Open Access

Dipionic transitions of $Y (4500)$ to $J / ψ$

Shi-Dong Liu ^1,*, Qi Wu ^2,†, and Gang Li ^1,‡

¹College of Physics and Engineering, Qufu Normal University, Qufu 273165, China
²Institute of Particle and Nuclear Physics, Henan Normal University, Xinxiang 453007, China

^*Contact author: liusd@qfnu.edu.cn
^†Contact author: wuqi@htu.edu.cn
^‡Contact author: gli@qfnu.edu.cn

Phys. Rev. D 112, 074036 – Published 28 October, 2025

DOI: https://doi.org/10.1103/fz1m-3mdg

Abstract

We, using an effective Lagrangian approach, investigated the dipionic transition of the $Y (4500)$ newly well established in the process $e^{+} e^{-} \to K^{+} K^{-} J / ψ$ . In this study, the $Y (4500)$ was considered as a mixture of the $ψ (5 S)$ and $ψ (4 {{}^{3}D}_{1})$ , and its dipionic decay to the $J / ψ$ was assumed to occur via charmed meson loops including box and two kinds of triangle loops. The calculated invariant mass spectra due to the different loop mechanisms exhibit distinct differences. These spectrum patterns are found to be nearly independent of the cutoff parameter, especially for the box and $R$ loops. By means of comparing our calculated results with the future experimental measurements of the $π^{+} π^{-}$ and $π^{\pm} J / ψ$ invariant mass distributions, we could judge which loop mechanism is of more importance in this dipionic transition. The interference among the different kinds of loops is also exhibited. Despite the unknown phase angles between different kinds of loop diagrams, the partial decay width for the process $Y (4500) \to π^{+} π^{-} J / ψ$ is estimated to be 250–700 keV, aligning with the estimation obtained by combining BESIII Collaboration measurements and theoretical predictions for $Y (4500) \to K^{+} K^{-} J / ψ$ . We hope that the present calculations would be tested by the future BESIII or Belle II experiments.

Physics Subject Headings (PhySH)

Article Text

References (100)

Z. Liu and R. E. Mitchell, New hadrons discovered at BESIII, Sci. Bull. 68, 2148 (2023).
T. Gershon (LHCb Collaboration), Exotic hadron naming convention, arXiv:2206.15233.
S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
X. H. Mo, G. Li, C. Z. Yuan, K. L. He, H. M. Hu, J. H. Hu, P. Wang, and Z. Y. Wang, Determining the upper limit of $Γ_{e e}$ for the $Y (4260)$ , Phys. Lett. B 640, 182 (2006).
J.-Z. Wang, D.-Y. Chen, X. Liu, and T. Matsuki, Constructing $J / ψ$ family with updated data of charmoniumlike $Y$ states, Phys. Rev. D 99, 114003 (2019).
J.-Z. Wang, Z.-F. Sun, X. Liu, and T. Matsuki, Higher bottomonium zoo, Eur. Phys. J. C 78, 915 (2018).
M. Ablikim et al. (BESIII Collaboration), Precise measurement of the $e^{+} e^{-} \to π^{+} π^{-} J / ψ$ cross section at center-of-mass energies from 3.77 to 4.60 GeV, Phys. Rev. Lett. 118, 092001 (2017).
J.-H. Chen, J. Chen, F.-K. Guo, Y.-G. Ma, C.-P. Shen, Q.-Y. Shou, Q. Shou, Q. Wang, J.-J. Wu, and B.-S. Zou, Production of exotic hadrons in pp and nuclear collisions, Nucl. Sci. Tech. 36, 55 (2025).
M.-Z. Liu, Y.-W. Pan, Z.-W. Liu, T.-W. Wu, J.-X. Lu, and L.-S. Geng, Three ways to decipher the nature of exotic hadrons: Multiplets, three-body hadronic molecules, and correlation functions, Phys. Rep. 1108, 1 (2025).
H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, The hidden-charm pentaquark and tetraquark states, Phys. Rep. 639, 1 (2016).
H.-X. Chen, W. Chen, X. Liu, Y.-R. Liu, and S.-L. Zhu, An updated review of the new hadron states, Rep. Prog. Phys. 86, 026201 (2022).
L. Meng, B. Wang, G.-J. Wang, and S.-L. Zhu, Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules, Phys. Rep. 1019, 1 (2023).
M. Ablikim et al. (BESIII Collaboration), Future physics programme of BESIII, Chin. Phys. C 44, 040001 (2020).
F.-K. Guo, X.-H. Liu, and S. Sakai, Threshold cusps and triangle singularities in hadronic reactions, Prog. Part. Nucl. Phys. 112, 103757 (2020).
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).
Y.-R. Liu, H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, Pentaquark and tetraquark states, Prog. Part. Nucl. Phys. 107, 237 (2019).
F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, and B.-S. Zou, Hadronic molecules, Rev. Mod. Phys. 90, 015004 (2018).
X. Liu, An overview of $X Y Z$ new particles, Chin. Sci. Bull. 59, 3815 (2014).
Z.-G. Wang, Review of the QCD sum rules for exotic states, Front. Phys. (Beijing) 21, 016300 (2025).
B. Aubert et al. (BABAR Collaboration, Observation of a broad structure in the $π^{+} π^{-} J / ψ$ mass spectrum around $4.26 − GeV / c^{2}$ , Phys. Rev. Lett. 95, 142001 (2005).
T. Coan, Y. Gao, F. Liu et al. (CLEO Collaboration), Charmonium decays of $Y (4260)$ , $ψ (4160)$ , and $ψ (4040)$ , Phys. Rev. Lett. 96, 162003 (2006).
C. Z. Yuan et al. (Belle Collaboration), Measurement of $e^{+} e^{-} \to π^{+} π^{-} J / ψ$ cross-section via initial state radiation at Belle, Phys. Rev. Lett. 99, 182004 (2007).
M. Ablikim et al. (BESIII Collaboration), Observation of the $Y (4230)$ and a new structure in $e^{+} e^{-} \to K^{+} K^{-} J / ψ$ , Chin. Phys. C 46, 111002 (2022).
M. Ablikim, M. N. Achasov, P. A. Adlarson et al. (BESIII Collaboration), Study of the resonance structures in $e^{+} e^{-} \to π^{+} π^{-} J / ψ$ process, Phys. Rev. D 106, 072001 (2022).
M. Ablikim, M. Achasov, P. Adlarson et al. (BESIII Collaboration), Observation of three charmoniumlike states with $J^{P C} = 1^{- -}$ in $e^{+} e^{-} \to D^{* 0} D^{* -} π^{+}$ , Phys. Rev. Lett. 130, 121901 (2023).
S.-L. Zhu, The possible interpretations of $Y (4260)$ , Phys. Lett. B 625, 212 (2005).
S. Dubnička, A. Dubničková, A. Issadykov, M. Ivanov, and A. Liptaj, $Y (4260)$ as a four-quark state, Phys. Rev. D 101, 094030 (2020).
Z.-G. Wang, Analysis of the vector tetraquark states with P-waves between the diquarks and antidiquarks via the QCD sum rules, Eur. Phys. J. C 79, 29 (2019).
Z.-G. Wang, Lowest vector tetraquark states: $Y (4260 / 4220)$ or $Z_{c} (4100)$ , Eur. Phys. J. C 78, 933 (2018).
T.-W. Chiu and T.-H. Hsieh (TWQCD Collaboration), $Y (4260)$ on the lattice, Phys. Rev. D 73, 094510 (2006).
C. Z. Yuan, P. Wang, and X. H. Mo, The $Y (4260)$ as an $ω χ_{c 1}$ molecular state, Phys. Lett. B 634, 399 (2006).
R. M. Albuquerque and M. Nielsen, QCD sum rules study of the $J^{P C} = 1^{- -}$ charmonium $Y$ mesons, Nucl. Phys. A815, 53 (2009).
G.-J. Ding, Are $Y (4260)$ and $Z_{2}^{+} (4250) D_{1} D$ or $D_{0} D^{*}$ hadronic molecules?, Phys. Rev. D 79, 014001 (2009).
F. Close, C. Downum, and C. E. Thomas, Novel charmonium and bottomonium spectroscopies due to deeply bound hadronic molecules from single pion exchange, Phys. Rev. D 81, 074033 (2010).
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).
G. Li and X.-H. Liu, Investigating possible decay modes of $Y (4260)$ under $D_{1} (2420) \bar{D} + c . c .$ molecular state ansatz, Phys. Rev. D 88, 094008 (2013).
X.-H. Liu and G. Li, Exploring the threshold behavior and implications on the nature of $Y (4260)$ and $Z_{c} (3900)$ , Phys. Rev. D 88, 014013 (2013).
Q. Wang, C. Hanhart, and Q. Zhao, Decoding the riddle of $Y (4260)$ and $Z_{c} (3900)$ , Phys. Rev. Lett. 111, 132003 (2013).
M. Cleven, Q. Wang, F.-K. Guo, C. Hanhart, U.-G. Meißner, and Q. Zhao, $Y (4260)$ as the first $S$ -wave open charm vector molecular state?, Phys. Rev. D 90, 074039 (2014).
F.-Z. Peng, M.-J. Yan, M. S. Sánchez, and M. P. Valderrama, Light- and heavy-quark symmetries and the $Y (4230)$ , $Y (4360)$ , $Y (4500)$ , $Y (4620)$ and $X (4630)$ resonances, Phys. Rev. D 107, 016001 (2023).
X.-K. Dong, Y.-H. Lin, and B.-S. Zou, Prediction of an exotic state around 4240 MeV with $J^{P C} = 1^{- +}$ as C-parity partner of $Y (4260)$ in molecular picture, Phys. Rev. D 101, 076003 (2020).
M. Cleven and Q. Zhao, Cross section line shape of $e^{+} e^{-} \to χ_{c 0} ω$ around the $Y (4260)$ mass region, Phys. Lett. B 768, 52 (2017).
G. Li, C.-S. An, P.-Y. Li, D. Liu, X. Zhang, and Z. Zhou, Investigations on the charmless decays of $Y (4260)$ , Chin. Phys. C 39, 063102 (2015).
C.-F. Qiao, One explanation for the exotic state $Y (4260)$ , Phys. Lett. B 639, 263 (2006).
Y.-H. Chen, L.-Y. Dai, F.-K. Guo, and B. Kubis, Nature of the $Y (4260)$ : A light-quark perspective, Phys. Rev. D 99, 074016 (2019).
H.-f. Fu and L. Jiang, Coupled-channel-induced $S - D$ mixing of charmonia and testing possible assignments for $Y (4260)$ and $Y (4360)$ , Eur. Phys. J. C 79, 460 (2019).
D.-Y. Chen, J. He, and X. Liu, Nonresonant explanation for the $Y (4260)$ structure observed in the $e^{+} e^{-} \to J / ψ π^{+} π^{-}$ process, Phys. Rev. D 83, 054021 (2011).
X.-H. Liu, Influence of threshold effects induced by charmed meson rescattering, Phys. Rev. D 90, 074004 (2014).
M. Ablikim, M. Achasov, P. Adlarson et al. (BESIII Collaboration), Observation of a Vector Charmoniumlike State at $4.7 GeV / c^{2}$ and Search for $Z_{c s}$ in $e^{+} e^{-} \to K^{+} K^{-} J / ψ$ , Phys. Rev. Lett. 131, 211902 (2023).
M. Ablikim et al. (BESIII Collaboration), Precise measurement of the $e^{+} e^{-} \to D_{s}^{* +} D_{s}^{* -}$ cross sections at center-of-mass energies from threshold to 4.95 GeV, Phys. Rev. Lett. 131, 151903 (2023).
M. Ablikim, M. N. Achasov, P. A. Adlarson et al. (BESIII Collaboration), Observation of structures in the processes $e^{+} e^{-} \to ω χ_{c 1}$ and $ω χ_{c 2}$ , Phys. Rev. Lett. 132, 161901 (2024).
M. Ablikim et al. (BESIII Collaboration), Observation of three resonant structures in the cross section of $e^{+} e^{-} \to π^{+} π^{-} h_{c}$ , Phys. Rev. Lett. 135, 071901 (2025).
Q. Deng, R.-H. Ni, Q. Li, and X.-H. Zhong, Charmonia in an unquenched quark model, Phys. Rev. D 110, 056034 (2024).
X.-K. Dong, F.-K. Guo, and B.-S. Zou, A survey of heavy-antiheavy hadronic molecules, Progr. Phys. 41, 65 (2021).
Z.-G. Wang, Analysis of the decay $Y (4500) \to D^{*} D^{-} π$ with the light-cone QCD sum rules, Nucl. Phys. B993, 116265 (2023).
Z.-G. Wang, Strong decays of the vector tetraquark states with the masses about 4.5 GeV via the QCD sum rules, Nucl. Phys. B1005, 116580 (2024).
J.-Z. Wang and X. Liu, Confirming the existence of a new higher charmonium $ψ (4500)$ by the newly released data of $e^{+} e^{-} \to K^{+} K^{-} J / ψ$ , Phys. Rev. D 107, 054016 (2023).
M. Ablikim, M. N. Achasov, S. A. N. Ahmed et al. (BESIII Collaboration), Measurement of $e^{+} e^{-} \to K \bar{K} J / ψ$ cross sections at center-of-mass energies from 4.189 to 4.600 GeV, Phys. Rev. D 97, 071101 (2018).
T.-M. Yan, Hadronic transitions between heavy quark states in quantum chromodynamics, Phys. Rev. D 22, 1652 (1980).
Y.-P. Kuang and T.-M. Yan, Predictions for hadronic transitions in the $b \bar{b}$ system, Phys. Rev. D 24, 2874 (1981).
B. Wang, H. Xu, X. Liu, D.-Y. Chen, S. Coito, and E. Eichten, Using $X (3823) \to J / ψ π^{+} π^{-}$ to identify coupled-channel effects, Front. Phys. (Beijing) 11, 111402 (2016).
Z.-S. Jia, Z.-H. Zhang, W.-H. Qin, and G. Li, Hunting for $X_{b}$ via hidden bottomonium decays $X_{b} \to π π χ_{b J}$ , Phys. Rev. D 109, 034017 (2024).
S.-D. Liu, F. Wang, Z.-S. Jia, G. Li, X.-H. Liu, and J.-J. Xie, Pionic transitions of the spin-2 partner of $X (3872)$ to $χ_{c J}$ , Phys. Rev. D 110, 054048 (2024).
Y.-H. Chen, Predictions of $ϒ (4 S) \to h_{b} (1 P, 2 P) π^{+} π^{-}$ transitions, Chin. Phys. C 44, 023103 (2020).
Y.-H. Chen, M. Cleven, J. T. Daub, F.-K. Guo, C. Hanhart, B. Kubis, U.-G. Meißner, and B.-S. Zou, Effects of $Z_{b}$ states and bottom meson loops on $ϒ (4 S) \to ϒ (1 S, 2 S) π^{+} π^{-}$ transitions, Phys. Rev. D 95, 034022 (2017).
A. M. Badalian, B. L. G. Bakker, and I. V. Danilkin, The $S - D$ mixing and di-electron widths of higher charmonium $1^{- -}$ states, Phys. At. Nucl. 72, 638 (2009).
T. Barnes, S. Godfrey, and E. S. Swanson, Higher charmonia, Phys. Rev. D 72, 054026 (2005).
D. Ebert, R. N. Faustov, and V. O. Galkin, Spectroscopy and regge trajectories of heavy quarkonia and bcmesons, Eur. Phys. J. C 71, 1825 (2011).
L.-C. Gui, L.-S. Lu, Q.-F. Lü, X.-H. Zhong, and Q. Zhao, Strong decays of higher charmonium states into open-charm meson pairs, Phys. Rev. D 98, 016010 (2018).
W.-J. Deng, H. Liu, L.-C. Gui, and X.-H. Zhong, Charmonium spectrum and electromagnetic transitions with higher multipole contributions, Phys. Rev. D 95, 034026 (2017).
D.-Y. Chen and X. Liu, Predicted charged charmoniumlike structures in the hidden-charm dipion decay of higher charmonia, Phys. Rev. D 84, 034032 (2011).
D.-Y. Chen, X. Liu, and T. Matsuki, Predictions of charged charmoniumlike structures with hidden-charm and open-strange channels, Phys. Rev. Lett. 110, 232001 (2013).
M. N. Anwar, Y. Lu, and B.-S. Zou, Modeling charmonium- $η$ decays of $J^{P C} = 1^{- -}$ higher charmonia, Phys. Rev. D 95, 114031 (2017).
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).
P. Colangelo, F. De Fazio, and T. Pham, Nonfactorizable contributions in b decays to charmonium: The case of $B^{-} \to K^{-} h_{c}$ , Phys. Rev. D 69, 054023 (2004).
A. Deandrea, G. Nardulli, and A. D. Polosa, $J / ψ$ couplings to charmed resonances and to $π$ , Phys. Rev. D 68, 034002 (2003).
A. M. Badalian, B. L. G. Bakker, and I. V. Danilkin, Dielectron widths of the $S$ -, $D$ -vector bottomonium states, Phys. At. Nucl. 73, 138 (2010).
G. Li, F.-l. Shao, C.-W. Zhao, and Q. Zhao, $Z_{b} / Z_{b}^{'} \to ϒ π$ and $h_{b} π$ decays in intermediate meson loops model, Phys. Rev. D 87, 034020 (2013).
S. Liu, Z. Cai, Z. Jia, G. Li, and J. Xie, Hidden-bottom hadronic transitions of $ϒ (10753)$ , Phys. Rev. D 109, 014039 (2024).
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).
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).
C. Isola, M. Ladisa, G. Nardulli, and P. Santorelli, Charming penguin contributions in $B \to K^{*} π, K (ρ, ω, ϕ)$ decays, Phys. Rev. D 68, 114001 (2003).
C. Meng and K.-T. Chao, Peak shifts due to $B^{(*)} - {\bar{B}}^{(*)}$ rescattering in $ϒ (5 S)$ dipion transitions, Phys. Rev. D 78, 034022 (2008).
Z.-Y. Bai, Y.-S. Li, Q. Huang, X. Liu, and T. Matsuki, $ϒ (10753) \to ϒ (n S) π^{+} π^{-}$ decays induced by hadronic loop mechanism, Phys. Rev. D 105, 074007 (2022).
D.-Y. Chen, J. He, X.-Q. Li, and X. Liu, Dipion invariant mass distribution of the anomalous $ϒ (1 S) π^{+} π^{-}$ and $ϒ (2 S) π^{+} π^{-}$ production near the peak of $ϒ (10860)$ , Phys. Rev. D 84, 074006 (2011).
D.-Y. Chen, X. Liu, and T. Matsuki, Search for missing $ψ (4 S)$ in the $e^{+} e^{-} \to π^{+} π^{-} ψ (2 S)$ process, Phys. Rev. D 93, 034028 (2016).
K. F. Chen et al. (Belle Collaboration), Observation of anomalous $ϒ (1 S) π^{+} π^{-}$ and $ϒ (2 S) π^{+} π^{-}$ production near the $ϒ (5 S)$ resonance, Phys. Rev. Lett. 100, 112001 (2008).
Y. Oh, T. Song, and S. H. Lee, $J / ψ$ absorption by $π$ and $ρ$ mesons in a meson exchange model with anomalous parity interactions, Phys. Rev. C 63, 034901 (2001).
Z. Lin and C. M. Ko, Model for $J / ψ$ absorption in hadronic matter, Phys. Rev. C 62, 034903 (2000).
M. P. Locher, Y. Lu, and B. S. Zou, Rates for the reactions $\bar{p} p \to π ϕ$ and $γ ϕ$ , Z. Phys. A 347, 281 (1994).
X.-Q. Li, D. V. Bugg, and B.-S. Zou, Possible explanation of the “ $ρ π$ puzzle” in $J / ψ$ , $ψ^{'}$ decays, Phys. Rev. D 55, 1421 (1997).
H.-Y. Cheng, C.-K. Chua, and A. Soni, Final state interactions in hadronic $B$ decays, Phys. Rev. D 71, 014030 (2005).
R. Mertig, M. Böhm, and A. Denner, Feyn calc—computer-algebraic calculation of Feynman amplitudes, Comput. Phys. Commun. 64, 345 (1991).
V. Shtabovenko, R. Mertig, and F. Orellana, feyncalc 9.3: New features and improvements, Comput. Phys. Commun. 256, 107478 (2020).
T. Hahn and M. Perez-Victoria, Automatized one-loop calculations in 4 and d dimensions, Comput. Phys. Commun. 118, 153 (1999).
M. Ablikim, M. Achasov, X. Ai et al. (BESIII Collaboration), Observation of a charged charmoniumlike structure in $e^{+} e^{-} \to π^{+} π^{-} J / ψ$ at $\sqrt{s} = 4.26 GeV$ , Phys. Rev. Lett. 110, 252001 (2013).
D.-Y. Chen, X. Liu, and T. Matsuki, Reproducing the $Z_{c} (3900)$ structure through the initial-single-pion-emission mechanism, Phys. Rev. D 88, 036008 (2013).
M. Ablikim et al. (BES Collaboration), Production of sigma in $ψ (2 S) \to π^{+} π^{-} J / ψ$ , Phys. Lett. B 645, 19 (2007).
D. Cronin-Hennessy et al. (CLEO Collaboration), Study of di-pion transitions among $ϒ (3 S)$ , $ϒ (2 S)$ , and $ϒ (1 S)$ states, Phys. Rev. D 76, 072001 (2007).
C. Meng and K.-T. Chao, Scalar resonance contributions to the dipion transition rates of $ϒ (4 S, 5 S)$ in the re-scattering model, Phys. Rev. D 77, 074003 (2008).

Phys. Rev. D 112, 074036– Published 28 October, 2025

Vol. 112, Iss. 7 — 1 October 2025

Received 24 April 2025
Accepted 9 October 2025

DOI: https://doi.org/10.1103/fz1m-3mdg

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physical Review D

Reuse & Permissions

Export citation

Export citation

Dipionic transitions of $Y (4500)$ to $J / ψ$

Abstract

Physics Subject Headings (PhySH)

Article Text

References (100)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

Dipionic transitions of Y(4500) to J/ψ

Abstract

Physics Subject Headings (PhySH)

Article Text

References (100)

Dipionic transitions of $Y (4500)$ to $J / ψ$