Extraction of top-Yukawa coupling from $t\bar{t}$ cross-section in single-leptonic final state with $\sqrt{s}=13\;\mathrm{TeV}$ data from the ATLAS detector

In the Standard Model (SM) of particle physics, the interaction of fermions with the Higgs field is referred to as the Yukawa interaction, the strength of which is proportional to the mass of the fermions. The top quark, being the heaviest fermion, exhibits the largest value of the Yukawa coupling strength. Conventionally, the $pp \rightarrow t\bar{t} H$ process has been extensively used to extract the top-Yukawa coupling. However, this thesis aims to measure the ratio of the top-Yukawa coupling strength over its SM value, i.e., $Y_{t} = g_t/ g_t^\text{SM}$ using differential distributions of the $t\bar{t}$ cross-section. This method has an advantage that the obtained $Y_{t}$ is independent of the Higgs coupling to other particles. The analysis is conducted on the single-leptonic decay channel using $2015-2018$ data with a centre-of-mass energy of $\sqrt{s} = 13\;\mathrm{TeV}$ from the ATLAS detector at the Large Hadron Collider (LHC), corresponding to an integrated luminosity of $140\;\mathrm{fb}^{-1}$. The presence of a virtual Higgs boson between the two top quarks modifies the $t\bar{t}$ differential cross-section. The electroweak correction, which is a function of $Y_{t}$, starts to enter the cross-section at one-loop order. The largest $Y_{t}$ sensitivity is observed in the regions close to the $t\bar{t}$ production threshold energy, i.e., at low $t\bar{t}$ invariant mass ($m_{t\bar{t}}$) regions. An angular dependence is also observed on the scattering angle of the top quark in the $t\bar{t}$ rest frame, at large $m_{t\bar{t}}$ values. Events are reconstructed with at least four jets in the final state, two of them with a requirement that they originate from a $B$-hadron decay. An algorithm is devised to specifically reconstruct the $m_{t\bar{t}}$ for each event. A detailed statistical analysis is then conducted, taking into account all relevant backgrounds, whose contribution to the total Monte Carlo prediction is very small. A profile likelihood fit is performed on data using binned $m_{t\bar{t}}$ distributions for different $Y_{t}$ values. Due to a linear dependence of the electroweak corrections on $Y_{t}^{2}$, the fit is performed with $Y_{t}^{2}$ as the parameter of interest. The analysis is dominated by systematic uncertainties, with the jet energy modelling and resolution uncertainties contributing the most to the resultant error on $Y_{t}^{2}$. This is followed by theoretical modelling uncertainties on the $t\bar{t}$ sample. The fit results in an expected $Y_{t}^{2}$ of $1.0^{+1.8}_{-1.7}$, with the observed $Y_{t}^{2}$ of $2.3^{+1.8}_{-1.7}$. An upper limit on $Y_{t}$ at 95\% confidence level is extracted using the obtained $Y_{t}^{2}$. An observed upper limit of 2.32 on $Y_{t}$ is thus achieved, with the expected upper limit of 2.06. The resulting $Y_{t}$ from this method is less precise, but complementary to the $Y_{t}$ obtained from other measurement methods due to its sensitivity to a heavy Higgs sector.