First Measurements of the Differential Cross Sections of Higgs Boson Production and Decay in the Four Lepton Final State

The discovery of a new scalar particle in the search for the Higgs boson at the Large Hadron Collider (LHC) was a great success for the ATLAS and CMS collaborations. Additional measurements of this new particle present opportunities to both test the Standard Model (SM) predictions for the Higgs boson and to search for non-SM properties of this new particle. This thesis presents measurements of the mass, signal strength, and production cross sections of the Higgs boson in the $H \rightarrow ZZ^{(*)} \rightarrow \ell\ell\ell'\ell' $($\ell,\ell'=e,\mu$) decay channel. The cross section measurements are performed using 20.3 fb$^{-1}$ of $pp$ collisions at center of mass energy $\sqrt{s}=8$ TeV collected by the ATLAS detector and the mass and signal strength measurements are performed using an additional 4.5 fb$^{-1}$ of $pp$ collisions at $\sqrt{s}=7$ TeV. From the data in the $H \rightarrow4\ell$ channel, the best estimate of the mass is $124.51~\pm~0.52~\rm{(stat)}~\pm 0.06~\rm{(syst)}$ GeV. The signal strength (the ratio of observed signal events to expected events from a Standard Model Higgs boson) is measured to be $1.64~\pm~0.38~\rm{(stat)}~\pm~0.18~\rm{(syst)}$. An inclusive cross section time branching ratio measurement is performed within a fiducial volume and found to be $2.11^{+0.53} _{ - 0.47}~(\text{stat})^{+ 0.08 } _{ - 0.08 }~(\text{syst})$ fb. Differential cross section measurements are performed for six observables which are sensitive to properties of the Higgs boson production and decay. An unfolding procedure is used to correct for detector effects in the differential measurements and comparisons are made to several theoretical calculations. No significant deviations from the SM predictions are observed.