Measurement of $t$-channel single top-quark production in proton-proton collisions at a center-of-mass energy of 13 TeV using the full ATLAS Run 2 dataset

This dissertation presents the measurement of the $t$-channel production of single top quarks and antiquarks using the complete Run 2 dataset recorded by the ATLAS detector. The cross-section of the process is measured separately for top quark and top antiquark production. Additionally, the ratio of these cross-sections, denoted as $R_t$, is also determined. The methodology involves a cut-based selection, a neural network for signal separation, and a binned maximum likelihood fit. The full Run 2 dataset from the ATLAS detector encompasses an integrated luminosity of $\mathcal{L}_{\text{int}} = 140\,\mathrm{fb}^{-1}$ from proton-proton collisions at a center-of-mass energy of $\sqrt{s} = 13\,\mathrm{TeV}$. The total cross-sections are measured to be $\sigma(tq) = 137^{+8}_{-8}\,\mathrm{pb}$ for top-quark production and $\sigma(\bar{t}q) = 84^{+6}_{-5}\,\mathrm{pb}$ for top-antiquark production. The combined cross-section is determined to be $\sigma(tq+\bar{t}q) = 221^{+13}_{-13}\,\mathrm{pb}$, and the cross-section ratio is $R_{t} = \sigma(tq)/\sigma(\bar{t}q) = 1.636^{+0.036}_{-0.034}$. The measured cross-sections align well with the predictions made at the next-to-next-to-leading order in quantum chromodynamics. The measured total cross-section is further used to derive a constraint on the CKM matrix element $|V_{tb}|>0.95$ at the 95% confidence level.