Performance analyses of low-energy secondary-vertex reconstruction and studies towards the extraction of the top-quark Yukawa coupling from the $t\bar{t}$ cross section with the ATLAS experiment

The Large Hadron Collider at CERN is the world's largest and most powerful particle accelerator. Among its various experiments, ATLAS plays a crucial role in probing the Standard Model of particle physics and searching for phenomena beyond it. This dissertation focuses on the development and calibration of two tools aimed at improving the reconstruction of low-energy (soft) secondary vertices as well as on the studies towards the measurement of the top-quark Yukawa coupling, a fundamental parameter of the Standard Model.

Several beyond the Standard Model processes studied at the ATLAS experiment produce soft $b$-quarks in the final state, which can fragment into \textit{b}-hadrons without forming a reconstructable jet. The tools described in this dissertation reconstruct secondary vertices that standard flavour-tagging algorithms may miss. Although the tools share a common goal, they differ in the algorithmic strategies and the software versions in which they are implemented.

The optimisation of the first tool leads to the definition of three working points, resulting in an estimated event efficiency (fake rate) that varies from 27% (0.5%) to 44% (7.1%).

The calibration of the second tool consists in extracting data-to-simulation scale factors, that are used to correct the algorithm's performance in simulated events. A single efficiency scale factor, $\mathrm{SF_{eff}}=0.86 \pm 0.10$, and two fake-rate scale factors (estimated separately for events with low and high average numbers of interactions per bunch crossing) $\mathrm{SF_{fake}^{\mu_L}}= 1.63 \pm 0.15$ and $\mathrm{SF_{fake}^{\mu_H}} = 1.58 \pm 0.13$, are measured. 

The top quark pair-production cross section as a function of the \ttbar invariant mass is sensitive to the top-quark Yukawa coupling in the threshold region. Studies towards the extraction of this parameter are carried out in two different final states. In the lepton+jets channel, an Asimov fit considering the full set of systematic uncertainties yields to $\mathrm{Y}_t^2= 1.00^{+1.21}_{-1.15}$. In the dileptonic final state two neutrinos are produced, which poses a challenge for event reconstruction. Regression methods for estimating the \ttbar invariant mass are presented, demonstrating that, considering only statistical uncertainties, they provide better sensitivity to the top-quark Yukawa coupling (approximately 11%) than the invariant mass of the system composed of the two $b$-hadrons and the two leptons (which provides a sensitivity of 15%).

The results presented in this dissertation not only demonstrate the enhanced capability of the ATLAS experiment to reconstruct soft secondary vertices but also introduce the indirect measurement of the top-quark Yukawa coupling using $t\bar{t}$ events in two different final states, enabled by new event reconstruction methods.