Executive Summary : | Precision physics is crucial for understanding fundamental interactions in high-energy colliders, as the top quark, the heaviest elementary particle in the standard Model (sM), has a strong potential to couple to new physics scenarios. The decay width (Γt) of the top quark is of special importance, as its large value indicates a short lifetime compared to its hadronization period. This allows us to study the properties of the top quark as a 'free' quark, allowing us to probe sM parameters more precisely and search for new physics scenarios. To achieve a precise decay width, state-of-the-art computations have been performed, obtaining next-to-leading order QCD & EW corrections and recently fully analytic next-to-next-to leading order (NNLO) QCD corrections. Current measurements of the decay width at ATLAs and CMs collaborations are at around 20% accuracy, but these measurements are expected to improve substantially at future colliders reaching percent level accuracy. To compare with these measurements, theoretical predictions must reach similar precision and compute beyond NNLO QCD. The proposed proposal aims to compute NNLO mixed QCD-EW corrections to the decay width, stabilizing dependence on EW input parameters and QCD scales. The strategy will involve computing two-loop virtual Feynman diagrams along with all real emission diagrams and summating them to find the finite decay width. The results will be a milestone in the study of top-quark properties, enriching our insight into EWsB and the existence of new physics. |