In this work we extend the $q_T$-subtraction formalism, originally developed for QCD corrections, to the case of mixed QCD$\otimes$QED corrections, and apply it to the fully exclusive calculation of the ${\cal{O}}(\alpha_s\alpha)$ contribution to the production of an off-shell $Z$ boson in hadronic collisions. We present explicit results for the subtraction term and the hard factor, therefore providing all the ingredients needed for the application of the formalism up to ${\cal{O}}(\alpha_s\alpha)$. To study the phenomenological impact we consider the decay of the off-shell $Z$ boson into a pair of neutrinos, and present kinematical distributions for the final-state leptons at LHC energies.

中文翻译：

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使用 qT 减法对独家 Drell Yan 生产进行混合 QCD⊗QED 校正

在这项工作中，我们将最初为 QCD 校正开发的 $q_T$ 减法形式扩展到混合 QCD$\otimes$QED 校正的情况，并将其应用于 ${\cal{O}} (\alpha_s\alpha)$ 对强子碰撞中壳外 $Z$ 玻色子的产生的贡献。我们给出了减法项和硬因子的明确结果，因此提供了形式主义应用所需的所有成分，最高可达 ${\cal{O}}(\alpha_s\alpha)$。为了研究现象学影响，我们考虑了壳外 $Z$ 玻色子衰变成一对中微子，并给出了 LHC 能量下终态轻子的运动学分布。