In this paper, we calculate the decay widths and branching fractions for the decays Z→H+γ up to O(αₛv²) accuracy within the framework of nonrelativistic QCD, where H stands for the S-wave quarkonium ηc, J/ψ, ηb, or Υ, respectively. To compare with the leading-order terms, those corrections show good perturbative behavior as expected. It is found that contributions from the next-to-leading order QCD correction O(αₛv⁰), the relativistic correction O(αₛ⁰v²) and their joint correction O(αₛv²) are sizable and comparable to each other, especially for the charmonium case. Thus we need to take all of them into consideration for a sound estimation. For a high luminosity electron-positron collider running around the Z pole, due to Z-boson resonance effect, sizable events could be produced from those rare decay channels.
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Wang et al. (2024) studied this question.
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