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Associated production of charmonia and bottomonia with color-octet channels at the Z factory, CEPC, and FCC-ee

Xiao-Peng Wang1, Yi-Jie Li1, Guang-Zhi Xu1,*, and Kui-Yong Liu2,1,†

  • *Contact author: xuguangzhi@lnu.edu.cn
  • †Contact author: liukuiyong@lnu.edu.cn
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Phys. Rev. D 114, 016016 – Published 22 July, 2026

DOI: https://doi.org/10.1103/69jq-85lt

Abstract

Within the nonrelativistic QCD framework, we investigate the associated production of charmonia and bottomonia at the future super Z-factory and at CEPC and FCC-ee. The color-octet (CO) channels in the γ*/Z0-propagated processes are considered in addition to the color-singlet (CS) channels. We find that the contributions from the CO channels are substantial or even dominant for nearly all processes from the production threshold to the Z0 pole region. However, estimates of the production rate are highly sensitive to long-distance matrix elements (LDMEs) selections, so different combinations of LDMEs produce markedly different production yields. For this reason, the study of charmonia-bottomonia production at the future super Z-factory can serve as a viable probe of the CO mechanism, and the comparison between the theoretical results and future experimental data may provide constraints on the CO matrix elements. In addition, we calculate the relativistic corrections to both the CS and CO channels, which decrease the cross sections significantly, yielding a K factor of approximately 0.5. The predicted event yields of (J/ψ+ϒ,ϒ+ηc) production, with J/ψ,ϒ reconstructed via lepton pairs and ηc reconstructed via hadronic decays, are (2, 4) and (18, 35) at the CEPC (2-year) and FCC-ee (4-year), respectively.

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Phys. Rev. D 114, 016016– Published 22 July, 2026
  • Received 13 February 2026
  • Accepted 12 June 2026
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