Double differential cross section for Drell-Yan production of high-mass $e^+ e^-$-pairs in $pp$ collisions at $\sqrt{s} = 8$ TeV with the ATLAS experiment

A precise prediction of the processes at the Large Hadron Collider at CERN is essential to do precise tests of the Standard Model and for the search of new physics phenomena. A key role for the precise prediction of these processes plays the knowledge of the parton distribution functions (PDFs) of the proton. In this thesis the measurement of the first double differential cross section of the process $pp \rightarrow Z / \gamma^* +X \rightarrow e^+e^- +X$, at a center of mass energy of $\sqrt{s} = 8$ TeV of the colliding protons, as a function of the invariant mass and rapidity of the $e^+e^-$-pair will be presented. The measurement covers an invariant mass range from $m_{e^+e^-} = 116$ GeV up to $m_{e^+e^-} = 1500$ GeV. The analyzed data set was recorded by the ATLAS experiment in the year 2012 and corresponds to an integrated luminosity of $20.3$ fb$^{-1}$. The rapidity and mass dependent cross section is expected to have sensitivity to the PDFs at very high values of the Bjorken-$x$ scaling variable. In particular sensitivity to the PDFs of the antiquarks in the proton is expected, since these are not well constrained at high values of $x$. The expected amount of $e^+e^-$-pairs produced by Standard Model processes will be carefully estimated using Monte Carlo simulations and data-driven methods. A main part of this thesis addresses the further development and understanding of data driven methods (fake factor method / matrix method) to determine the fake background which arises if one or both of the $e^+$/$e^-$-candidates are jets and wrongly identified as a $e^+$/$e^-$-candidate. The measured cross section is compared to several theory predictions using different calculations and PDFs. A small tension between data and theory is seen especially in the invariant mass range of $150$ to $300$ GeV. Additionally a study will be presented which shows that, despite this small tension between theory and data, the uncertainty on the antiquark distributions at high $x$ can be improved using the presented measurement.