Z+$\gamma$ differential cross section measurements and the digital timing calibration of the level-1 calorimeter trigger cluster processor system in ATLAS.

This thesis investigates the reconstruction of $Z(\rightarrow ee)\gamma$ events with the ATLAS detector at the LHC. The capabilities of the detector are explored for the initial run scenario with a proton-proton centre of mass collision energy of $\sqrt{s}$ = 7TeV, and an integrated luminosity of $\mathcal{L} = 1,fb^{-1}$. Monte Carlo simulations are used to predict the expected precision of a differential cross-section measurement for initial state radiation $Z+\gamma$ events, both with respect to the transverse momentum of the photon, $p_{T}(\gamma)$, and the three body $ee\gamma$ invariant mass. A bin-by-bin correction is used to account for the signal selection efficiency and purity, and to correct the measured (simulated) distribution back to the theoretical prediction. The main backgrounds are found to be from the final state radiation $Z+\gamma$ process, and from jets faking photons in $Z \rightarrow ee$ events. The possible QCD multijet background is studied using a fake-rate method, and found to be negligible for the particle identification cuts used in the analysis. The main systematic uncertainties on the differential cross-section measurements are explored with Monte Carlo simulations, and found to be of a similar scale to the statistical errors for the chosen distribution binning. The three body $ee\gamma$ invariant mass distribution was then used as the basis of an exclusion study on new particles decaying to the $Z(ee)\gamma$ final state. Under the assumption that the measured data agrees with the Standard Model prediction, exclusion limits were placed at $95%$ confidence level on the cross-section times branching ratio for a new scalar (modelled by SM Higgs process), or vector (based on a low-scale technicolor process) particle hypothesis, for particles in the mass range $200$ to $900,$GeV. Limits of the order $\mathcal{O}(0.01)$ - $\mathcal{O}(0.1),$pb on the cross section times branching ratios are predicted, which would improve on the equivalent limits previously calculated by the DO{} experiment at the Tevatron collider, albeit in a different $\sqrt{s}$ region, where cross-sections will generally be higher for new massive particles. In addition to the $Z\gamma$ measurements, a digital timing calibration procedure was developed for the Cluster Processor (CP) subsystem of the level-1 calorimeter trigger. This work was essential to providing a repeatable and robust mechanism for timing in the digital processing in the CP system, a necessary ingredient for a robust and reliable trigger system; a pre-requisite of any physics analysis. This calibration procedure is described here.