Lepton angular distribution of W boson productions

The lepton angular distribution coefficients ${A}_{i}$ for $Z$ boson production in $pp$ and $\overline{p}p$ collisions have been measured at the LHC and the Tevatron. A recent study showed that many features of the measured angular distribution coefficients, including the transverse momentum (${q}_{T}$) and rapidity dependencies and the violation of the Lam-Tung relation, can be well described using an intuitive geometric approach. In this paper, we extend this geometric approach to describe the angular distribution coefficients for $W$ boson produced in $\overline{p}p$ collisions at the Tevatron. We first compare the data with a perturbative QCD calculation at $\mathcal{O}({\ensuremath{\alpha}}_{s}^{2})$. We then show that the data and QCD calculations can be well described with the geometric approach. Implications for future studies at the LHC energy are also discussed.