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Dispersive analysis of the J/ψ→π0γ* transition form factor with ρ–ω mixing effects

Xiong-Hui Cao1,*, Feng-Kun Guo1,2,†, Christoph Hanhart3,‡, and Bastian Kubis4,§

  • *Contact author: xhcao@itp.ac.cn
  • †Contact author: fkguo@itp.ac.cn
  • ‡Contact author: c.hanhart@fz-juelich.de
  • §Contact author: kubis@hiskp.uni-bonn.de
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Phys. Rev. D 113, 074030 – Published 27 April, 2026

DOI: https://doi.org/10.1103/gmj6-hd9j

Abstract

Motivated by the discrepancies noted recently between the theoretical predictions of the electromagnetic J/ψ→π0γ* transition form factor and the BESIII data, we reanalyze this transition form factor using the dispersive Khuri-Treiman equations, with final-state interactions in both the direct channel and the crossed channels properly considered. This improved framework incorporates ρ–ω mixing effects. The effect of four-pion states is evaluated through a dispersively improved vector-meson-dominance model. From this information, we propose a two-parameter fit that provides an excellent description of the BESIII data over the broad energy range from 0 to 2.8 GeV. We demonstrate that the ρπ0 decay mode of the J/ψ is dominated by strong interaction, while the ωπ0 mode is dominated by one-photon exchange. From this, we extract the relative phase between the strong and the one-virtual-photon (electromagnetic) modes in hadronic decays of J/ψ as (62±21)°. This could provide useful information in understanding the long-standing ρπ puzzle in J/ψ decays.

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References (102)

  1. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  2. D. Besson et al. (CLEO Collaboration), Inclusive radiative J/ψ decays, Phys. Rev. D 78, 032012 (2008).
  3. M. Ablikim et al. (BESIII Collaboration), Observation of electromagnetic Dalitz decays J/ψ→Pe+e−, Phys. Rev. D 89, 092008 (2014).
  4. J. J. Sakurai, Theory of strong interactions, Ann. Phys. (N.Y.) 11, 1 (1960).
  5. J. Fu, H.-B. Li, X. Qin, and M.-Z. Yang, Study of the electromagnetic transitions J/ψ→Pl+l− and probe dark photon, Mod. Phys. Lett. A 27, 1250223 (2012).
  6. Q. Zhao, Understanding the radiative decays of vector charmonia to light pseudoscalar mesons, Phys. Lett. B 697, 52 (2011).
  7. Y.-H. Chen, Z.-H. Guo, and B.-S. Zou, Unified study of J/ψ→PV, Pγ(*) and light hadron radiative processes, Phys. Rev. D 91, 014010 (2015).
  8. L.-W. Yan, Y.-H. Chen, C.-G. Duan, and Z.-H. Guo, Effective-Lagrangian study of ψ′(J/ψ)→VP and the insights into the ρπ puzzle, Phys. Rev. D 107, 034022 (2023).
  9. X. Jiang, F. Chen, Y. Chen, M. Gong, N. Li, Z. Liu, W. Sun, and R. Zhang, Radiative decay width of J/ψ→γη(2) from Nf=2 lattice QCD, Phys. Rev. Lett. 130, 061901 (2023).
  10. C. Shi, Y. Chen, X. Jiang, M. Gong, Z. Liu, and W. Sun, Form factor for Dalitz decays from J/ψ to light pseudoscalars, Chin. Phys. C 48, 113105 (2024).
  11. M. Batelaan, J. J. Dudek, and R. G. Edwards, η and η′ meson production in J/ψ radiative decays from lattice QCD, Phys. Rev. D 112, 074505 (2025).
  12. M. Batelaan, J. J. Dudek, and R. G. Edwards, η and η′ production in J/ψ radiative decays from quantum chromodynamics, Phys. Rev. Lett. 135, 161904 (2025).
  13. S. Holz, C. Hanhart, M. Hoferichter, and B. Kubis, A dispersive analysis of η′→π+π−γ and η′→ℓ+ℓ−γ, Eur. Phys. J. C 82, 434 (2022); 82, 1159(A) (2022).
  14. R. Aliberti et al., The anomalous magnetic moment of the muon in the standard model: An update, Phys. Rep. 1143, 1 (2025).
  15. M. Ablikim et al. (BESIII Collaboration), Study of the electromagnetic Dalitz decay J/ψ→e+e−π0, Phys. Rev. D 112, L011101 (2025).
  16. B. Kubis and F. Niecknig, Analysis of the J/ψ→π0γ* transition form factor, Phys. Rev. D 91, 036004 (2015).
  17. N. N. Khuri and S. B. Treiman, Pion-pion scattering and K±→3π decay, Phys. Rev. 119, 1115 (1960).
  18. L. G. Landsberg, Electromagnetic decays of light mesons, Phys. Rep. 128, 301 (1985).
  19. T. W. B. Kibble, Kinematics of general scattering processes and the Mandelstam representation, Phys. Rev. 117, 1159 (1960).
  20. M. Jacob and G. C. Wick, On the general theory of collisions for particles with spin, Ann. Phys. (N.Y.) 7, 404 (1959).
  21. J. A. Oller, A Brief Introduction to Dispersion Relations, Springer Briefs in Physics (Springer, Cham, 2019), 10.1007/978-3-030-13582-9.
  22. D.-L. Yao, L.-Y. Dai, H.-Q. Zheng, and Z.-Y. Zhou, A review on partial-wave dynamics with chiral effective field theory and dispersion relation, Rep. Prog. Phys. 84, 076201 (2021).
  23. G. Köpp, Dispersion calculation of the transition form-factor Fπωγ(t) with cut contributions, Phys. Rev. D 10, 932 (1974).
  24. V. A. Matveev, R. M. Muradian, and A. N. Tavkhelidze, Automodellism in the large–angle elastic scattering and structure of hadrons, Lett. Nuovo Cimento 7, 719 (1973).
  25. S. J. Brodsky and G. R. Farrar, Scaling laws at large transverse momentum, Phys. Rev. Lett. 31, 1153 (1973).
  26. S. J. Brodsky and G. R. Farrar, Scaling laws for large momentum transfer processes, Phys. Rev. D 11, 1309 (1975).
  27. G. P. Lepage and S. J. Brodsky, Exclusive processes in quantum chromodynamics: Evolution equations for hadronic wave functions and the form-factors of mesons, Phys. Lett. 87B, 359 (1979).
  28. G. P. Lepage and S. J. Brodsky, Exclusive processes in perturbative quantum chromodynamics, Phys. Rev. D 22, 2157 (1980).
  29. S.-S. Fang, B. Kubis, and A. Kupść, What can we learn about light-meson interactions at electron–positron colliders?, Prog. Part. Nucl. Phys. 120, 103884 (2021).
  30. F.-K. Guo, U.-G. Meißner, and W. Wang, On the constituent counting rule for hard exclusive processes involving multi-quark states, Chin. Phys. C 41, 053108 (2017).
  31. P. Guo, R. Mitchell, and A. P. Szczepaniak, The role of P-wave inelasticity in J/ψ→π+π−π0, Phys. Rev. D 82, 094002 (2010).
  32. R. Omnès, On the solution of certain singular integral equations of quantum field theory, Nuovo Cimento 8, 316 (1958).
  33. H. Leutwyler, Electromagnetic form-factor of the pion, in Continuous Advances in QCD 2002/ARKADYFEST (Honoring the 60th Birthday of Professor Arkady Vainshtein) (2002), pp. 23–40, arXiv:hep-ph/0212324.
  34. B. Ananthanarayan, I. Caprini, and I. S. Imsong, Implications of the recent high statistics determination of the pion electromagnetic form factor in the timelike region, Phys. Rev. D 83, 096002 (2011).
  35. S. P. Schneider, B. Kubis, and F. Niecknig, The ω→π0γ* and ϕ→π0γ* transition form factors in dispersion theory, Phys. Rev. D 86, 054013 (2012).
  36. J. R. Peláez, P. Rabán, and J. Ruiz de Elvira, Global parametrizations of ππ scattering with dispersive constraints: Beyond the S0 wave, Phys. Rev. D 111, 074003 (2025).
  37. P. Roig, Hadronic Currents for τ−→π−π0ντ and other decays of interest in TAUOLA, Nucl. Phys. B, Proc. Suppl. 225–227, 161 (2012).
  38. S. Gonzàlez-Solís and P. Roig, A dispersive analysis of the pion vector form factor and τ−→K−KSντ decay, Eur. Phys. J. C 79, 436 (2019).
  39. E. Ruiz Arriola and P. Sánchez-Puertas, Phase of the electromagnetic form factor of the pion, Phys. Rev. D 110, 054003 (2024).
  40. B. Moussallam, Nf dependence of the quark condensate from a chiral sum rule, Eur. Phys. J. C 14, 111 (2000).
  41. F.-K. Guo, C. Hanhart, F. J. Llanes-Estrada, and U.-G. Meißner, Quark mass dependence of the pion vector form factor, Phys. Lett. B 678, 90 (2009).
  42. G. Colangelo, M. Hoferichter, and P. Stoffer, Two-pion contribution to hadronic vacuum polarization, J. High Energy Phys. 02 (2019) 006.
  43. A. P. Szczepaniak and M. R. Pennington, Application of the Veneziano model in charmonium Dalitz plot analysis, Phys. Lett. B 737, 283 (2014).
  44. M. Albaladejo et al. (JPAC Collaboration), Khuri-Treiman analysis of J/ψ→π+π−π0, Phys. Rev. D 108, 014035 (2023).
  45. S. M. Roy, Exact integral equation for pion pion scattering involving only physical region partial waves, Phys. Lett. 36B, 353 (1971).
  46. X.-H. Cao, Q.-Z. Li, Z.-H. Guo, and H.-Q. Zheng, Roy equation analyses of ππ scatterings at unphysical pion masses, Phys. Rev. D 108, 034009 (2023).
  47. A. Rodas, J. J. Dudek, and R. G. Edwards (Hadron Spectrum Collaboration), Determination of crossing-symmetric ππ scattering amplitudes and the quark mass evolution of the σ constrained by lattice QCD, Phys. Rev. D 109, 034513 (2024).
  48. X.-H. Cao, F.-K. Guo, Z.-H. Guo, and Q.-Z. Li, Rigorous Roy-Steiner equation analysis of πK scattering at unphysical quark masses, Phys. Rev. D 112, L031503 (2025).
  49. X.-H. Cao, F.-K. Guo, Z.-H. Guo, and Q.-Z. Li, Revisiting Roy-Steiner-equation analysis of pion-kaon scattering from lattice QCD data, Phys. Rev. D 112, 034042 (2025).
  50. M. Albaladejo, N. Sherrill, C. Fernández-Ramírez, A. Jackura, V. Mathieu, M. Mikhasenko, J. Nys, A. Pilloni, and A. P. Szczepaniak (JPAC Collaboration), Khuri–Treiman equations for ππ scattering, Eur. Phys. J. C 78, 574 (2018).
  51. F. Niecknig, B. Kubis, and S. P. Schneider, Dispersive analysis of ω→3π and ϕ→3π decays, Eur. Phys. J. C 72, 2014 (2012).
  52. M. Hoferichter, B. Kubis, and D. Sakkas, Extracting the chiral anomaly from γπ→ππ, Phys. Rev. D 86, 116009 (2012).
  53. I. V. Danilkin, C. Fernández-Ramírez, P. Guo, V. Mathieu, D. Schott, M. Shi, and A. P. Szczepaniak, Dispersive analysis of ω/ϕ→3π,πγ*, Phys. Rev. D 91, 094029 (2015).
  54. J. Stern, H. Sazdjian, and N. H. Fuchs, What π−π scattering tells us about chiral perturbation theory, Phys. Rev. D 47, 3814 (1993).
  55. M. Knecht, B. Moussallam, J. Stern, and N. H. Fuchs, The low-energy ππ amplitude to one and two loops, Nucl. Phys. B457, 513 (1995).
  56. J. Bijnens and K. Ghorbani, η→3π at two loops in chiral perturbation theory, J. High Energy Phys. 11 (2007) 030.
  57. M. Zdráhal and J. Novotný, Dispersive approach to chiral perturbation theory, Phys. Rev. D 78, 116016 (2008).
  58. D. Stamen, T. Isken, B. Kubis, M. Mikhasenko, and M. Niehus, Analysis of rescattering effects in 3π final states, Eur. Phys. J. C 83, 510 (2023); 83, 586(E) (2023).
  59. O. Babelon, J. L. Basdevant, D. Caillerie, and G. Mennessier, Unitarity and inelastic final state interactions, Nucl. Phys. B113, 445 (1976).
  60. M. Albaladejo, I. Danilkin, S. Gonzàlez-Solís, D. Winney, C. Fernández-Ramírez, A. N. H. Blin, V. Mathieu, M. Mikhasenko, A. Pilloni, and A. Szczepaniak (JPAC Collaboration), ω→3π and ωπ0 transition form factor revisited, Eur. Phys. J. C 80, 1107 (2020).
  61. A. García-Lorenzo, M. Albaladejo, S. Gonzàlez-Solís, N. Hammoud, V. Mathieu, G. Montaña, A. Pilloni, D. Winney, and A. P. Szczepaniak (JPAC Collaboration), ϕ→3π and ϕπ0 transition form factor from Khuri-Treiman equations, arXiv:2505.15309.
  62. J. Kambor, C. Wiesendanger, and D. Wyler, Final state interactions and Khuri-Treiman equations in η→3π decays, Nucl. Phys. B 465, 215 (1996).
  63. J. B. Bronzan and C. Kacser, Khuri-Treiman representation and perturbation theory, Phys. Rev. 132, 2703 (1963).
  64. I. J. R. Aitchison and R. Pasquier, Three-body unitarity and Khuri-Treiman amplitudes, Phys. Rev. 152, 1274 (1966).
  65. J. Gasser and A. Rusetsky, Solving integral equations in η→3π, Eur. Phys. J. C 78, 906 (2018).
  66. M. Niehus, M. Hoferichter, and B. Kubis, The γπ→ππ anomaly from lattice QCD and dispersion relations, J. High Energy Phys. 12 (2021) 038.
  67. S. P. Schneider, Analysis tools for precision studies of hadronic three-body decays and transition form factors, Ph.D. thesis, Bonn University, HISKP, 2012, https://bonndoc.ulb.uni-bonn.de/xmlui/handle/20.500.11811/5628.
  68. F. Niecknig and B. Kubis, Dispersion-theoretical analysis of the D+→K−π+π+ Dalitz plot, J. High Energy Phys. 10 (2015) 142.
  69. F. Niecknig, Dispersive analysis of charmed meson decays, Ph.D. thesis, Bonn University, HISKP, 2016, https://bonndoc.ulb.uni-bonn.de/xmlui/handle/20.500.11811/6854.
  70. M. Albaladejo, D. Winney, I. V. Danilkin, C. Fernández-Ramírez, V. Mathieu, M. Mikhasenko, A. Pilloni, J. A. Silva-Castro, and A. P. Szczepaniak (JPAC Collaboration), Khuri-Treiman equations for 3π decays of particles with spin, Phys. Rev. D 101, 054018 (2020).
  71. T. P. Leplumey and P. Stoffer, Dispersive analysis of the pion vector form factor without zeros, arXiv:2501.09643.
  72. M. Zanke, M. Hoferichter, and B. Kubis, On the transition form factors of the axial-vector resonance f1(1285) and its decay into e+e−, J. High Energy Phys. 07 (2021) 106.
  73. H. Yan, M. Mai, M. Garofalo, U.-G. Meißner, C. Liu, L. Liu, and C. Urbach, ω meson from lattice QCD, Phys. Rev. Lett. 133, 211906 (2024).
  74. V. Bernard, N. Kaiser, and U.-G. Meißner, Nucleon electroweak form-factors: Analysis of their spectral functions, Nucl. Phys. A611, 429 (1996).
  75. N. Kaiser and E. Passemar, Spectral functions of nucleon form factors: Three-pion continua at low energies, Eur. Phys. J. A 55, 16 (2019).
  76. J. P. Lees et al. (BABAR Collaboration), Study of the process e+e−→π+π−π0 using initial state radiation with BABAR, Phys. Rev. D 104, 112003 (2021).
  77. M. Hoferichter, B.-L. Hoid, B. Kubis, and D. Schuh, Isospin-breaking effects in the three-pion contribution to hadronic vacuum polarization, J. High Energy Phys. 08 (2023) 208.
  78. M. Hoferichter, B. Kubis, J. Ruiz de Elvira, H.-W. Hammer, and U.-G. Meißner, On the ππ continuum in the nucleon form factors and the proton radius puzzle, Eur. Phys. J. A 52, 331 (2016).
  79. K. Nakano, Two potential formalisms and the coulomb-nuclear interfrerence, Phys. Rev. C 26, 1123 (1982).
  80. C. Hanhart, A new parameterization for the pion vector form factor, Phys. Lett. B 715, 170 (2012).
  81. S. Ropertz, C. Hanhart, and B. Kubis, A new parametrization for the scalar pion form factors, Eur. Phys. J. C 78, 1000 (2018).
  82. L. von Detten, F. Noël, C. Hanhart, M. Hoferichter, and B. Kubis, On the scalar πK form factor beyond the elastic region, Eur. Phys. J. C 81, 420 (2021).
  83. L. A. Heuser, G. Chanturia, F.-K. Guo, C. Hanhart, M. Hoferichter, and B. Kubis, From pole parameters to line shapes and branching ratios, Eur. Phys. J. C 84, 599 (2024).
  84. J. Gasser and H. Leutwyler, Quark masses, Phys. Rep. 87, 77 (1982).
  85. R. Urech, ρ0–ω mixing in chiral perturbation theory, Phys. Lett. B 355, 308 (1995).
  86. G. Colangelo, M. Hoferichter, B. Kubis, and P. Stoffer, Isospin-breaking effects in the two-pion contribution to hadronic vacuum polarization, J. High Energy Phys. 10 (2022) 032.
  87. J. M. Dias, T. Ji, X.-K. Dong, F.-K. Guo, C. Hanhart, U.-G. Meißner, Y. Zhang, and Z.-H. Zhang, Dispersive analysis of the isospin breaking in the X(3872)→J/ψπ+π− and X(3872)→J/ψπ+π0π− decays, Phys. Rev. D 111, 014031 (2025).
  88. H.-J. Jing, X.-H. Cao, and F.-K. Guo, Discontinuity calculus and applications to two-body coupled-channel scattering, Front. Phys. (Beijing) 21, 056201 (2026).
  89. I. J. R. Aitchison and C. Kacser, Complex propagators in perturbation theory, Phys. Rev. 133, B1239 (1964).
  90. C. A. Dominguez, Pion form-factor in large Nc QCD, Phys. Lett. B 512, 331 (2001).
  91. J. P. Lees et al. (BABAR Collaboration), Precise measurement of the e+e−→π+π−(γ) cross section with the initial-state radiation method at BABAR, Phys. Rev. D 86, 032013 (2012).
  92. M. N. Achasov et al., Updated measurement of the e+e−→ωπ0→π0π0γ cross section with the SND detector, Phys. Rev. D 94, 112001 (2016).
  93. B. Aubert et al. (BABAR Collaboration, The e+e−→2(π+π−)π0, 2(π+π−)η, K+K−π+π−π0 and K+K−π+π−η cross sections measured with initial-state radiation, Phys. Rev. D 76, 092005 (2007); 77, 119902(E) (2008).
  94. J. P. Lees et al. (BABAR Collaboration), Study of the process e+e−→π+π−η using initial state radiation, Phys. Rev. D 97, 052007 (2018).
  95. S. Holz, J. Plenter, C.-W. Xiao, T. Dato, C. Hanhart, B. Kubis, U.-G. Meißner, and A. Wirzba, Towards an improved understanding of η→γ*γ*, Eur. Phys. J. C 81, 1002 (2021).
  96. M. Ablikim et al. (BESIII Collaboration), Observation of the electromagnetic doubly OZI-suppressed decay J/ψ→ϕπ0, Phys. Rev. D 91, 112001 (2015).
  97. F. James and M. Roos, minuit: A system for function minimization and analysis of the parameter errors and correlations, Comput. Phys. Commun. 10, 343 (1975).
  98. H. Dembinski, P. Ongmongkolkul et al., iminuit: python interface for the minuit2 c++ library, 10.5281/zenodo.3949207 (2020).
  99. A. Anastasi et al. (KLOE-2 Collaboration), Measurement of the ϕ→π0e+e− transition form factor with the KLOE detector, Phys. Lett. B 757, 362 (2016).
  100. G. López Castro, J. L. Lucio M., and J. Pestieau, Tests of flavor symmetry in J/ψ decays, AIP Conf. Proc. 342, 441 (1995).
  101. J. M. Gérard and J. Weyers, Phases and amplitudes in inclusive Ψ and Ψ′ decays, Phys. Lett. B 462, 324 (1999).
  102. Y.-H. Zhang, S.-Z. Jiang, and L.-Y. Dai, An anlaysis on Jψ→π0γ* within resonance chiral theory, Eur. Phys. J. C 86, 375 (2026).

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Phys. Rev. D 113, 074030– Published 27 April, 2026
  • Received 10 December 2025
  • Accepted 3 April 2026
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