Hadronic $ZZ$, $W^- W^+$, and $W^{\pm} Z$ Production with QCD Corrections and Leptonic Decays

The processes $p p \rightarrow V_1 V_2 + X \rightarrow \ell_1 \bar \ell_1 \ell_2 \bar \ell_2 + X$, where $V_i = W^{\pm}$ or $Z$ and $\ell_i$ denotes a lepton, are calculated to ${\cal O}(\alpha_s)$. Total and differential cross sections, with acceptance cuts imposed on the final state leptons, are given for the Tevatron and LHC center of mass energies. Inclusive and exclusive $0$-jet and $1$-jet cross sections are given. The transverse momenta spectra of the leptons are significantly enhanced at high $p_T^{}$ by the QCD radiative corrections, especially at the LHC energy. Invariant mass and angular distributions are scaled up in magnitude by the QCD radiative corrections, but are little changed in shape.