Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Hidden charmed decays of X(3872) within the DD¯* molecular framework

Hao-Dong Cai1, Zhao-Sai Jia1,2, Gang Li1,*, and Shi-Dong Liu1,†

  • *Contact author: gli@qfnu.edu.cn
  • †Contact author: liusd@qfnu.edu.cn

Phys. Rev. D 111, 114024 – Published 20 June, 2025

DOI: https://doi.org/10.1103/gn25-fc9q

Abstract

The dipionic transition of the X(3872) to the ηc was investigated using an effective Lagrangian approach. In this study, the X(3872) was assumed to be a DD¯*+c.c. bound state with the quantum numbers JPC=1++ and to decay via triangle and box loops. It is found that the partial decay widths arising from the box loops are one order of magnitude greater than those from the triangle ones. The decay widths are model-dependent, as characterized by the cutoff parameter introduced in the form factor. Moreover, the charged and neutral DD¯* configurations of the X(3872) and its mass also influence the decay widths. With our model parameters, the decay widths for the X(3872)→π+π−ηc can reach up to several tens of keV. We hope that the current calculations within the molecular interpretation will be helpful for the future experiments.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (80)

  1. S. K. Choi et al. (Belle Collaboration), Observation of a narrow charmonium-like state in exclusive B±→K±π+π−J/ψ decays, Phys. Rev. Lett. 91, 262001 (2003).
  2. B. Aubert et al. (BABAR Collaboration), Study of the B→J/ψK−π+π− decay and measurement of the B→X(3872)K− branching fraction, Phys. Rev. D 71, 071103 (2005).
  3. B. Aubert et al. (BABAR Collaboration), A study of B→X(3872)K, with X(3872)→J/Ψπ+π−, Phys. Rev. D 77, 111101 (2008).
  4. V. M. Abazov et al. (D0 Collaboration), Observation and properties of the X(3872) decaying to J/ψπ+π− in pp¯ collisions at s=1.96  TeV, Phys. Rev. Lett. 93, 162002 (2004).
  5. D. Acosta et al. (CDF Collaboration), Observation of the narrow state X(3872)→J/ψπ+π− in p¯p collisions at s=1.96  TeV, Phys. Rev. Lett. 93, 072001 (2004).
  6. R. Aaij et al. (LHCb Collaboration), Determination of the X(3872) meson quantum numbers, Phys. Rev. Lett. 110, 222001 (2013).
  7. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  8. F. E. Close and P. R. Page, The D*0D¯0 threshold resonance, Phys. Lett. B 578, 119 (2004).
  9. S. Pakvasa and M. Suzuki, On the hidden charm state at 3872 MeV, Phys. Lett. B 579, 67 (2004).
  10. E. S. Swanson, Short range structure in the X(3872), Phys. Lett. B 588, 189 (2004).
  11. E. S. Swanson, Diagnostic decays of the X(3872), Phys. Lett. B 598, 197 (2004).
  12. N. A. Tornqvist, Isospin breaking of the narrow charmonium state of Belle at 3872 MeV as a deuson, Phys. Lett. B 590, 209 (2004).
  13. M. B. Voloshin, Interference and binding effects in decays of possible molecular component of X(3872), Phys. Lett. B 579, 316 (2004).
  14. C.-Y. Wong, Molecular states of heavy quark mesons, Phys. Rev. C 69, 055202 (2004).
  15. M. T. AlFiky, F. Gabbiani, and A. A. Petrov, X(3872): Hadronic molecules in effective field theory, Phys. Lett. B 640, 238 (2006).
  16. E. Braaten and M. Lu, Operator product expansion in the production and decay of the X(3872), Phys. Rev. D 74, 054020 (2006).
  17. S. Fleming, M. Kusunoki, T. Mehen, and U. van Kolck, Pion interactions in the X(3872), Phys. Rev. D 76, 034006 (2007).
  18. G.-J. Ding, J.-F. Liu, and M.-L. Yan, Dynamics of hadronic molecule in one-boson exchange approach and possible heavy flavor molecules, Phys. Rev. D 79, 054005 (2009).
  19. Y. Dong, A. Faessler, T. Gutsche, S. Kovalenko, and V. E. Lyubovitskij, X(3872) as a hadronic molecule and its decays to charmonium states and pions, Phys. Rev. D 79, 094013 (2009).
  20. I. W. Lee, A. Faessler, T. Gutsche, and V. E. Lyubovitskij, X(3872) as a molecular DD* state in a potential model, Phys. Rev. D 80, 094005 (2009).
  21. N. Lee, Z.-G. Luo, X.-L. Chen, and S.-L. Zhu, Possible deuteron-like molecular states composed of heavy baryons, Phys. Rev. D 84, 014031 (2011).
  22. X. Liu, Z.-G. Luo, Y.-R. Liu, and S.-L. Zhu, X(3872) and other possible heavy molecular states, Eur. Phys. J. C 61, 411 (2009).
  23. J.-R. Zhang and M.-Q. Huang, {Qq¯}{Q¯′q} molecular states, Phys. Rev. D 80, 056004 (2009).
  24. D. Gamermann, J. Nieves, E. Oset, and E. Ruiz Arriola, Couplings in coupled channels versus wave functions: Application to the X(3872) resonance, Phys. Rev. D 81, 014029 (2010).
  25. T. Mehen and R. Springer, Radiative decays X(3872)→ψ(2S)γ and ψ(4040)→X(3872)γ in effective field theory, Phys. Rev. D 83, 094009 (2011).
  26. J. Nieves and M. P. Valderrama, Deriving the existence of BB¯* bound states from the X(3872) and heavy quark symmetry, Phys. Rev. D 84, 056015 (2011).
  27. J. Nieves and M. P. Valderrama, The heavy quark spin symmetry partners of the X(3872), Phys. Rev. D 86, 056004 (2012).
  28. N. Li and S.-L. Zhu, , Isospin breaking, Coupled-channel effects and diagnosis of X(3872), Phys. Rev. D 86, 074022 (2012).
  29. Z.-F. Sun, X. Liu, M. Nielsen, and S.-L. Zhu, Hadronic molecules with both open charm and bottom, Phys. Rev. D 85, 094008 (2012).
  30. F.-K. Guo, C. Hidalgo-Duque, J. Nieves, and M. P. Valderrama, Consequences of heavy quark symmetries for hadronic molecules, Phys. Rev. D 88, 054007 (2013).
  31. J. He, Study of the BB¯*/DD¯* bound states in a Bethe-Salpeter approach, Phys. Rev. D 90, 076008 (2014).
  32. L. Zhao, L. Ma, and S.-L. Zhu, Spin-orbit force, recoil corrections, and possible BB¯* and DD¯* molecular states, Phys. Rev. D 89, 094026 (2014).
  33. F.-K. Guo, C. Hanhart, Y. S. Kalashnikova, U.-G. Meißner, and A. V. Nefediev, What can radiative decays of the X(3872) teach us about its nature? Phys. Lett. B 742, 394 (2015).
  34. F. K. Guo, C. Hidalgo-Duque, J. Nieves, A. Ozpineci, and M. P. Valderrama, Detecting the long-distance structure of the X(3872), Eur. Phys. J. C 74, 2885 (2014).
  35. E. Braaten and M. Kusunoki, Low-energy universality and the new charmonium resonance at 3870 MeV, Phys. Rev. D 69, 074005 (2004).
  36. Q. Wu, D.-Y. Chen, and T. Matsuki, A phenomenological analysis on isospin-violating decay of X(3872), Eur. Phys. J. C 81, 193 (2021).
  37. Y. Yamaguchi, A. Hosaka, S. Takeuchi, and M. Takizawa, Heavy hadronic molecules with pion exchange and quark core couplings: a guide for practitioners, J. Phys. G 47, 053001 (2020).
  38. F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, and B.-S. Zou, Hadronic molecules, Rev. Mod. Phys. 90, 015004 (2018); 94, 029901(E) (2022).
  39. Y. S. Kalashnikova and A. V. Nefediev, X(3872) in the molecular model, Phys. Usp. 62, 568 (2019).
  40. Y.-b. Dong, A. Faessler, T. Gutsche, and V. E. Lyubovitskij, Estimate for the X(3872)→γJ/ψ decay width, Phys. Rev. D 77, 094013 (2008).
  41. M. Suzuki, The X(3872) boson: Molecule or charmonium, Phys. Rev. D 72, 114013 (2005).
  42. L. Maiani, F. Piccinini, A. D. Polosa, and V. Riquer, Diquark-antidiquarks with hidden or open charm and the nature of X(3872), Phys. Rev. D 71, 014028 (2005).
  43. L. Maiani, V. Riquer, F. Piccinini, and A. D. Polosa, Four quark interpretation of Y(4260), Phys. Rev. D 72, 031502 (2005).
  44. L. Maiani, A. D. Polosa, and V. Riquer, Indications of a four-quark structure for the X(3872) and X(3876) particles from recent Belle and BABAR Data, Phys. Rev. Lett. 99, 182003 (2007).
  45. K. Terasaki, A new tetra-quark interpretation of X(3872), Prog. Theor. Phys. 118, 821 (2007).
  46. S. Dubnička, A. Z. Dubničková, M. A. Ivanov, and A. Liptaj, Dynamical approach to decays of XYZ states, Symmetry 12, 884 (2020).
  47. Z.-G. Wang, Decipher the width of the X(3872) via the QCD sum rules, Phys. Rev. D 109, 014017 (2024).
  48. Z.-G. Wang, Analysis of the hidden-charm tetraquark mass spectrum with the QCD sum rules, Phys. Rev. D 102, 014018 (2020).
  49. T. Barnes and S. Godfrey, Charmonium options for the X(3872), Phys. Rev. D 69, 054008 (2004).
  50. S. K. Choi et al. (Belle Collaboration), Bounds on the width, mass difference and other properties of X(3872)→π+π−J/ψ decays, Phys. Rev. D 84, 052004 (2011).
  51. B. Aubert et al. (BABAR Collaboration), Search for a charged partner of the X(3872) in the B meson decay B→X−K, X−→J/ψπ−π0, Phys. Rev. D 71, 031501 (2005).
  52. D. Gamermann and E. Oset, Isospin breaking effects in the X(3872) resonance, Phys. Rev. D 80, 014003 (2009).
  53. K. Abe et al. (Belle Collaboration), Evidence for X(3872)→γJ/ψ and the sub-threshold decay X(3872)→ωJ/ψ, arXiv:hep-ex/0505037.
  54. Y. Dong, A. Faessler, T. Gutsche, and V. E. Lyubovitskij, J/ψγ and ψ(2S)γ decay modes of the X(3872), J. Phys. G 38, 015001 (2011).
  55. Y. Wang, Q. Wu, G. Li, W.-H. Qin, X.-H. Liu, C.-S. An, and J.-J. Xie, Investigations of charmless decays of X(3872) via intermediate meson loops, Phys. Rev. D 106, 074015 (2022).
  56. S. Fleming and T. Mehen, Hadronic decays of the X(3872) to χcJ in effective field theory, Phys. Rev. D 78, 094019 (2008).
  57. N. N. Achasov and G. N. Shestakov, Tentative estimates of B(X(3872)→π0π0χc1) and B(X(3872)→π+π−χc1), Phys. Rev. D 110, 016023 (2024).
  58. J. P. Lees et al. (BABAR Collaboration), Search for resonances decaying to ηcπ+π− in two-photon interactions, Phys. Rev. D 86, 092005 (2012).
  59. V. Baru, J. Haidenbauer, C. Hanhart, Y. Kalashnikova, and A. E. Kudryavtsev, Evidence that the a0(980) and f0(980) are not elementary particles, Phys. Lett. B 586, 53 (2004).
  60. S. Weinberg, Evidence that the deuteron is not an elementary particle, Phys. Rev. 137, B672 (1965).
  61. F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, and Q. Zhao, Production of the X(3872) in charmonia radiative decays, Phys. Lett. B 725, 127 (2013).
  62. P. Colangelo, F. De Fazio, and T. N. Pham, Nonfactorizable contributions in B decays to charmonium: The case of B−→K−hc, Phys. Rev. D 69, 054023 (2004).
  63. Q. Wu, Y. Zheng, S. Liu, and G. Li, Investigations on the light hadron decays of Zb(10610) and Zb(10650), Phys. Rev. D 107, 034028 (2023).
  64. Y. Zheng, Z. Cai, G. Li, S. Liu, J. Wu, and Q. Wu, Hidden charmonium decays of spin-2 partner of X(3872), Phys. Rev. D 109, 014027 (2024).
  65. B. Grinstein, E. E. Jenkins, A. V. Manohar, M. J. Savage, and M. B. Wise, Chiral perturbation theory for fDs/fD and BBs/BB, Nucl. Phys. B380, 369 (1992).
  66. R. Casalbuoni, A. Deandrea, N. Di Bartolomeo, R. Gatto, F. Feruglio, and G. Nardulli, Phenomenology of heavy meson chiral Lagrangians, Phys. Rep. 281, 145 (1997).
  67. S. Ahmed et al. (CLEO Collaboration), First measurement of Γ(D*+), Phys. Rev. Lett. 87, 251801 (2001).
  68. Z.-w. Lin and C. M. Ko, A model for J/ψ absorption in hadronic matter, Phys. Rev. C 62, 034903 (2000).
  69. K. L. Haglin, Charmonium dissociation in hadronic matter, Phys. Rev. C 61, 031902 (2000).
  70. T. Hahn and M. Perez-Victoria, Automatized one loop calculations in four-dimensions and D-dimensions, Comput. Phys. Commun. 118, 153 (1999).
  71. A. Denner, Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200, Fortschr. Phys. 41, 307 (1993).
  72. H.-Y. Cheng, C.-K. Chua, and A. Soni, Final state interactions in hadronic B decays, Phys. Rev. D 71, 014030 (2005).
  73. Q. Wu, G. Li, F. Shao, and R. Wang, Investigations on the charmless decay modes of Zc(3900) and Zc(4025), Phys. Rev. D 94, 014015 (2016).
  74. X.-D. Guo, D.-Y. Chen, H.-W. Ke, X. Liu, and X.-Q. Li, Study on the rare decays of Y(4630) induced by final state interactions, Phys. Rev. D 93, 054009 (2016).
  75. T. Mehen, Hadronic loops versus factorization in effective field theory calculations of X(3872)→χcJπ0, Phys. Rev. D 92, 034019 (2015).
  76. Z.-H. Zhang, T. Ji, X.-K. Dong, F.-K. Guo, C. Hanhart, U.-G. Meißner, and A. Rusetsky, Predicting isovector charmonium-like states from X(3872) properties, J. High Energy Phys. 08 (2024) 130.
  77. C. Meng and K.-T. Chao, Decays of the X(3872) and χc1(2P) charmonium, Phys. Rev. D 75, 114002 (2007).
  78. J. Ferretti and E. Santopinto, Threshold corrections of χc(2P) and χb(3P) states and J/ψρ and J/ψω transitions of the χ (3872) in a coupled-channel model, Phys. Lett. B 789, 550 (2019).
  79. M. Ablikim et al. (BESIII Collaboration), Search for the decay χc1(3872)→π+π−χc1, Phys. Rev. D 109, L071101 (2024).
  80. M. Ablikim et al. (BESIII Collaboration), Search for X(3872)→π0χc0 and X(3872)→ππχc0 at BESIII, Phys. Rev. D 105, 072009 (2022).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation