Probing EFT Wilson Coefficients in the $Wtb$ vertex at the HL-LHC

The $Wtb$ vertex, central to top quark phenomenology, provides a unique window into potential new physics beyond the Standard Model, particularly through the framework of Effective Field Theory (EFT). This thesis presents a comprehensive projection for the High Luminosity phase of the LHC (HL-LHC) of constraints on dimension-6 EFT operators affecting the Wtbinteraction, using a global analysis that simultaneously incorporates multiple observables, including single top production cross sections, $W$ boson helicity fractions, and angular asymmetries, across several top quark production and decay modes. A novel fitting methodology is implemented to treat EFT Wilson coefficients consistently, avoiding over-simplifying assumptions made in more traditional approaches. Results show that although the projected sensitivities match current experimental bounds, this underwhelming improvement challenges the justification of HL-LHC expectations and underscores the need for more general and rigorous methodologies. This work demonstrates that global fits can yield more conservative yet robust limits and calls into question the assumptions embedded in prevalent analysis strategies.