Non-linear effects in the ATLAS track-counting luminosity measurement

In this thesis the linearity of the ATLAS track-counting luminosity measurement is studied using two different sets Monte Carlo simulated crossings of proton-proton bunches. A primary high-momentum, or hard, interaction must be chosen for the Monte Carlo simulation. The first of the two sets is simulated using $Z\rightarrow\mu\mu$ as primary hard scatter in the bunch crossings while the second set is simulated with a single neutrino particle gun as the primary hard scatter. The luminosity can be determined by track counting from the relationship between the number of reconstructed charged particle tracks and the number of proton-proton interactions per bunch crossing in the ATLAS detector. The relationship between the two is theoretically linear but is affected by non-linear effects from the presence of fake tracks and the reduced tracking efficiency at large $\mu$. The linearity is studied and compared for eight different sets of track selection criteria called working points. Four of the working points were used during Run 2 of the Large Hadron Collider and four are introduced for Run 3. It is found that the use of the physical hard scatter, $Z\rightarrow\mu\mu$, in the Monte Carlo generation results in the appearance of tracks at all interaction rates, to a degree that does not agree with experiment. The use of the single neutrino particle gun for the simulation of hard scatter interactions is found to be more suitable for the track counting studies. Two of the working points introduced for Run 3, called $\textit{TightModHighPtStrictLumi}$ and $\textit{TightModFullEtaHighPtStrictLumi}$, are found to outperform the rest of the working points.