Electroweak corrections to the angular coefficients in finite-$p_T$ $Z$-boson production and dilepton decay

We present next-to-leading order (NLO) electroweak corrections to the dominant five angular coefficients parametrizing the Drell-Yan process in the $Z$-boson mass peak range for finite-$p_T$ vector boson production. The results are presented differentially in the vector boson transverse momentum. The Lam-Tung violating difference $A_0-A_2$ is examined alongside the coefficients. A single lepton transverse momentum cut is needed in the case of electroweak corrections to avoid a double singularity in the photon induced diagrams, and the dependence on the value of this cut is examined. We compare the electroweak corrections to the angular coefficients to the NLO QCD corrections, including the single lepton cut. The size of the single lepton cut is found to affect the two coefficients $A_0$ and $A_2$ to largest extent. The relative size of the electroweak corrections to the coefficients is moderate for all single lepton cut values, and by extrapolation to the inclusive results, is moderate also for the full dilepton phase space case. However, for the Lam-Tung violation, there is a significant contribution from the electroweak corrections for low $p_T$ of the lepton pair.