A study of the Higgs boson decay $H\rightarrow ZZ^{(*)}\rightarrow4 \ell$ and inner detector performance studies with the ATLAS experiment

The Higgs mechanism is the last piece of the SM to be discovered which is responsible for giving mass to the electroweak $W^{\pm}$ and $Z$ bosons. Experimental evidence for the Higgs boson is therefore important and is currently explored at the Large Hadron Collider (LHC) at CERN. The ATLAS experiment (A Toroidal LHC ApparatuS) is analysing a wide range of physics processes from collisions produced by the LHC at a centre-of-mass energy of 7-8$\,$TeV and a peak luminosity of $7.73\times10^{33}\,\mathrm{cm^{-2}s^{-1}}$. This thesis concentrates on the discovery and mass measurement of the Higgs boson. The analysis using the $H\rightarrow ZZ^{(*)}\rightarrow4 \ell$ channel is presented, where $\ell$ denotes electrons or muons. Statistical methods with non-parametric models are successfully cross-checked with parametric models. The per-event errors studied to improve the mass determination decreases the total mass uncertainty by $9\%$. The other main focus is the performance of the initial, and possible upgraded, layouts of the ATLAS inner detector. The silicon cluster size, channel occupancy and track separation in jets are analysed for a detailed understanding of the inner detector. The inner detector is exposed to high particle fluxes and is crucial for tracking and vertexing. The simulation of the detector performance is improved by adjusting the cross talk of adjacent hit pixels and the Lorentz Angle in the digitisation. To improve the ATLAS detector for upgrade conditions, the performance is studied with pile-up of up to 200. Several possible layout configurations were considered before converging on the baseline one used for the Letter of Intent. This includes increased granularity in the Pixel and SCT and additional silicon detector layers. This layout was validated to accomplish the design target of an occupancy $< 1\%$ throughout the whole inner detector. The $H\rightarrow ZZ^{(*)}\rightarrow4 \ell$ analysis benefits from the excellent momentum resolution, particularly for leptons down to $p_T = 6\,$GeV. The current inner detector is designed to provide momentum measurements of low $p_T$ charged tracks with resolution of $\sigma_{p_T}/p_T=0.05\%\,p_T\oplus1\%$ over a range of $|\eta| < 2.5$. The discovery of a new particle in July 2012 which is compatible with the Standard model Higgs boson included the $3.6\sigma$ excess of events observed in the $H\rightarrow ZZ^{(*)}\rightarrow4 \ell$ channel at 125$\,$GeV. The per-event error was studied using a narrow mass range, concentrated around the signal peak ($110\,$GeV$<m_H<150\,$GeV). The error on the four-lepton invariant mass is derived and its probability density function (pdf) is multiplied by the conditional pdf of the four-lepton invariant mass given the error. Applying a systematics model dependent on the true mass of the discovered particle, the new fitting machinery was developed to exploit additional statistical methods for the mass measurement resulting in a discovery with $6.6\sigma$ at $m_H = 124.3^{+0.6}_{-0.5} (stat)^{+0.5}_{-0.3} (syst) \,$GeV and $\mu=1.7\pm0.5$ using the full 2011 and 2012 datasets.