Modelling Uncertainties for Measurements of the $H\rightarrow\gamma\gamma$ Channel with the ATLAS Detector at the LHC

The Higgs boson to diphoton $H\rightarrow\gamma\gamma$ branching ratio is only 0.227%, but this final state has yielded some of the most precise measurements of the particle. As measurements of the Higgs boson become increasingly precise, greater import is placed on the factors that constitute the uncertainty. Reducing the effects of these uncertainties requires an understanding of their causes. The research presented in this thesis aims to illuminate how uncertainties on simulation modelling are determined and proffers novel techniques in deriving them. The upgrade of the FastCaloSim tool is described, used for simulating events in the ATLAS calorimeter at a rate far exceeding the nominal detector simulation, Geant4. The integration of a method that allows the toolbox to emulate the accordion geometry of the liquid argon calorimeters is detailed. This tool allows for the production of larger samples while using significantly fewer computing resources. A measurement of the total Higgs boson production cross-section multiplied by the diphoton branching ratio $(\sigma\times B_{\gamma\gamma})$ is presented, where this value was determined to be $(\sigma\times B_{\gamma\gamma})_{obs}=$ 127 $\pm$ 7 (stat.) $\pm$ 7 (syst.) fb, within agreement with the Standard Model prediction. The signal and background shape modelling is described, and the contribution of the background modelling uncertainty to the total uncertainty ranges from 18−2.4%, depending on the Higgs boson production mechanism. A method for estimating the number of events in a Monte Carlo background sample required to model the shape is detailed. It was found that the size of the nominal $\gamma\gamma$ background events sample required a multiplicative increase by a factor of 3.60 to adequately model the background with a confidence level of 68%, or a factor of 7.20 for a confidence level of 95%. Based on this estimate, 0.5 billion additional simulated events were produced, substantially reducing the background modelling uncertainty. A technique is detailed for emulating the effects of Monte Carlo event generator differences using multivariate reweighting. The technique is used to estimate the event generator uncertainty on the signal modelling of $tHqb$ events, improving the reliability of estimating the $tHqb$ production cross-section. Then this multivariate reweighting technique is used to estimate the generator modelling uncertainties on background $V\gamma\gamma$ samples for the first time. The estimated uncertainties were found to be covered by the currently assumed background modelling uncertainty.