Dielectron production in proton-proton collisions with ALICE

Ultrarelativistic hadron collisions, such as delivered since a couple of years at the Large Hadron Collider (LHC), provide new insights into the properties of strongly interacting matter at high temperatures and densities, which is expected to have existed a few of a millionth seconds after the big bang. Electromagnetic probes, such as leptons and photons, are emitted during the entire collision. Since they do not undergo strong interactions, they reflect the entire evolution of the collision.\\ Pairs of leptons, so called dileptons, have the advantage compared to real photons, that they do not only carry momentum, but also have a non-zero invariant mass. The invariant mass spectrum of dileptons is a superposition of several components and allows to address different characteristics of the medium.\\ To understand dielectron production in heavy-ion collisions, reference measurements in proton-proton (pp) collisions are necessary. pp collisions reflect the vacuum contribution of the particles produced in heavy-ion collisions. The analysis of pp collisions is an essential step towards the extraction of medium influences on the vector meson spectral functions and the thermal radiation in heavy-ion collisions.\\ In this thesis, the production of electron-positron pairs (dielectrons) in pp collisions at a collision energy of $7$~TeV in the ALICE central barrel is analysed. ALICE has unique particle identification capabilities at low momentum. Electrons and positrons are identified with a high purity and combined to pairs. The invariant mass distribution of dielectrons is corrected for detector effects and the selection criteria in the analysis with Monte Carlo simulations.\\ The dielectron invariant mass spectrum of known hadronic sources is calculated based on the cross sections measured in other decay channels using the known decay kinematics. This so called hadronic cocktail represents the dielectron spectrum at the moment of kinematic freeze-out and can be compared to the measured dielectron invariant mass spectrum. The cocktail is consistent with the measured dielectron invariant mass spectrum within the quoted statistical and systematic uncertainties. \\ Additionally, the fraction of direct over inclusive virtual photons is measured as a function of transverse momentum from dielectron yields at high pair momentum. The ratio is used to calculate the cross section of direct real photons, which is compared to next-to-leading order perturbative Quantum-Chromodynamics calculations. The theoretical calculations are consistent with the measurement for pp collisions at a centre-of-mass energy of $7$~TeV.\\ The analysis and results of this work are the basis for future dielectron measurements of heavier collision systems.