Interpretation of Angular Distributions of $Z$-boson Production at Colliders

High precision data of dilepton angular distributions in $\gamma^*/Z$ production were reported recently by the CMS Collaboration covering a broad range of the dilepton transverse momentum, $q_T$, up to $\sim 300$ GeV. Pronounced $q_T$ dependencies of the $\lambda$ and $\nu$ parameters, characterizing the $\cos^2\theta$ and $\cos 2\phi$ angular distributions, were found. Violation of the Lam-Tung relation was also clearly observed. We show that the $q_T$ dependence of $\lambda$ allows a determination of the relative contributions of the $q \bar q$ annihilation versus the $qG$ Compton process. The violation of the Lam-Tung relation is attributed to the presence of a non-zero component of the $q - \bar q$ axis in the direction normal to the "hadron plane" formed by the colliding hadrons. The magnitude of the violation of the Lam-Tung relation is shown to reflect the amount of this `non-coplanarity". The observed $q_T$ dependencies of $\lambda$ and $\nu$ from the CMS and the earlier CDF data can be well described using this approach.