Searches for Vector-Like Quarks decaying to W bosons and module placement quality assurance for the ATLAS ITk upgrade.

This dissertation explores the realm of particle physics through two distinct yet interconnected lenses: the search for Vector-Like Quarks (VLQs), and the quality assurance in module placement for the ATLAS Inner Tracker (ITk) upgrade in preparation for the High Luminosity Large Hadron Collider (HL-LHC). The Standard Model (SM) of particle physics explains many natural phenomena yet remains incomplete. VLQs lie at the heart of many extensions to the SM seeking to address the hierarchy problem. VLQs could be produced either singly or in pairs, and then decay to a SM boson and a third-generation quark. While single-production depends on the coupling of the VLQ to the SM particles, pair-production via the QCD interaction provides a model-independent test for VLQs. This paper presents a search for singly- and pair-produced VLQs. The pair-production analysis considers VLQs that decay into a $W$ boson and a bottom quark, with one $W$ decaying leptonically while the other decays hadronically. The analysis uses b-tagging algorithms, charge asymmetry metrics, multiple on-line triggers, and data driven corrections of the ttbar and $W$ +jets back- ground Monte Carlo samples to improve sensitivity during the analysis of the full LHC Run 2 ATLAS dataset. Maximum excluded mass limits were set in this analysis at 1500 GeV for the $B$($T$ → $W$) = 1 scenario. Similar methodologies were followed in the Single VLQ analysis, but remains in the stages of unblinding. Finally, the paper explores the technical challenges and innovations surrounding the ATLAS ITk upgrade, focusing on ensuring the utmost precision in module placement for the inner detector rings and staves. Through comprehensive data analysis and experimental rigor, this dissertation not only contributes to our understanding of fundamental particles but also enhances the technological framework essential for future discoveries in high-energy physics.