We present the first analytical results for the $\mathcal{O}(\alpha {\alpha }_s)$ corrections to the total cross section for the inclusive production of an on-shell $Z$ boson at hadron colliders. We include the complete set of contributions, with photonic and massive weak gauge boson effects, which have been computed in analytical form and expressed in terms of polylogarithmic and elliptic integrals. We present numerical results, relevant for the precision studies at the LHC. These corrections increase the accuracy of the predictions and contribute to the reduction of the QCD component of the theoretical uncertainty.

• Received 18 July 2020
• Revised 12 October 2020
• Accepted 29 October 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.232004

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Published by the American Physical Society