Nested soft-collinear subtractions. Integrated subtraction terms and QCD-electroweak corrections to on-shell vector boson production at the LHC

In the forthcoming years, precise measurements at the LHC and its high-luminosity upgrade will scrutinise the inner workings of the Standard Model of particle physics to an unprecedented level. Among the most ambitious goals of this physics program is the determination of the W-boson mass with the astounding precision of O(0.01%). Such a precision would match the precision achieved in electroweak fits and will allow for a powerful test of the SM at the quantum level. The recent shift of focus from direct searches for New Physics to precision studies at the LHC is the consequence of the fact that clear evidence of physics beyond the Standard Model is so far absent. We note, however, that precision studies at the LHC are made possible by a remarkable progress on the theory side, culminating in the fully-differential description of a vast number of phenomenologically relevant processes with NNLO QCD accuracy. Two main obstacles in such computations that need to be addressed are the complicated structure of two-loop multi-scale scattering amplitudes and the appearance of infrared singularities. This thesis consists of two parts. In the first part, we discuss the recently proposed nested soft-collinear subtraction scheme which allows for a modular, analytic and local way of handling infrared singularities at NNLO. We analytically compute a number of single- and double-unresolved integrated subtraction terms that arise in the process of regulating real-emission contributions. More specifically, we compute integrated triple-collinear subtraction terms for all possible partonic splittings, both initial- and final-state. We also obtain integrated double-soft subtraction terms that arise in the context of colour-singlet decays to massive partons. These results improve the efficiency and numerical stability of practical computations and contribute towards establishing a NNLO QCD subtraction formula for arbitrary hard scattering processes at hadron colliders. In the second part of this thesis, we make use of the nested soft-collinear subtraction scheme to describe mixed QCD-EW corrections to on-shell vector-boson production at the LHC at a fully-differential level. We first obtain mixed QCD-QED corrections to on-shell Z-boson production by abelianising the corresponding NNLO QCD calculation. We then extend these results by including mixed QCD-weak corrections into theoretical description of this process. In the case of W-boson production, we focus on simplifications that arise in the regularisation of double-real contributions. We study phenomenological impact of these corrections for a number of observables studied in Zand W-boson production processes and specifically discuss their implications for the W-boson mass measurement at the LHC.