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Electroweak corrections to $Z$-boson hadroproduction at finite transverse momentum

We calculate the full one-loop electroweak radiative corrections, of ${\cal O}(α^2α_s)$, to the cross section of single $Z$-boson inclusive hadroproduction at finite transverse momentum ($p_T$). This includes the ${\cal O}(α)$ corrections to $Z+j$ production, the ${\cal O}(α_s)$ corrections to $Z+γ$ production, and certain QCD-electroweak interference contributions involving a single quark trace. We recover the QCD and purely weak corrections and study the QED corrections and the QCD-electroweak interference contributions for the first time. We also consider direct and resolved photoproduction in elastic and inelastic scattering. We present $p_T$ and rapidity distributions for the experimental conditions at the Fermilab Tevatron and the CERN LHC and assess the significance of the various contributions.