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

Long-distance contributions to light vector mesons and radiative decays of ηc

Xiao-Yu Qi1, Qi Wu2, and Dian-Yong Chen1,3,*

  • *Contact author: chendy@seu.edu.cn

Phys. Rev. D 114, 074048 – Published 21 October, 2026

DOI: https://doi.org/10.1103/mp2z-yvm7

Abstract

In the present work, we investigate the long-distance contributions to light hadrons and radiative decays of ηc, where the long-distance contribution is phenomenologically described by the meson loops. Our estimations indicate that the branching fractions of ηc→VV,V=(ρ,ω,ϕ), can be roughly reproduced in the range 1.4<α<1.6, while the parameter range for ηc→γV is determined by the similarity of ηc→γV/VV and χc1→γV/VV. In this parameter range, our estimations indicate that the branching fractions for the processes ηc→γρ0 and ηc→γω are of the order of 10−4, while the one for the process ηc→γϕ is of the order of 10−5. The estimations in the present work are expected to be accessible by future experiments at BESIII and Belle II.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (71)

  1. E. Eichten, K. Gottfried, T. Kinoshita, J. B. Kogut, K. D. Lane, and T.-M. Yan, Phys. Rev. Lett. 34, 369 (1975); 36, 1276(E) (1976).
  2. E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, and T.-M. Yan, Phys. Rev. D 17, 3090 (1978); 21, 313(E) (1980).
  3. S. Godfrey and N. Isgur, Phys. Rev. D 32, 189 (1985).
  4. T. Barnes, S. Godfrey, and E. S. Swanson, Phys. Rev. D 72, 054026 (2005).
  5. D. Ebert, R. N. Faustov, and V. O. Galkin, Eur. Phys. J. C 71, 1825 (2011).
  6. R. Partridge et al., Phys. Rev. Lett. 45, 1150 (1980).
  7. T. Himel et al., Phys. Rev. Lett. 45, 1146 (1980).
  8. R. M. Baltrusaitis et al. (MARK-III Collaboration), Phys. Rev. Lett. 52, 2126 (1984).
  9. S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024).
  10. M. Ambrogiani et al. (Fermilab E835 Collaboration), Phys. Lett. B 566, 45 (2003).
  11. B. Aubert et al. (BABAR Collaboration, Phys. Rev. Lett. 92, 142002 (2004).
  12. D. M. Asner et al. (CLEO Collaboration), Phys. Rev. Lett. 92, 142001 (2004).
  13. P. del Amo Sanchez et al. (BABAR Collaboration, Phys. Rev. D 84, 012004 (2011).
  14. F. Fang et al. (Belle Collaboration), Phys. Rev. Lett. 90, 071801 (2003).
  15. A. Vinokurova et al. (Belle Collaboration), Phys. Lett. B 706, 139 (2011).
  16. J. Z. Bai et al. (BES Collaboration), Phys. Lett. B 555, 174 (2003).
  17. R. E. Mitchell et al. (CLEO Collaboration), Phys. Rev. Lett. 102, 011801 (2009); 106, 159903(E) (2011).
  18. M. Ablikim et al. (BESIII Collaboration), Phys. Rev. Lett. 108, 222002 (2012).
  19. S. J. Brodsky and G. P. Lepage, Phys. Rev. D 24, 2848 (1981).
  20. V. L. Chernyak and A. R. Zhitnitsky, Nucl. Phys. B201, 492 (1982); B214, 547(E) (1983).
  21. V. L. Chernyak and A. R. Zhitnitsky, Phys. Rep. 112, 173 (1984).
  22. M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 100, 052012 (2019).
  23. M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 95, 092004 (2017).
  24. M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 112, 012012 (2025).
  25. Z. Q. Liu et al. (Belle Collaboration), Phys. Rev. Lett. 108, 232001 (2012).
  26. Q. Zhao, Phys. Lett. B 636, 197 (2006).
  27. Q. Wang, X.-H. Liu, and Q. Zhao, arXiv:1010.1343.
  28. Q. Wang, X.-H. Liu, and Q. Zhao, Phys. Lett. B 711, 364 (2012).
  29. D.-Y. Chen, Y.-B. Dong, and X. Liu, Eur. Phys. J. C 70, 177 (2010).
  30. D.-Y. Chen, J. He, X.-Q. Li, and X. Liu, Phys. Rev. D 81, 074006 (2010).
  31. M. Ablikim et al. (BESII Collaboration), Phys. Rev. Lett. 107, 092001 (2011).
  32. X.-H. Liu and Q. Zhao, Phys. Rev. D 81, 014017 (2010).
  33. Y.-J. Gao, Y.-J. Zhang, and K.-T. Chao, Chin. Phys. Lett. 23, 2376 (2006).
  34. J. V. Bennett et al. (CLEO Collaboration), Phys. Rev. Lett. 101, 151801 (2008).
  35. M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 83, 112005 (2011).
  36. Y.-J. Gao, Y.-J. Zhang, and K.-T. Chao, arXiv:hep-ph/0701009.
  37. M. Ablikim et al. (BES Collaboration), Phys. Rev. D 72, 072005 (2005).
  38. Z.-Y. Bai, D.-Y. Chen, Q. Huang, X. Liu, S.-Q. Luo, and J.-Z. Wang, Phys. Rep. 1204, 1 (2027).
  39. H. J. Lipkin, Phys. Lett. B 179, 278 (1986).
  40. R. Casalbuoni, A. Deandrea, N. Di Bartolomeo, R. Gatto, F. Feruglio, and G. Nardulli, Phys. Rep. 281, 145 (1997).
  41. O. Kaymakcalan, S. Rajeev, and J. Schechter, Phys. Rev. D 30, 594 (1984).
  42. Y.-s. Oh, T. Song, and S. H. Lee, Phys. Rev. C 63, 034901 (2001).
  43. T. Mannel, Rep. Prog. Phys. 60, 1113 (1997).
  44. N. Brambilla, A. Pineda, J. Soto, and A. Vairo, Rev. Mod. Phys. 77, 1423 (2005).
  45. P. Colangelo, F. De Fazio, and T. N. Pham, Phys. Rev. D 69, 054023 (2004).
  46. A. F. Falk and M. E. Luke, Phys. Lett. B 292, 119 (1992).
  47. T.-M. Yan, H.-Y. Cheng, C.-Y. Cheung, G.-L. Lin, Y. C. Lin, and H.-L. Yu, Phys. Rev. D 46, 1148 (1992); 55, 5851(E) (1997).
  48. H.-Y. Cheng, C.-Y. Cheung, G.-L. Lin, Y. C. Lin, T.-M. Yan, and H.-L. Yu, Phys. Rev. D 47, 1030 (1993).
  49. M. B. Wise, Phys. Rev. D 45, R2188 (1992).
  50. R. Casalbuoni, A. Deandrea, N. Di Bartolomeo, R. Gatto, F. Feruglio, and G. Nardulli, Phys. Lett. B 292, 371 (1992).
  51. R. Casalbuoni, A. Deandrea, N. Di Bartolomeo, R. Gatto, F. Feruglio, and G. Nardulli, Phys. Lett. B 299, 139 (1993).
  52. Y. Dong, A. Faessler, T. Gutsche, and V. E. Lyubovitskij, J. Phys. G 38, 015001 (2011).
  53. X.-Q. Li, X. Liu, and Z.-T. Wei, Front. Phys. China 4, 49 (2009).
  54. G. Li, Q. Zhao, and B.-S. Zou, Phys. Rev. D 77, 014010 (2008).
  55. C.-J. Xiao and D.-Y. Chen, Phys. Rev. D 96, 014035 (2017).
  56. H.-S. Gao, Z.-X. Cai, G. Li, and S.-D. Liu, Chin. Phys. Lett. 42, 100201 (2025).
  57. M. A. Ivanov, J. G. Korner, and P. Santorelli, Phys. Rev. D 70, 014005 (2004).
  58. Z.-L. Yue, C.-J. Xiao, and D.-Y. Chen, Eur. Phys. J. C 83, 769 (2023).
  59. R. P. Feynman, Phys. Rev. 76, 769 (1949).
  60. T. Hahn and M. Perez-Victoria, Comput. Phys. Commun. 118, 153 (1999).
  61. N. A. Tornqvist, Nuovo Cimento Soc. Ital. Fis. 107A, 2471 (1994).
  62. N. A. Tornqvist, Z. Phys. C 61, 525 (1994).
  63. M. P. Locher, Y. Lu, and B. S. Zou, Z. Phys. A 347, 281 (1994).
  64. X.-Q. Li, D. V. Bugg, and B.-S. Zou, Phys. Rev. D 55, 1421 (1997).
  65. D.-Y. Chen, X. Liu, and T. Matsuki, Phys. Rev. D 91, 094023 (2015).
  66. D. Becirevic and B. Haas, Eur. Phys. J. C 71, 1734 (2011).
  67. S.-L. Zhu, W.-Y. P. Hwang, and Z.-s. Yang, Mod. Phys. Lett. A 12, 3027 (1997).
  68. Y.-b. Dong, A. Faessler, T. Gutsche, and V. E. Lyubovitskij, Phys. Rev. D 77, 094013 (2008).
  69. S. Gasiorowicz and J. L. Rosner, Am. J. Phys. 49, 954 (1981).
  70. J. L. Rosner, Phys. Rev. D 88, 034034 (2013).
  71. Y. Meng, J.-L. Dang, C. Liu, Z. Liu, T. Shen, H. Yan, and K.-L. Zhang, Phys. Rev. D 109, 074511 (2024).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation