SECOND ORDER VIRTUAL ELECTROWEAK EFFECTS IN THE STANDARD MODEL

Over the last decades, the Standard Model of particle physics has predicted with spectacular agreement various experimental results, the latter being the discovery of the Higgs boson in 2012 at the CERN Large Hadron Collider (LHC). Nevertheless, several unresolved problems still affect the theory, from the missing description of Gravity to the absence of a candidate elementary constituent for Dark Matter, indicating that the Standard Model cannot represent the ultimate fundamental theory of the Universe. Given the absence of direct discovery expectations within a specific energy range, the most efficient strategy is to search for possible new physics signatures through high-precision analyses. Considering the striking statistical enhancement that is expected for the High Luminosity program of LHC and the Future Circular Collider, the theoretical predictions are required to match a tremendous level of precision in order to perform a significant comparison. Within this scenario, the evaluation of the second order electroweak (EW) corrections for a wide class of processes is of pivotal necessity. This thesis focuses on the latest developments that provide the fundamental building blocks for the accomplishment of such a challenging task. We will detail the modern machinery for the computation of two-loop EW virtual amplitudes, from the Ultraviolet Renormalization procedure to the Infrared Subtraction of singularities, from the γ_5 treatment in dimensional regularization to the automated evaluation of multi-loop Feynman diagrams and associated integrals. We will discuss the issues associated to the presence of unstable particles and we will present our first results for the case of the Neutral-Current Drell-Yan process, that represents the standard candle for the precision physics program at hadron colliders. This calculation allowed us to test our theoretical and computational workflow across different complementary aspects, and represents a fundamental milestone to assess the numerical stability and physical reliability of our future results.