Measurement of the Drell-Yan Four-foldDifferential Cross Section with the ATLASExperiment

With the discovery of the Higgs boson in 2012 at the Large Hadron Collider at CERN,the final elementary particle predicted by the Standard Model of particle physics wasdiscovered. Since then the study of the Standard Model has focussed on precision mea-surements of various parameters and processes of the theory in the hope of measuringsubtle differences between the theoretically predicted values and those observed in na-ture. This thesis presents one such measurement, that of the Drell-Yan cross sectionthrough its decomposition to a set of 8 angular coefficients, 9 harmonic polynomialsand an unpolarised cross section. This decomposition allows for a measurement of theDrell-Yan cross section in the phase space defined by the Z boson mass, transverse mo-mentum and rapidity which is unaffected by kinematic cuts on the decay leptons. Thismeasurement uses the Run 2 dataset of the ATLAS experiment collected between 2015and 2018 which encompasses 140 fb −1 of data recorded at ps = 13 TeV from proton-proton collisions. The angular coefficients and unpolarised cross section are measured inboth the Z ! e + e − and Z ! μ + μ − decay channels as well as the combination of bothchannels which provides a more precise result than what can be found in the literature.The combination result is also compared to theoretical predictions where it is found tobe in good agreement with the Standard Model.A further Asimov sensitivity study on the effective leptonic weak mixing angle is pre-sented through the reparameterisation of the A 4 angular coefficient previously measured.In this study the Z ! e + e − channel is extended to include electrons with pseudorapidityvalues in the range 2.5 < |⌘| < 4.9 where the sensitivity to the weak mixing angle is atits greatest. The calibration process to use these forward electrons for physics analysispurposes is described and results in a good agreement between the data and simulatedZ boson mass spectra. The results of this sensitivity study show that the combinationof the electron and muon channels may provide the most precise measurement of theweak mixing angle from a hadron collider and become competitive with the sensitivitiesachieved at lepton colliders.