Measurement of the $t\bar{t}H$ production cross-section with a collimated $H \rightarrow b\bar{b}$ decay in $pp$ collisions at $\sqrt{s} = 13$ TeV with the ATLAS detector

The predictions of the Standard Model (SM) of particle physics have been probed with remarkable accuracy, so far. The Large Hadron Collider (LHC) at CERN has significantly contributed to this quest. A remarkable achievement of the ATLAS and CMS experiments at the LHC was the discovery of the Higgs boson in 2012, the last missing piece of the SM. With the increasing amount of proton-proton collisions delivered by the LHC, more precise measurements of the Higgs boson are now possible, while rare processes are accessible as well. A property of the Higgs boson that is of particular importance is its coupling to the top quark, which is expected to be the strongest in the SM due to the high mass of the top quark. Therefore, its precise measurement is a stringent test of the SM. A direct measurement of the top-quark Yukawa coupling can be assessed through the Higgs-boson production in association with a pair of top quarks ($t\bar{t}H$). This thesis presents the measurement of the $t\bar{t}H$ process with a subsequent Higgs-boson decay to a pair of $b$-quarks ($H\rightarrow b\bar{b}$), the decay mode with the largest branching ratio. The measurement is performed with data collected by the ATLAS detector, corresponding to an integrated luminosity of 139 fb$^{-1}$ at a center-of-mass energy of 13 TeV. Events with one or two charged leptons from the $t\bar{t}$ decay in the final state are considered to the measurement. The main challenge of the $t\bar{t}H (H\rightarrow b\bar{b})$ channel emerges from the large SM backgrounds from the production of top-quark pairs with additional jets ($t\bar{t}$+jets). Also the many jets coming from $b$-hadrons ($b$-jets) in the final state cause combinatorial ambiguities. Thus, the identification of such jets is decisive in order to determine the signal and reject many background processes. The $t\bar{t}H$ events are split into exclusive analysis regions, based on the number of leptons, jets, and jets tagged as $b$-jets, providing regions enhanced in signal, or in the main background components. Specifically in the single-lepton channel, a boosted category is defined by selecting events in which the Higgs boson and possibly also the hadronically decaying top quark are produced with high transverse momentum ($p_{T}$), with their decay products being collimated in large-radius jets. The single-lepton boosted channel targets events with Higgs-boson candidate $p_T\geq 300$ GeV and is the main scope of this thesis. To identify the reconstructed objects with the underlying particles and to maximise the discrimination of the $t\bar{t}H$ signal from the overwhelming $t\bar{t}$+jets background events in the signal-enriched regions, machine-learning algorithms are employed. The background is dominated by a $t\bar{t}$ process with an additional gluon in the final state which further splits into a pair of $b$-quarks ($t\bar{t}+b\bar{b}$). Besides, a large number of heavy-flavour jets in the final state is not well modelled, thus many systematic uncertainties have to be considered, decreasing the sensitivity of the measurement. All the defined analysis regions are analysed together in a combined profile likelihood fit to test for the presence of signal. The fit simultaneously determines the event yields for the signal and the most important background component, while constraining the overall background model within the assigned systematic uncertainties. Eventually, the ratio of the measured $t\bar{t}H$ cross section to the SM expectation in the inclusive cross-section measurement is found to be $0.35^{+0.36}_{-0.34}$, corresponding to an observed (expected) significance of 1.0 (2.7) standard deviations. A $t\bar{t}H$ signal strength larger than the SM prediction is excluded at 95\% confidence level. The measurement uncertainty is dominated by systematic uncertainties, mainly regarding the theoretical knowledge of the $t\bar{t}+{\geq} 1b$ background process. Finally, to further test the SM, the cross-section is measured differentially as a function of the generator-level Higgs-boson $p_T$, taking advantage of the reconstruction of the Higgs-boson kinematics.