Measurements of the vector boson production with the ATLAS detector

Measurements of the Drell-Yan production of $W$ and $Z$ bosons at the LHC provide a benchmark of our understanding of perturbative QCD and probe the proton structure in a unique way. The ATLAS collaboration has performed new high precision measurements at center-of-mass energies of 7 TeV. The measurements are performed for $W^+$, $W^{-}$ and $Z$ bosons integrated and as a function of the boson or lepton rapidity and the $Z$ mass. Unprecedented precision is reached and strong constraints on Parton Distribution Functions, in particular the strange density are found. $Z$ boson cross sections are also measured at a center-of-mass energies of 8 TeV and 13 TeV, and cross-section ratios to the top-quark pair production have been derived. This ratio measurement leads to a cancellation of systematic effects and allows for a high precision comparison to the theory predictions. The production of jets in association with vector bosons is a further important process to study perturbative QCD in a multi-scale environment. The ATLAS collaboration has performed new measurements of $Z$ boson plus jets cross sections, differential in several kinematic variables, in proton-proton collision data taken at center-of-mass energies of 13 TeV. The measurements are compared to state-of-the art theory predictions. They are sensitive to higher-order pQCD effects, probe flavour and mass schemes and can be used to constrain the proton structure. In addition, a new measurement of the splitting scales of the $k_t$ jet-clustering algorithm for final states containing a $Z$ boson candidate at a centre-of-mass energy of 8 TeV is presented