Study of the Drell-Yan process with the ATLAS detector at the LHC

The Large Hadron Collider (LHC) at CERN, at which protons collide at unprecedented center of mass energies and very high instantaneous luminosity, gives unique possibilities for precise tests of the Standard Model and to search for new physics phenomena. A precise prediction of the processes at the LHC is essential and the knowledge of the parton density functions (PDFs) of the proton plays a key role in this. In this thesis, three analyses covering different aspects of the Drell-Yan process are presented. In the first analysis a new heavy neutral gauge boson, a so-called $Z'$ boson, is searched for. Those new gauge bosons are predicted by some theories extending the Standard Model gauge group to solve some of its conceptual problems. Decays of the $Z'$ boson in final states with a lepton ($\ell = e^{\pm},\mu^{\pm}$) and the corresponding anti-lepton are considered. The data in use were collected by the ATLAS experiment in the year 2015+2016 at a center of mass energy of $\sqrt{s}$ = 13 TeV. The collected data corresponds to an integrated luminosity of 36.1 fb$^{-1}$. The Standard Model prediction for the expected background is estimated with Monte Carlo simulations and methods based on data. The resulting spectrum of the di-lepton invariant mass is tested, using statistical methods, for differences between data and the Standard Model predictions. No significant deviation from the Standard Model predictions is found. Much more stringent limits have been set on the parameters of interest for various models comparing with the Run 1 results. For new gauge bosons, $Z'_{SSM}$ , $Z'_{\chi}$ and $Z'_{\psi}$ predicted in extended gauge theory models, the observed lower limits on mass have been set to be 4.5 TeV, 4.1 TeV and 3.8 TeV at 95$\%$ confidence level, respectively. While for the Contact Interactions, the observed lower limits on the corresponding energy scale $\Lambda$ are set between 24 TeV and 40 TeV depending on the different scenarios. In the second analysis, the double-differential cross section measurement of the process $pp\rightarrow Z/\gamma^{*}\rightarrow \ell^{+} \ell^{-}$ at a center of mass energy of $\sqrt{s}$ = 8 TeV is used in a PDF fit to put constraints on the photon PDF of the proton. The analysed data were recorded by the ATLAS experiment in the year 2012 and correspond to an integrated luminosity of 20.3 fb$^{-1}$. These data are sensitive to the photon structure of the photon and allow a determination of $x\gamma(x, Q^2)$ with uncertainties at the 30\% level for $0.02 \le x \le 0.1$. The results of this study, is in agreement and exhibit smaller PDF uncertainties that the only other existing photon PDF fit from LHC data, the NNPDF3.0QED analysis, based on previous LHC Drell-Yan measurements. The results are also in agreement within uncertainties with two recent theoretical calculations of the photon PDF, LUXqed and HKR16. In the third analysis, a measurement of the double-differential Drell-Yan cross section in the di-muon channel is presented differentially in terms of di-muon invariant mass and double differentially in terms of di-muon invariant mass and rapidity. The cross sections are measured using 3.2 fb$^{-1}$ of ATLAS data taken during 2015 at a centre of mass energy of $\sqrt{s}$ = 13 TeV. Dedicated studies to address the main challenges of the analysis, namely the understanding of the trigger SF and of the muon isolation are reported, and the data-driven methods for estimating the QCD/multijet background are described in detail. The extracted fiducial cross sections agree within uncertainties with the theoretical predictions from Powheg interfaced with the Pythia v8.1 parton shower program.