Luminosity Measurement at the Large Hadron Collider

Two novel methods of measuring the luminosity delivered to the ATLAS Experiment at the CERN Large Hadron Collider experiments are presented. The production of $\mu^{+}\mu^{-}$ pair via two photon interactions and single $W^{\pm}/Z^{0}$ boson production are evaluated as methods for the measurement and monitoring of the proton-proton luminosity at the LHC. The characteristics of the $\mu^{+}\mu^{-}$ pairs from coherent $\gamma \gamma$ interactions are examined for both matrix element and equivalent photon based monte carlo generators with subsequent simulation of the ATLAS detector effects. The application of specific kinematic and vertex fit requirements is shown to offer a strong method of isolating signal from background and in turn yield an accurate offline measurement of the delivered luminosity via the pure QED process. The choice of kinematic cuts is shown to reduce the overall uncertainty in the method by limiting the size of corrections to the two photon interaction cross section to the level of 1\%. Based upon these developed criteria, the results of a first search for the exclusive production of $\mu^{+}\mu^{-}$ events from two photon interactions at CDF and the Fermilab Tevatron are presented, providing preliminary evidence for the first observation of two photon process at a hadron collider. The observation of single gauge boson production is also reviewed as a promising method for online luminosity monitoring at the LHC. The theoretical and experimental considerations are examined. Event selection criteria, efficiencies and rates are outlined based upon the trigger conditions of the ATLAS experiment. The combined effect of recent theoretical developments in the computation of higher order QCD corrections and parton distribution function (PDF) error sets are incorporated into simulation studies performed for the LHC. An implementation of new PDF reweighting method by which it is possible to calculate the effective uncertainty on physically measureable quantities, without requiring the repeated simulation of identical events with separate PDF error sets as input, is described. The error in acceptance for the observation of $Z^{0} \rightarrow e^{+}e^{-}$ due to the most recent CTEQ PDF error set is shown to be less than 1\%