The Standard Model Higgs boson produced in association with a $t$-quark pair and decaying to a $b$-quark pair from LHC Run-2 proton-proton 13 TeV collisions in ATLAS

Discovery of the Standard Model Higgs boson in 2012 by the ATLAS and CMS Collaborations at the LHC was an extraordinary moment in the advancement of science. In this thesis the author presents the theory, methodology and results of a search for the Standard Model Higgs boson produced in association with a ${t}$-quark pair and decaying to a ${b}$-quark pair as it was published in 2018. This search lead to evidence for ${t\bar{t}H}$ and subsequent discovery. The data used are from proton-proton (${pp}$) collisions in A Toroidal LHC ApparatuS (ATLAS) at CERN during Run-2 of the Large Hadron Collider (LHC) at centre-of-mass energy ${\sqrt{s}=13}$ TeV corresponding to an integrated luminosity of ${36.1\pm0.8}$ ${\text{fb}^{-1}}$. Events were selected to contain one electron or one muon from the ${t}$-quark decays and the events were then categorised according to the number of jets counted in the event and the number of those jets which were identified as likely ${b}$-jets. Many backgrounds were considered in the analysis and all are dominated by ${t\bar{t}+\textrm{jets}}$ production. An analysis framework was developed and validated and was successful in the analysis at finding evidence for Higgs bosons in ${t\bar{t}H\left(b\bar{b}\right)}$, as presented in this thesis, and was subsequently used successfully in observation of ${t\bar{t}H}$. Multivariate methods were used to discriminate between signal and background events, and this thesis presents both the standard analysis methods and newer multivariate methods of a more tentative nature used for classification of events as signal ${t\bar{t}H\left(b\bar{b}\right)}$ and background ${t\bar{t}b\bar{b}}$ in order to investigate the efficacy of these methods. Novel techniques were developed for interpretation of training data and for improvement of both classification efficiency and interpretability of modelling for the purposes of classification. A highly-parameterised inception convolutional neural network (ICNN) model was compared with the standard analysis boosted decision tree (BDT) model for classification of events as signal and background. The ICNN was observed to classify a fraction of ${0.7006\pm 0.0097\left(\textrm{stat.}\right)^{+0.0033}_{-0.0028}\left(\textrm{syst.}\right)}$ events correctly while the BDT was observed to classify a fraction of ${0.6979\pm 0.0136\left(\textrm{stat.}\right)^{+0.0027}_{-0.0031}\left(\textrm{syst.}\right)}$ events correctly. Further, the ICNN and other newer models also made accessible alternative and additional insights and interpretations of their respectively achieved classification modelling. These included the techniques of mean saliency mapping and activation maximisation. Saliency mapping provided not only a means of ranking features in data on a per-class basis, but also a means of providing saliency measures for individual features in data on a per-event basis, something not obviously possible using conventional models such as decision trees. In the full combined analysis, for a Standard Model Higgs boson of ${125}$ GeV, the ratio of the observed signal ${t\bar{t}H}$ cross-section ${\sigma_{t\bar{t}H}^{\textrm{obs.}}}$ to the cross-section expectation of the Standard Model ${\sigma_{t\bar{t}H}^{\textrm{SM}}}$, ${\mu_{t\bar{t}H}=\sigma_{t\bar{t}H}^{\textrm{obs.}}/\sigma_{t\bar{t}H}^{\textrm{SM}}}$ (signal strength), was found to be ${\mu_{t\bar{t}H}=0.84^{+0.64}_{-0.61}}$, with signal strength greater than 2 excluded at the 95 % confidence level and the expected exclusion limit in the absence of signal being 1.2. A ${1.4\sigma}$ excess above the expected background was observed, while an excess of ${1.6\sigma}$ was expected with the existence of the Standard Model Higgs boson. Evidence of ${t\bar{t}H}$ was declared in 2018. The ${t\bar{t}H\left(b\bar{b}\right)}$ analysis, one of the most complicated ATLAS analyses to date, led to observation of the ${t\bar{t}H}$ process, enabling direct investigation of the mechanism of electroweak symmetry breaking and the matter-Higgs relationships predicted by electroweak symmetry breaking in the Standard Model. The observation of the ${t\bar{t}H}$ process used data corresponding to an integrated luminosity of ${79.8}$ ${\text{fb}^{-1}}$ and a combination of results from Higgs boson decays to ${b\bar{b}}$, ${WW^{*}}$, ${\tau^{+}\tau^{-}}$, ${\gamma\gamma}$ and ${ZZ^{*}}$ with an observed significance of ${5.8\sigma}$, compared to an expected significance of ${4.9\sigma}$. Combined with ${t\bar{t}H}$ search results using data recorded at centre-of-mass energies of ${\sqrt{s}=7}$ TeV and ${\sqrt{s}=8}$ TeV, the observed significance was ${6.3\sigma}$, compared to an expected significance of ${5.1\sigma}$. Assuming Standard Model branching fractions, the ${t\bar{t}H}$ production cross-section at ${\sqrt{s}=13}$ TeV was measured as ${670\pm 90\left(\textrm{stat.}\right)_{-100}^{+110}\left(\textrm{syst.}\right)}$ ${\text{fb}}$, which is in agreement with the Standard Model theoretical prediction of ${507_{-50}^{+35}}$ ${\text{fb}}$.