- Open Access
Hidden charmed decays of within the molecular framework
Phys. Rev. D 111, 114024 – Published 20 June, 2025
DOI: https://doi.org/10.1103/gn25-fc9q
Abstract
The dipionic transition of the to the was investigated using an effective Lagrangian approach. In this study, the was assumed to be a bound state with the quantum numbers 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 configurations of the and its mass also influence the decay widths. With our model parameters, the decay widths for the 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.
Physics Subject Headings (PhySH)
Article Text
References (80)
- S. K. Choi et al. (Belle Collaboration), Observation of a narrow charmonium-like state in exclusive decays, Phys. Rev. Lett. 91, 262001 (2003).
- B. Aubert et al. (BABAR Collaboration), Study of the decay and measurement of the branching fraction, Phys. Rev. D 71, 071103 (2005).
- B. Aubert et al. (BABAR Collaboration), A study of , with , Phys. Rev. D 77, 111101 (2008).
- V. M. Abazov et al. (D0 Collaboration), Observation and properties of the decaying to in collisions at , Phys. Rev. Lett. 93, 162002 (2004).
- D. Acosta et al. (CDF Collaboration), Observation of the narrow state in collisions at , Phys. Rev. Lett. 93, 072001 (2004).
- R. Aaij et al. (LHCb Collaboration), Determination of the meson quantum numbers, Phys. Rev. Lett. 110, 222001 (2013).
- S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
- F. E. Close and P. R. Page, The threshold resonance, Phys. Lett. B 578, 119 (2004).
- S. Pakvasa and M. Suzuki, On the hidden charm state at 3872 MeV, Phys. Lett. B 579, 67 (2004).
- E. S. Swanson, Short range structure in the , Phys. Lett. B 588, 189 (2004).
- E. S. Swanson, Diagnostic decays of the , Phys. Lett. B 598, 197 (2004).
- N. A. Tornqvist, Isospin breaking of the narrow charmonium state of Belle at 3872 MeV as a deuson, Phys. Lett. B 590, 209 (2004).
- M. B. Voloshin, Interference and binding effects in decays of possible molecular component of , Phys. Lett. B 579, 316 (2004).
- C.-Y. Wong, Molecular states of heavy quark mesons, Phys. Rev. C 69, 055202 (2004).
- M. T. AlFiky, F. Gabbiani, and A. A. Petrov, : Hadronic molecules in effective field theory, Phys. Lett. B 640, 238 (2006).
- E. Braaten and M. Lu, Operator product expansion in the production and decay of the , Phys. Rev. D 74, 054020 (2006).
- S. Fleming, M. Kusunoki, T. Mehen, and U. van Kolck, Pion interactions in the , Phys. Rev. D 76, 034006 (2007).
- 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).
- Y. Dong, A. Faessler, T. Gutsche, S. Kovalenko, and V. E. Lyubovitskij, as a hadronic molecule and its decays to charmonium states and pions, Phys. Rev. D 79, 094013 (2009).
- I. W. Lee, A. Faessler, T. Gutsche, and V. E. Lyubovitskij, as a molecular state in a potential model, Phys. Rev. D 80, 094005 (2009).
- 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).
- X. Liu, Z.-G. Luo, Y.-R. Liu, and S.-L. Zhu, and other possible heavy molecular states, Eur. Phys. J. C 61, 411 (2009).
- J.-R. Zhang and M.-Q. Huang, molecular states, Phys. Rev. D 80, 056004 (2009).
- D. Gamermann, J. Nieves, E. Oset, and E. Ruiz Arriola, Couplings in coupled channels versus wave functions: Application to the resonance, Phys. Rev. D 81, 014029 (2010).
- T. Mehen and R. Springer, Radiative decays and in effective field theory, Phys. Rev. D 83, 094009 (2011).
- J. Nieves and M. P. Valderrama, Deriving the existence of bound states from the and heavy quark symmetry, Phys. Rev. D 84, 056015 (2011).
- J. Nieves and M. P. Valderrama, The heavy quark spin symmetry partners of the , Phys. Rev. D 86, 056004 (2012).
- N. Li and S.-L. Zhu, , Isospin breaking, Coupled-channel effects and diagnosis of , Phys. Rev. D 86, 074022 (2012).
- 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).
- 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).
- J. He, Study of the bound states in a Bethe-Salpeter approach, Phys. Rev. D 90, 076008 (2014).
- L. Zhao, L. Ma, and S.-L. Zhu, Spin-orbit force, recoil corrections, and possible and molecular states, Phys. Rev. D 89, 094026 (2014).
- F.-K. Guo, C. Hanhart, Y. S. Kalashnikova, U.-G. Meißner, and A. V. Nefediev, What can radiative decays of the teach us about its nature? Phys. Lett. B 742, 394 (2015).
- F. K. Guo, C. Hidalgo-Duque, J. Nieves, A. Ozpineci, and M. P. Valderrama, Detecting the long-distance structure of the , Eur. Phys. J. C 74, 2885 (2014).
- E. Braaten and M. Kusunoki, Low-energy universality and the new charmonium resonance at 3870 MeV, Phys. Rev. D 69, 074005 (2004).
- Q. Wu, D.-Y. Chen, and T. Matsuki, A phenomenological analysis on isospin-violating decay of , Eur. Phys. J. C 81, 193 (2021).
- 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).
- 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).
- Y. S. Kalashnikova and A. V. Nefediev, in the molecular model, Phys. Usp. 62, 568 (2019).
- Y.-b. Dong, A. Faessler, T. Gutsche, and V. E. Lyubovitskij, Estimate for the decay width, Phys. Rev. D 77, 094013 (2008).
- M. Suzuki, The boson: Molecule or charmonium, Phys. Rev. D 72, 114013 (2005).
- L. Maiani, F. Piccinini, A. D. Polosa, and V. Riquer, Diquark-antidiquarks with hidden or open charm and the nature of , Phys. Rev. D 71, 014028 (2005).
- L. Maiani, V. Riquer, F. Piccinini, and A. D. Polosa, Four quark interpretation of , Phys. Rev. D 72, 031502 (2005).
- L. Maiani, A. D. Polosa, and V. Riquer, Indications of a four-quark structure for the and particles from recent Belle and BABAR Data, Phys. Rev. Lett. 99, 182003 (2007).
- K. Terasaki, A new tetra-quark interpretation of , Prog. Theor. Phys. 118, 821 (2007).
- S. Dubnička, A. Z. Dubničková, M. A. Ivanov, and A. Liptaj, Dynamical approach to decays of states, Symmetry 12, 884 (2020).
- Z.-G. Wang, Decipher the width of the via the QCD sum rules, Phys. Rev. D 109, 014017 (2024).
- Z.-G. Wang, Analysis of the hidden-charm tetraquark mass spectrum with the QCD sum rules, Phys. Rev. D 102, 014018 (2020).
- T. Barnes and S. Godfrey, Charmonium options for the , Phys. Rev. D 69, 054008 (2004).
- S. K. Choi et al. (Belle Collaboration), Bounds on the width, mass difference and other properties of decays, Phys. Rev. D 84, 052004 (2011).
- B. Aubert et al. (BABAR Collaboration), Search for a charged partner of the X(3872) in the meson decay , , Phys. Rev. D 71, 031501 (2005).
- D. Gamermann and E. Oset, Isospin breaking effects in the resonance, Phys. Rev. D 80, 014003 (2009).
- K. Abe et al. (Belle Collaboration), Evidence for and the sub-threshold decay , arXiv:hep-ex/0505037.
- Y. Dong, A. Faessler, T. Gutsche, and V. E. Lyubovitskij, and decay modes of the , J. Phys. G 38, 015001 (2011).
- Y. Wang, Q. Wu, G. Li, W.-H. Qin, X.-H. Liu, C.-S. An, and J.-J. Xie, Investigations of charmless decays of via intermediate meson loops, Phys. Rev. D 106, 074015 (2022).
- S. Fleming and T. Mehen, Hadronic decays of the to in effective field theory, Phys. Rev. D 78, 094019 (2008).
- N. N. Achasov and G. N. Shestakov, Tentative estimates of and , Phys. Rev. D 110, 016023 (2024).
- J. P. Lees et al. (BABAR Collaboration), Search for resonances decaying to in two-photon interactions, Phys. Rev. D 86, 092005 (2012).
- V. Baru, J. Haidenbauer, C. Hanhart, Y. Kalashnikova, and A. E. Kudryavtsev, Evidence that the and are not elementary particles, Phys. Lett. B 586, 53 (2004).
- S. Weinberg, Evidence that the deuteron is not an elementary particle, Phys. Rev. 137, B672 (1965).
- F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, and Q. Zhao, Production of the in charmonia radiative decays, Phys. Lett. B 725, 127 (2013).
- P. Colangelo, F. De Fazio, and T. N. Pham, Nonfactorizable contributions in decays to charmonium: The case of , Phys. Rev. D 69, 054023 (2004).
- Q. Wu, Y. Zheng, S. Liu, and G. Li, Investigations on the light hadron decays of and , Phys. Rev. D 107, 034028 (2023).
- Y. Zheng, Z. Cai, G. Li, S. Liu, J. Wu, and Q. Wu, Hidden charmonium decays of spin-2 partner of , Phys. Rev. D 109, 014027 (2024).
- B. Grinstein, E. E. Jenkins, A. V. Manohar, M. J. Savage, and M. B. Wise, Chiral perturbation theory for and , Nucl. Phys. B380, 369 (1992).
- 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).
- S. Ahmed et al. (CLEO Collaboration), First measurement of , Phys. Rev. Lett. 87, 251801 (2001).
- Z.-w. Lin and C. M. Ko, A model for absorption in hadronic matter, Phys. Rev. C 62, 034903 (2000).
- K. L. Haglin, Charmonium dissociation in hadronic matter, Phys. Rev. C 61, 031902 (2000).
- T. Hahn and M. Perez-Victoria, Automatized one loop calculations in four-dimensions and -dimensions, Comput. Phys. Commun. 118, 153 (1999).
- A. Denner, Techniques for calculation of electroweak radiative corrections at the one loop level and results for physics at LEP-200, Fortschr. Phys. 41, 307 (1993).
- H.-Y. Cheng, C.-K. Chua, and A. Soni, Final state interactions in hadronic decays, Phys. Rev. D 71, 014030 (2005).
- Q. Wu, G. Li, F. Shao, and R. Wang, Investigations on the charmless decay modes of and , Phys. Rev. D 94, 014015 (2016).
- X.-D. Guo, D.-Y. Chen, H.-W. Ke, X. Liu, and X.-Q. Li, Study on the rare decays of induced by final state interactions, Phys. Rev. D 93, 054009 (2016).
- T. Mehen, Hadronic loops versus factorization in effective field theory calculations of , Phys. Rev. D 92, 034019 (2015).
- 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 properties, J. High Energy Phys. 08 (2024) 130.
- C. Meng and K.-T. Chao, Decays of the and charmonium, Phys. Rev. D 75, 114002 (2007).
- J. Ferretti and E. Santopinto, Threshold corrections of and states and and transitions of the (3872) in a coupled-channel model, Phys. Lett. B 789, 550 (2019).
- M. Ablikim et al. (BESIII Collaboration), Search for the decay , Phys. Rev. D 109, L071101 (2024).
- M. Ablikim et al. (BESIII Collaboration), Search for and at BESIII, Phys. Rev. D 105, 072009 (2022).