Angular Distributions of Drell-Yan Lepton Pairs at the Tevatron: Order $\alpha_s^2$ Corrections and Monte Carlo Studies

We investigate the angular distribution of the lepton pair in the process $p \bar{p} \rightarrow \gamma^{\ast} + X \rightarrow \ell^+\ell^- + X$, where the virtual photon is produced at high transverse momentum. The angular distribution of the leptons is very sensitive to possible nonperturbative effects, such as a nontrivial vacuum structure of QCD, and offers a good chance to test such effects. We present complete ${\cal O}(\alpha_s^2)$ calculations of the decay lepton distributions in the lepton pair rest frame. An order ${\cal O}(\alpha_s)$ Monte Carlo study of the lepton angular distributions, with acceptance cuts and energy resolution smearing applied to the leptons, is also presented.