Measurement of $Z/\gamma^{*} \rightarrow \mu\mu$ differential cross section with the ATLAS experiment at LHC

This thesis presents the measurement of the Drell-Yan inclusive $pp \rightarrow Z/\gamma^{*} \rightarrow \mu\mu + X$ cross section with the ATLAS experiment on 36.2 pb$^{-1}$ of data collected during 2010 at an energy in the center of mass of $\sqrt{s} = 7$ TeV. As the measurement accuracy reaches a few percent and the simulations at NNLO are calculated with a precision of no more than 1\%, particular attention is payed to the estimation of the uncertainties. Within the W/Z group responsible for the analysis, my task has been to calculate the acceptance and extrapolation factors adopted to extend the cross section measurements obtained in the fiducial volume to the total phase space and to a larger combination volume. An exhaustive coverage of the associated systematic uncertainties is provided as integral part of my work. These uncertainties are in fact expected to become the largest ones affecting the experimental measure since those arising from luminosity and statistics will gradually decrease with the increase of the available amount of data.