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Helicity Amplitudes for ${\cal O}(α_s)$ Production of $W^+ W^-, W^\pm Z, Z Z, W^\pm γ,$ or $Z γ$ Pairs at Hadron Colliders

We present the one-loop QCD corrections to the helicity amplitudes for the processes $q\qb \to W^+ W^-, Z Z, W^\pm Z, W^\pm γ$, or $Z γ$, including the subsequent decay of each massive vector boson into a pair of leptons. We also give the corresponding tree-level amplitudes with an additional gluon radiated off the quark line. Together, these amplitudes provide all the necessary input for the calculation of the next-to-leading order QCD corrections to the production of any electroweak vector boson pair at hadron colliders, including the full spin and decay angle correlations.