Search for the Supersymmetric Partner of the Top Quark with the ATLAS Detector via $\tilde{t}^{}_{1} \rightarrow t \widetilde{\chi}^{0}_{1}$ and $\tilde{t}^{}_{1} \rightarrow b \widetilde{\chi}^{\pm}_{1}$ Decays

The elementary particles composing matter and their interactions are described by the Standard Model of particle physics. The Standard Model of particle physics enabled predictions that were experimentally verified and has been confirmed throughout the past decades by data. Nevertheless, there are several theoretical reasons not to consider it as the ultimate theory. The strongest motivation to expect Physics beyond the Standard Model is the hierarchy problem. The radiative corrections to the mass of the Higgs boson grow quadratically with the square of the energy scale at which the Standard Model is considered to be valid. As a result, the parameters of the Standard Model need to be fine-tuned in order for the mass of the Higgs boson to acquire the value experimentally measured, despite the possibly large corrections. Supersymmetry is a promising theory extending the Standard Model which solves many of its shortcomings, including the hierarchy problem. Supersymmetry postulates a new fermion-boson symmetry resulting in the introduction of new particles, called superpartners, with the same quantum numbers and masses as the Standard Model particles, except for the spin, differing by half a unit. This new symmetry enables a cancellation of the radiative corrections due to the Standard Model particles with the corrections due to the newly introduced superpartners, contributing with opposite sign. Since no superpartners with the same mass as the Standard Model particles have been observed, Supersymmetry must be broken to allow the superpartners to have a mass different from the mass of the corresponding Standard Model particles. In the minimal version of Supersymmetry in terms of new particles, the Minimal Supersymmetric Standard Model, the hierarchy problem can still be solved with a moderate amount of fine-tuning if the masses of at least some of the superpartners are at the TeV energy scale. The conservation of a new multiplicative quantum number, the R-parity, can be assumed to prevent phenomena in contrast with experimental evidences, as the proton decay. Superpartners have R-parity -1, and Standard Model particles R-parity +1. If the conservation of R-parity is assumed, in collider experiments supersymmetric particles can only be produced in even numbers (usually two), and the lightest supersymmetric particles (LSP, usually taken to be the neutralino), is stable. The LHC (Large Hadron Collider), is a hadron collider able to accelerate protons to unprecedented energies. Between 2010 and 2012 it operated at a centre-of-mass energy of the proton-proton collisions of 7 and 8 TeV. Its general-purpose experiments, ATLAS (A Toroidal LHC Apparatus) and CMS (Compact Muon Spectrometer) collected data corresponding to about 5 $fb^{-1}$ at $\sqrt{s}$ = 7 TeV and 20 $fb^{-1}$ at $\sqrt{s}$ = 8 TeV. The LHC and its experiments have been built with the main motivations of searching for the Higgs boson, discovered by the ATLAS and CMS experiments in 2012, and searching for signals of Supersymmetry. There are strong theoretical reasons to expect the supersymmetric particles to lie at the TeV energy scale, which would make them accessible at the LHC. In the Minimal Supersymmetric Standard Model, the lightest superpartner of the top quark, light stop is very likely to be lighter than the superpartners of the other quarks. This thesis focuses on the search for direct stop pair production with the data collected by the ATLAS experiment. Two analyses have been performed, addressing different final states and decay modes. The first analysis targets stop masses close to the mass of the top quark, ideal to solve the hierarchy problem. The mass spectrum assumed is such that m(stop) < m(t) and m(chargino)+m(b)Under this assumption, the decay mode stop $\rightarrow$ b chargino is favoured. The chargino is assumed to further decay via chargino $\rightarrow$ W neutralino. The analysis targets scenarios in which both W bosons are assumed to decay leptonically. The expected final state is therefore composed of two b-jets, two leptons of opposite charge, and missing transverse energy due to the presence of the neutralino, which is assumed to be the LSP. To enhance the acceptance of the analysis to the signal, in the event selection process only one of the jets is required to be b-tagged. The same final state is expected from di-leptonic decays of top-antitop pairs, that is therefore the main background to this search. To discriminate signal and background, the final state objects are used to construct a variable providing the minimum energy compatible with the mass scale of the subsystem of interest. This variable is expected to peak at about 2 times the mass of the top quark for the top-antitop background, while for the signal the position of the peak depends on the stop mass. Further discriminating power is given by the different masses of the invisible particles in signal and background. Two regions where the presence of the signal is enhanced have been defined, called signal regions. A careful estimation of the background from Standard Model processes has been performed, and the background prediction compared to the number of events observed in data. No significant excess of data over the Standard Model expectation, hinting towards the presence of signals from new physics processes, has been observed. The results have been interpreted in terms of 95 % CL exclusion limits. Both model-independent exclusion limits on the number of signal events from new physics processes and model-dependent exclusion limits have been derived. The model-dependent limits are given in the (stop-neutralino)-mass plane, under different hypotheses on the masses of the supersymmetric particles. They have been derived combining the results of the two-lepton analysis briefly described above with the results of an analysis performed in the one-lepton channel conduced in parallel, optimised on the same scenarios and showing a similar sensitivity. A wide range of stop masses around and below the top mass have been excluded. In particular, in the scenario where the chargino mass is set to twice the neutralino mass, that has been explored for the first time with this analysis, stop masses between 120 GeV and the top mass have been excluded for a neutralino mass of 55 GeV. For a chargino mass just above the experimental limit of 106~GeV set by LEP, stop masses between 120 GeV and the the top mass are excluded for a neutralino mass of 55 GeV, and masses between 130 and 155 GeV are excluded for a neutralino mass of 75 GeV. These results significantly extend the limits available on this scenario from searches at the Tevatron and from a previous search of the ATLAS collaboration. The rise of the centre-of-mass energy of the proton-proton collisions from 7 to 8 TeV made possible the exploration of higher stop masses. An analysis targeting stop masses between 300 and 700 GeV has been performed in the hadronic channel, characterised by the largest branching ratio and therefore suitable to address scenarios where the top squark mass is high. The stop is assumed to decay via stop $\rightarrow$ t neutralino and stop $\rightarrow$ b chargino. Scenarios where both decay modes are present simultaneously with different branching ratios have been considered for the first time. Three different signal regions optimised for different values of the stop mass and different assumptions on the branching ratios in the two decay modes have been defined. The nominal signature of the signal is six jets, out of which two are b-jets, and missing transverse energy. The number of jets can be reduced if the mass spectrum is compressed, or if the top quarks produced in the decay of the stop have significant boost, and therefore its decay products are very collimated. The main backgrounds to this search are top-antitop pairs production, W and Z boson production in association with heavy flavour jets. The estimation of this last source of background is particularly challenging, because the signal regions requirements make any control sample have a few events in it. To overcome this problem, a technique has been developed to measure the fraction of Z boson plus four to six jets events having at least two b-tagged jets. This technique allows to define the control sample without any requirement on the number of b-tagged jets, and thus to significantly reduce the uncertainty on the estimation of this background. The numbers of events observed in data in the different signal regions have been compared to the background prediction. No significant excess has been observed, therefore exclusion limits have been set. To derive model-dependent limits, the results of the signal regions have been combined. The results are given in the (stop-neutralino)-mass plane for different values of the branching ratio BR(stop $\rightarrow$ top neutralino)=1-BR(stop $\rightarrow$ b chargino). For BR(stop $\rightarrow$ t neutralino)=100 %, stop masses between 270 and 546 GeV are excluded for a neutralino lighter than 30 GeV. These limits significantly extend the previous results. For BR(stop $\rightarrow$ t neutralino)=50 %, stop masses between 250 and 550 GeV are excluded for a neutralino lighter than 60 GeV. The searches performed in the context of this thesis and other results from the ATLAS and CMS collaborations allowed to exclude a large variety of stop masses under different assumptions on the decay modes and on the mass spectra. Nevertheless, even under the strong assumptions of 100 % branching ratio decays, the exclusion limits are still in the sub-TeV range. This year the ATLAS experiment will restart collecting data at the increased centre-of-mass energy of the proton-proton collisions of 13 TeV. The searches for direct stop pair production will continue to be of primary importance in the physics program of ATLAS, and need to be designed to explore all the possibilities not covered so far. Due to the increase in the centre-of-mass energy, many interesting final states will be characterised by very collimated and energetic decay products. The capability of tagging energetic b-jets in environments characterised by a high density of particles will therefore be an important requirement for stop searches. Among the aspects concurring to this goal, a tracking algorithm able to resolve tracks close to each other is of crucial importance. In view of this, the reconstruction efficiency of the track reconstruction algorithm of the ATLAS experiment has been studied on a simulated sample of $B^0$ mesons. This study contributed to the identification of a step of the track reconstruction procedure that needs to be modified to achieve good performance in case the tracks originate from particles which have a separation below the size of the pixel sensors of the tracker of the ATLAS experiment.