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  • Letter
  • Open Access

Nature of the X(6900) in partial wave decomposition of J/ψJ/ψ scattering

Qi Zhou, Di Guo, Shi-Qing Kuang, Qin-He Yang, and Ling-Yun Dai*

  • School of Physics and Electronics, Hunan University, Changsha 410082, China and Hunan Provincial Key Laboratory of High-Energy Scale Physics and Applications, Hunan University, Changsha 410082, China

  • *dailingyun@hnu.edu.cn
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Phys. Rev. D 106, L111502 – Published 20 December, 2022

DOI: https://doi.org/10.1103/PhysRevD.106.L111502

Abstract

In this paper, we perform partial wave decomposition on coupled-channel scattering amplitudes, J/ψJ/ψ−J/ψψ(2S)−J/ψψ(3770), to study the resonance appears in these processes. Effective Lagrangians are used to describe the interactions of four charmed vector mesons, and the scattering amplitudes are calculated up to the next-to-leading order. Partial wave projections are performed, and unitarization is implemented by Padé approximation. Then we fit the amplitudes to the J/ψJ/ψ invariant mass spectra measured by LHCb and determine the unknown couplings. The pole parameters of the X(6900) are extracted as M=6861.0−8.8+6.3  MeV and Γ=129.0−3.4+5.6  MeV. Our analysis implies that its quantum number prefers to be 0++. The pole counting rule and phase shifts show that it is a normal Breit-Wigner resonance and, hence, should be a compact tetraquark.

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References (56)

  1. M. Gell-Mann, Phys. Lett. 8, 214 (1964).
  2. G. Zweig, Report No. CERN-TH-401.
  3. G. Zweig, Report No. CERN-TH-412.
  4. F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, and B.-S. Zou, Rev. Mod. Phys. 90, 015004 (2018).
  5. N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev, C.-P. Shen, C. E. Thomas, A. Vairo, and C.-Z. Yuan, Phys. Rep. 873, 1 (2020).
  6. D.-L. Yao, L.-Y. Dai, H.-Q. Zheng, and Z.-Y. Zhou, Rep. Prog. Phys. 84, 076201 (2021).
  7. H.-X. Chen, W. Chen, X. Liu, Y.-R. Liu, and S.-L. Zhu, arXiv:2204.02649 [Rep. Prog. Phys. (to be published)].
  8. M. Ablikim et al. (BESIII Collaboration), Phys. Rev. Lett. 110, 252001 (2013).
  9. Z. Q. Liu et al. (Belle Collaboration), Phys. Rev. Lett. 110, 252002 (2013); 111, 019901(E) (2013).
  10. R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 115, 072001 (2015).
  11. R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 122, 222001 (2019).
  12. R. Aaij et al. (LHCb Collaboration), Sci. Bull. 65, 1983 (2020).
  13. X.-K. Dong, V. Baru, F.-K. Guo, C. Hanhart, and A. Nefediev, Phys. Rev. Lett. 126, 132001 (2021); 127, 119901(E) (2021).
  14. J.-Z. Wang, D.-Y. Chen, X. Liu, and T. Matsuki, Phys. Rev. D 103, L071503 (2021).
  15. C. Gong, M.-C. Du, Q. Zhao, X.-H. Zhong, and B. Zhou, Phys. Lett. B 824, 136794 (2022).
  16. Q.-F. Cao, H. Chen, H.-R. Qi, and H.-Q. Zheng, Chin. Phys. C 45, 103102 (2021).
  17. Z.-H. Guo and J. A. Oller, Phys. Rev. D 103, 034024 (2021).
  18. Z.-R. Liang, X.-Y. Wu, and D.-L. Yao, Phys. Rev. D 104, 034034 (2021).
  19. X.-Y. Wang, Q.-Y. Lin, H. Xu, Y.-P. Xie, Y. Huang, and X. Chen, Phys. Rev. D 102, 116014 (2020).
  20. H.-W. Ke, X. Han, X.-H. Liu, and Y.-L. Shi, Eur. Phys. J. C 81, 427 (2021).
  21. H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, Sci. Bull. 65, 1994 (2020).
  22. J.-Z. Wang and X. Liu, Phys. Rev. D 106, 054015 (2022).
  23. L.-Y. Dai and M. R. Pennington, Phys. Lett. B 736, 11 (2014).
  24. L.-Y. Dai and M. R. Pennington, Phys. Rev. D 90, 036004 (2014).

  25. For instance, in the ππ,πK scatterings, the phase shifts [26, 27] help to confirm the existence of the light scalars σ, κ [28, 29, 30, 31].

  26. B. Hyams et al., Nucl. Phys. B64, 134 (1973).
  27. D. Aston et al., Nucl. Phys. B296, 493 (1988).
  28. S. Ishida, M. Ishida, H. Takahashi, T. Ishida, K. Takamatsu, and T. Tsuru, Prog. Theor. Phys. 95, 745 (1996).
  29. S. Ishida, M. Ishida, T. Ishida, K. Takamatsu, and T. Tsuru, Prog. Theor. Phys. 98, 621 (1997).
  30. Z. Xiao and H. Q. Zheng, Nucl. Phys. A695, 273 (2001).
  31. Z. Y. Zhou, G. Y. Qin, P. Zhang, Z. Xiao, H. Q. Zheng, and N. Wu, J. High Energy Phys. 02 (2005) 043.
  32. D. Morgan, Nucl. Phys. A543, 632 (1992).
  33. L. Y. Dai, X. G. Wang, and H. Q. Zheng, Commun. Theor. Phys. 57, 841 (2012).
  34. C. Gong, M.-C. Du, and Q. Zhao, Phys. Rev. D 106, 054011 (2022).
  35. R. Casalbuoni, A. Deandrea, N. Di Bartolomeo, R. Gatto, F. Feruglio, and G. Nardulli, Phys. Rep. 281, 145 (1997).

  36. Higher-order Lagrangians with derivatives will be suppressed by HQSS, too. The momentum coming from derivatives will be carried mainly by the velocity v=(1,0→), and one has v·V(′,′′)=0.

  37. Notice that the NLO results would supply not only higher -order energy-dependent potentials, but also the left-hand cut contributions.

  38. A. D. Martin and T. D. Spearman, Elementary Partical Theory (North-Holland, Amsterdam, 1970), p. 70–97206.
  39. P. A. Zyla et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2020, 083C01 (2020).

  40. Higher-order Lagrangians with derivatives could contribute to the higher partial waves. However, they are suppressed by HQSS. Furthermore, a reliable description of them relies on the angular distributions, and it is expected that future experiments can supply more measurements to ensure a more detailed analysis.

  41. S. U. Chung, Report No. CERN-71-08, 10.5170/CERN-1971-008.
  42. J. A. Oller, Prog. Part. Nucl. Phys. 110, 103728 (2020).
  43. S.-Q. Kuang, L.-Y. Dai, X.-W. Kang, and D.-L. Yao, Eur. Phys. J. C 80, 433 (2020).
  44. T. N. Truong, Phys. Rev. Lett. 61, 2526 (1988).
  45. L.-Y. Dai, X.-G. Wang, and H.-Q. Zheng, Commun. Theor. Phys. 58, 410 (2012).
  46. A. Dobado and J. R. Pelaez, Phys. Rev. D 56, 3057 (1997).
  47. J. A. Oller, E. Oset, and J. R. Pelaez, Phys. Rev. Lett. 80, 3452 (1998).
  48. A. Gomez Nicola and J. R. Pelaez, Phys. Rev. D 65, 054009 (2002).
  49. L.-Y. Dai, X. Sun, X.-W. Kang, A. P. Szczepaniak, and J.-S. Yu, Phys. Rev. D 105, L051507 (2022).
  50. K. Au, D. Morgan, and M. Pennington, Phys. Rev. D 35, 1633 (1987).
  51. L.-Y. Dai and M. R. Pennington, Phys. Rev. D 94, 116021 (2016).
  52. F. James and M. Roos, Comput. Phys. Commun. 10, 343 (1975).
  53. B. Efron, Ann. Statist. 7, 1 (1979).

  54. Very recently, another state, X(6600) was found in di-J/ψ invariant mass spectra by CMS [55]. In contrast, it is not clear in the 4μ [J/ψJ/ψ and J/ψψ(2S)] spectra as measured by ATLAS [56]. Here, the resonant structure around 6600 MeV of LHCb is not obvious, and, in practice, we do not find such a resonance; see Fig. 2.

  55. Zhang Jingqing and Yi Kai CMS Collaboration, Proc. Sci. ICHEP2022 (2022) 775.
  56. Xu Yue ATLAS Collaboration, ATLAS results on exotic hadronic resonances, 2022, arXiv:2209.12173.

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Phys. Rev. D 106, L111502– Published 20 December, 2022
  • Received 18 July 2022
  • Accepted 28 November 2022
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