(4450)^{+}}\). Phys. Rev. Lett. 122, 222001 (2019). https://doi.org/10.1103/physrevlett.122.222001. arXiv:1904.03947 [hep-ex]

  19. R. Aaij et al., (LHCb Collaboration), Observation of a \({J/\psi \Lambda }\) Resonance consistent with a strange pentaquark candidate in \({B^{-} \rightarrow J/\psi \Lambda \overline{p}}\) decays. Phys. Rev. Lett. 131, 031901 (2023). https://doi.org/10.1103/PhysRevLett.131.031901. arXiv:2210.10346 [hep-ex]

  20. H.-X. Chen, W. Chen, X. Liu, Y.-R. Liu, S.-L. Zhu, An updated review of the new hadron states. Rep. Prog. Phys. 86, 026201 (2022). https://doi.org/10.1088/1361-6633/aca3b6. arXiv:2204.02649 [hep-ph]

  21. M. Anselmino, E. Predazzi, S. Ekelin, S. Fredriksson, D.B. Lichtenberg, Diquarks. Rev. Mod. Phys. 65, 1199 (1993). https://doi.org/10.1103/RevModPhys.65.1199

    Article  ADS  Google Scholar 

  22. L. Maiani, F. Piccinini, A.D. Polosa, V. Riquer, Diquark-antidiquarks with hidden or open charm and the nature of X(3872). Phys. Rev. D 71, 014028 (2005). https://doi.org/10.1103/PhysRevD.71.014028. arXiv:hep-ph/0412098

    Article  ADS  Google Scholar 

  23. D. Ebert, R.N. Faustov, V.O. Galkin, Masses of heavy tetraquarks in the relativistic quark model. Phys. Lett. B 634, 214 (2006). https://doi.org/10.1016/j.physletb.2006.01.026. arXiv:hep-ph/0512230

    Article  ADS  Google Scholar 

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

  25. S. Dubynskiy, M.B. Voloshin, Hadro-charmonium. Phys. Lett. B 666, 344 (2008). https://doi.org/10.1016/j.physletb.2008.07.086. arXiv:0803.2224 [hep-ph]

    Article  ADS  Google Scholar 

  26. M.B. Voloshin, Charmonium. Prog. Part. Nucl. Phys. 61, 455 (2008). https://doi.org/10.1016/j.ppnp.2008.02.001

    Article  ADS  Google Scholar 

  27. E.S. Swanson, \({Z_{b}}\) and \({Z_{c}}\) exotic states as coupled channel cusps. Phys. Rev. D 91, 034009 (2015). https://doi.org/10.1103/PhysRevD.91.034009. arXiv:1409.3291 [hep-ph]

    Article  ADS  Google Scholar 

  28. K.-T. Chao, The \({(cc)-({\bar{c}}{\bar{c}})}\) (diquark–antidiquark) states in \({e^{+}e^{-}}\) annihilation. Zeitschrift für Physik C Part. Fields 7, 317 (1981). https://doi.org/10.1007/BF01431564

    Article  ADS  Google Scholar 

  29. J.P. Ader, J.M. Richard, P. Taxil, Do narrow heavy multiquark states exist? Phys. Rev. D 25, 2370 (1982). https://doi.org/10.1103/PhysRevD.25.2370

    Article  ADS  Google Scholar 

  30. L. Heller, J.A. Tjon, On bound states of heavy \({{Q}^{2}\overline{Q}^{2}}\) Systems. Phys. Rev. D 32, 755 (1985). https://doi.org/10.1103/PhysRevD.32.755

    Article  ADS  Google Scholar 

  31. S. Zouzou, B. Silvestre-Brac, C. Gignoux, J.M. Richard, Four-quark bound states. Zeitschrift für Physik C Part. Fields 30, 457 (1986). https://doi.org/10.1007/BF01557611

    Article  ADS  Google Scholar 

  32. A.M. Badalian, B.L. Ioffe, A.V. Smilga, Four-quark states in heavy quark systems. Nucl. Phys. B 281, 85 (1987). https://doi.org/10.1016/0550-3213(87)90248-3

    Article  ADS  Google Scholar 

  33. P. Bicudo, K. Cichy, A. Peters, B. Wagenbach, M. Wagner, Evidence for the existence of \({ud{\bar{b}}{\bar{b}}}\) and the non-existence of \({ss{\bar{b}}{\bar{b}}}\) and \({cc{\bar{b}}{\bar{b}}}\) tetraquarks from lattice QCD. Phys. Rev. D 92, 014507 (2015). https://doi.org/10.1103/physrevd.92.014507. arXiv:1505.00613 [hep-lat]

    Article  ADS  Google Scholar 

  34. M.N. Anwar, J. Ferretti, F.-K. Guo, E. Santopinto, B.-S. Zou, Spectroscopy and decays of the fully-heavy tetraquarks. Eur. Phys. J. C 78, 647 (2018). https://doi.org/10.1140/epjc/s10052-018-6073-9. arXiv:1710.02540 [hep-ph]

    Article  ADS  Google Scholar 

  35. J. Wu, Y.-R. Liu, K. Chen, X. Liu, S.-L. Zhu, Heavy-flavored tetraquark states with the \({QQ{\bar{Q}}{\bar{Q}}}\) configuration. Phys. Rev. D 97, 094015 (2018). https://doi.org/10.1103/PhysRevD.97.094015

    Article  ADS  Google Scholar 

  36. X. Chen, Fully-heavy tetraquarks: \({bb{\bar{c}}{\bar{c}}}\) and \({bc{\bar{b}}{\bar{c}}}\). Phys. Rev. D 100, 094009 (2019). https://doi.org/10.1103/PhysRevD.100.094009. arXiv:1908.08811 [hep-ph]

    Article  ADS  Google Scholar 

  37. G. Li, X.-F. Wang, Y. Xing, Fully heavy tetraquark \({bb {\bar{c}} {\bar{c}}}\): lifetimes and weak decays. Eur. Phys. J. C (2019). https://doi.org/10.1140/epjc/s10052-019-7150-4arXiv:1902.05805 [hep-ph]

  38. M.-S. Liu, Q.-F. Lü, X.-H. Zhong, Q. Zhao, All-heavy tetraquarks. Phys. Rev. D 100, 016006 (2019). https://doi.org/10.1103/PhysRevD.100.016006

    Article  ADS  MathSciNet  Google Scholar 

  39. G.-J. Wang, L. Meng, S.-L. Zhu, Spectrum of the fully-heavy tetraquark state \({QQ{\bar{Q}}^{\prime }{\bar{Q}}^{\prime }}\). Phys. Rev. D 100, 096013 (2019). https://doi.org/10.1103/PhysRevD.100.096013

    Article  ADS  Google Scholar 

  40. M.A. Bedolla, J. Ferretti, C.D. Roberts, E. Santopinto, Spectrum of fully-heavy tetraquarks from a diquark+antidiquark perspective. Eur. Phys. J. C 80, 1004 (2020). https://doi.org/10.1140/epjc/s10052-020-08579-3. arXiv:1911.00960 [hep-ph]

    Article  ADS  Google Scholar 

  41. M.C. Gordillo, F. De Soto, J. Segovia, Diffusion Monte Carlo calculations of fully-heavy multiquark bound states. Phys. Rev. D 102, 114007 (2020). https://doi.org/10.1103/PhysRevD.102.114007. arXiv:2009.11889 [hep-ph]

    Article  ADS  Google Scholar 

  42. C. Deng, H. Chen, J. Ping, Towards the understanding of fully-heavy tetraquark states from various models. Phys. Rev. D 103, 014001 (2021). https://doi.org/10.1103/PhysRevD.103.014001

    Article  ADS  Google Scholar 

  43. Q.-N. Wang, Z.-H. Yang, W. Chen, H.-X. Chen, Mass spectra for the \({cc\bar{b}\bar{b}}\) and \({bb\bar{c}\bar{c}}\) tetraquark states. Phys. Rev. D 104, 014020 (2021). https://doi.org/10.1103/physrevd.104.014020. arXiv:2106.05550 [hep-ph]

    Article  ADS  Google Scholar 

  44. X.-Z. Weng, X.-L. Chen, W.-Z. Deng, S.-L. Zhu, Systematics of fully heavy tetraquarks. Phys. Rev. D 103, 034001 (2021). https://doi.org/10.1103/PhysRevD.103.034001

    Article  ADS  Google Scholar 

  45. G. Yang, J. Ping, J. Segovia, Exotic resonances of fully-heavy tetraquarks in a lattice-QCD insipired quark model. Phys. Rev. D 104, 014006 (2021). https://doi.org/10.1103/PhysRevD.104.014006

    Article  ADS  Google Scholar 

  46. W. Chen, Q.-N. Wang, Z.-Y. Yang, H.-X. Chen, X. Liu, T.G. Steele, S.-L. Zhu, Searching for fully-heavy tetraquark states in QCD moment sum rules. Nucl. Part. Phys. Proc. 318–323, 73 (2022). https://doi.org/10.1016/j.nuclphysbps.2022.09.016. arXiv:2212.03689 [hep-ph]

    Article  Google Scholar 

  47. H. Mutuk, Spectrum of \({cc\bar{b}\bar{b}}\), \({bc\bar{c}\bar{c}}\), and \({bc\bar{b}\bar{b}}\) tetraquark states in the dynamical diquark model. Phys. Lett. B 834, 137404 (2022). https://doi.org/10.1016/j.physletb.2022.137404. arXiv:2208.11048 [hep-ph]

    Article  Google Scholar 

  48. J. Zhang, J.-B. Wang, G. Li, C.-S. An, C.-R. Deng, J.-J. Xie, Spectrum of the S-wave fully-heavy tetraquark states. Eur. Phys. J. C 82, 1126 (2022). https://doi.org/10.1140/epjc/s10052-022-11111-4. arXiv:2209.13856 [hep-ph]

    Article  ADS  Google Scholar 

  49. H.-T. An, S.-Q. Luo, Z.-W. Liu, X. Liu, Spectroscopic behavior of fully heavy tetraquarks. Eur. Phys. J. C 83, 740 (2023). https://doi.org/10.1140/epjc/s10052-023-11847-7. arXiv:2208.03899 [hep-ph]

    Article  ADS  Google Scholar 

  50. B. Silvestre-Brac, Systematics of \({Q^{2}({\overline{Q}}^{2})}\) systems with a chromomagnetic interaction. Phys. Rev. D 46, 2179 (1992). https://doi.org/10.1103/PhysRevD.46.2179

    Article  ADS  Google Scholar 

  51. J.-M. Richard, A. Valcarce, J. Vijande, String dynamics and metastability of all-heavy tetraquarks. Phys. Rev. D 95, 054019 (2017). https://doi.org/10.1103/PhysRevD.95.054019. arXiv:1703.00783 [hep-ph]

    Article  ADS  Google Scholar 

  52. A. Czarnecki, B. Leng, M.B. Voloshin, Stability of tetrons. Phys. Lett. B 778, 233 (2018). https://doi.org/10.1016/j.physletb.2018.01.034. arXiv:1708.04594 [hep-ph]

    Article  ADS  Google Scholar 

  53. R.N. Faustov, V.O. Galkin, E.M. Savchenko, Masses of the \({QQ{\bar{Q}}{\bar{Q}}}\) tetraquarks in the relativistic diquark-antidiquark picture. Phys. Rev. D 102, 114030 (2020). https://doi.org/10.1103/PhysRevD.102.114030. arXiv:2009.13237 [hep-ph]

    Article  ADS  Google Scholar 

  54. R.N. Faustov, V.O. Galkin, E.M. Savchenko, Heavy tetraquarks in the relativistic quark model. Universe 7, 94 (2021). https://doi.org/10.3390/universe7040094. arXiv:2103.01763 [hep-ph]

    Article  ADS  Google Scholar 

  55. R.N. Faustov, V.O. Galkin, E.M. Savchenko, Fully heavy tetraquark spectroscopy in the relativistic quark model. Symmetry 14, 2504 (2022). https://doi.org/10.3390/sym14122504. arXiv:2210.16015 [hep-ph]

    Article  ADS  Google Scholar 

  56. R. Aaij et al., Search for beautiful tetraquarks in the \({\Upsilon }\)(1S)\(\mu ^{+}\mu ^{-}\) invariant-mass spectrum. J. High Energy Phys. 10, 1 (2018). https://doi.org/10.1007/JHEP10(2018)086. arXiv:1806.09707 [hep-ex]

    Article  ADS  Google Scholar 

  57. V. Khachatryan et al., (CMS Collaboration), Observation of \({\Upsilon (1{s})}\) pair production in proton–proton collisions at \({\sqrt{s}=8}\) TeV. J. High Energy Phys 5, 1 (2017). https://doi.org/10.1007/JHEP05(2017)013. arXiv:1610.07095 [hep-ex]

  58. A.M. Sirunyan et al., (CMS Collaboration), Measurement of the \({\Upsilon (1{s})}\) pair production cross section and search for resonances decaying to \({\Upsilon }\)(1S)\(\mu ^{+}\mu ^{-}\) in proton-proton collisions at \(\sqrt{s}=13\) TeV. Phys. Lett. B 808, 135578 (2020). https://doi.org/10.1016/j.physletb.2020.135578. arXiv:2002.06393

  59. R.L. Workman, V.D. Burkert, V. Crede, E. Klempt, U. Thoma, L. Tiator, K. Agashe, G. Aielli, B.C. Allanach, C. Amsler et al., Review of particle physics. Prog. Theor. Exp. Phys. 2022, 083C01 (2022). https://doi.org/10.1093/ptep/ptac097

    Article  Google Scholar 

  60. I. Bigi, Y. Dokshitzer, V. Khoze, J. Kühn, P. Zerwas, Production and decay properties of ultra-heavy quarks. Phys. Lett. B 181, 157 (1986). https://doi.org/10.1016/0370-2693(86)91275-x

    Article  ADS  Google Scholar 

  61. D. Ebert, R.N. Faustov, V.O. Galkin, Masses of heavy baryons in the relativistic quark model. Phys. Rev. D 72, 034026 (2005). https://doi.org/10.1103/PhysRevD.72.034026. arXiv:hep-ph/0504112 [hep-ph]

    Article  ADS  Google Scholar 

  62. D. Ebert, R.N. Faustov, V.O. Galkin, Spectroscopy and Regge trajectories of heavy baryons in the relativistic quark-diquark picture. Phys. Rev. D 84, 014025 (2011). https://doi.org/10.1103/PhysRevD.84.014025. arXiv:1105.0583 [hep-ph]

    Article  ADS  Google Scholar 

  63. D. Ebert, R.N. Faustov, V.O. Galkin, Properties of heavy quarkonia and \({B_c}\) mesons in the relativistic quark model. Phys. Rev. D 67, 014027 (2003). https://doi.org/10.1103/PhysRevD.67.014027. arXiv:hep-ph/0210381

    Article  ADS  Google Scholar 

  64. D. Ebert, R.N. Faustov, V.O. Galkin, Spectroscopy and Regge trajectories of heavy quarkonia and\({B_{c}}\) mesons. Eur. Phys. J. C (2011). https://doi.org/10.1140/epjc/s10052-011-1825-9

  65. A.A. Logunov, A.N. Tavkhelidze, Quasi-Optical Approach in Quantum Field Theory. Il Nuovo Cimento 29, 380 (1963). https://doi.org/10.1007/BF02750359

    Article  ADS  MathSciNet  Google Scholar 

  66. A.P. Martynenko, R.N. Faustov, Relativistic reduced mass and quasipotential equation. Theor. Math. Phys. 64, 765 (1985). https://doi.org/10.1007/BF01017955

    Article  Google Scholar 

  67. V.O. Galkin, R.N. Faustov, Some properties of the solutions of a quasipotential equation. Theor. Math. Phys. 85, 1119 (1990). https://doi.org/10.1007/bf01017254

    Article  MathSciNet  Google Scholar 

  68. D. Ebert, R.N. Faustov, V.O. Galkin, A.P. Martynenko, Mass spectra of doubly heavy baryons in the relativistic quark model. Phys. Rev. D 66, 014008 (2002). https://doi.org/10.1103/PhysRevD.66.014008. arXiv:hep-ph/0201217

    Article  ADS  Google Scholar 

  69. D. Ebert, R.N. Faustov, V.O. Galkin, W. Lucha, Masses of tetraquarks with two heavy quarks in the relativistic quark model. Phys. Rev. D 76, 114015 (2007). https://doi.org/10.1103/PhysRevD.0706.3853

    Article  ADS  Google Scholar 

  70. Y.A. Simonov, Perturbation theory in the nonperturbative QCD vacuum. Phys. Atom. Nucl. 58, 107 (1995). https://doi.org/10.48550/arXiv.HEP-PH/9311247. arXiv:hep-ph/9311247 [hep-ph]

  71. A.M. Badalian, A.I. Veselov, B.L.G. Bakker, Restriction on the strong coupling constant in the IR region from the 1D–1P splitting in bottomonium. Phys. Rev. D 70, 016007 (2004). https://doi.org/10.1103/PhysRevD.70.016007

    Article  ADS  Google Scholar 

  72. A. De-Shalit, I. Talmi, Nuclear Shell Theory (publisher Dover Publications, Mineola, New York, 2004) (Academic Press, New York, 1963), p.592

    Google Scholar 

  73. W. Lucha, F.F. Schöberl, Solving the Schrödinger equation for bound states with mathematica 3.0,. Int. J. Mod. Phys. C 10, 607 (1999). https://doi.org/10.1142/s0129183199000450

  74. V.O. Galkin, R.N. Faustov, Relativistic corrections to radiative decay widths of vector mesons. Sov. J. Nucl. Phys. 44, 1575 (1986)

    Google Scholar 

  75. V.O. Galkin, A.Y. Mishurov, R.N. Faustov, Radiative E1 decays of quarkonium in the framework of relativistic quark model. Sov. J. Nucl. Phys. 51, 705 (1990)

    Google Scholar 

  76. V.O. Galkin, A.Y. Mishurov, R.N. Faustov, Meson masses in the relativistic quark model. Sov. J. Nucl. Phys 55, 1207 (1992)

    Google Scholar 

  77. R.N. Faustov, V.O. Galkin, Heavy quark \({1/m_{Q}}\) expansion of meson weak decay form-factors in the relativistic quark model. Z. Phys. C 66, 119 (1995). https://doi.org/10.1007/BF01496586

    Article  ADS  Google Scholar 

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Acknowledgements

The authors are grateful to D. Ebert and A.V. Berezhnoy for useful discussions. The work of Elena M. Savchenko was supported in part by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS” grant number 22-2-10-3-1.

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  1. Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Vavilov Street 40, 119333, Moscow, Russia

    V. O. Galkin & E. M. Savchenko

  2. Faculty of Physics, M.V.Lomonosov Moscow State University, Leninskie Gory 1-2, 119991, Moscow, Russia

    E. M. Savchenko

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Galkin, V.O., Savchenko, E.M. Relativistic description of asymmetric fully heavy tetraquarks in the diquark–antidiquark model. Eur. Phys. J. A 60, 96 (2024). https://doi.org/10.1140/epja/s10050-024-01311-9

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