Measurement of Vector Boson polarisation in $WZ$ production at the LHC with the ATLAS detector

The measurements presented in this thesis use proton-proton collision data from 2015 and 2016 recorded by the ATLAS experiment at the Large Hadron Collider. The data-taking period was successful and data with an integrated luminosity of 36.1~$\text{fb}^{-1}$ has been collected. The knowledge of the efficiency of electron identification in the ATLAS detector is very important for ATLAS analyses. The electron identification efficiency has been measured in data and simulation and correction factors to the simulation have been derived. These correction factors are applied to all ATLAS analyses using electrons in 2015 and 2016. Focus is laid on studies of potential biases and a possible improvement of the method is presented. The electron identification efficiency and its uncertainty is also an important input to the measurement of $WZ$ production using fully leptonic decays to electrons, muons and a neutrino. Measurements of the $WZ$ production are sensitive to the $WWZ$ vector boson coupling. An important difficulty of the measurement is the determination of the background from misidentified leptons. It is the dominant background and also the dominant source of systematic uncertainty. It is determined using a data-driven method, with a precision of 30% which contributes with a relative uncertainty of 1.9% to the $WZ$ production cross-section measurement. The latter has a total precision of 4.6% and the result is well compatible with predictions at next-to-leading order in QCD. Finally, the first polarisation measurement of pair-produced bosons in hadronic collisions has been presented. The measurement is a first step of the characterization of the polarisation in vector boson scattering events. The longitudinal polarisation is directly related to the Electroweak Symmetry breaking mechanism. A fraction of longitudinally polarised $W$ ($Z$) bosons of 26% (24%) is observed with an observed significance of 4.2 $\sigma$ (6.5 $\sigma$). The uncertainty is dominated by the statistical uncertainty.