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Analytical two-loop amplitudes of e+e−→J/ψ+ηc at B factories

Xiang Chen1,*, Xin Guan2,†, Chuan-Qi He3,4,5,‡, Yan-Qing Ma6,7,§, Jian Wang8,7,∥, and Da-Jiang Zhang8,¶

  • *Contact author: xiang.chen@physik.uzh.ch
  • †Contact author: guanxin@slac.stanford.edu
  • ‡Contact author: legend_he@m.scnu.edu.cn
  • §Contact author: yqma@pku.edu.cn
  • ∥Contact author: j.wang@sdu.edu.cn
  • Contact author: zhangdajiang@mail.sdu.edu.cn
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Phys. Rev. D 113, 074023 – Published 17 April, 2026

DOI: https://doi.org/10.1103/93kb-dqz6

Abstract

In double charmonium production, a long-standing challenge is that the theoretical predictions are not consistent with the measurements at B factories. Within the Non-Relativistic Quantum Chromodynamics (NRQCD) framework, the next-to-leading order calculation has proved its power to cut down the discrepancy between theory and experiments. To further clarify this puzzle, we have performed the next-to-next-to-leading order calculation. The amplitude is obtained as an analytical asymptotic expansion in the ratio of the squared charm-quark mass over the squared center-of-mass energy, mc2/s. We investigate the origin of the leading logarithms by performing a region analysis, revealing the intricate factorization structure in this process. We provide numerical predictions on the total cross sections of J/ψ+ηc production, which agree with the experimental results. Extension of our computation to ϒ+ηb production is also discussed.

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Phys. Rev. D 113, 074023– Published 17 April, 2026
  • Received 25 September 2025
  • Accepted 24 March 2026
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