Weak bosons are by now a well-established and observed block of the elementary particles table, but the era of Precision Physics opens up new ways of utilising them in an attempt to uncover the mystery of physics beyond the Standard Model. Being central to what is called Electroweak Symmetry Breaking mechanism, they obtain mass by interacting with the Higgs field. Their longitudinal polarisation is induced by the Goldstone modes of the Higgs field and provides a direct handle on any massive new physics models.

In this thesis, we devote a particular focus on the polarised W-boson production in the context of two processes at the LHC and explore applications of our results. We discuss in depth the current approaches to simulate and measure weak boson polarisation, and present NNLO studies of W+j and W+ W− production at the LHC. We explore the effects and significance of observed perturbative corrections, and in the context of W+j, comment on their application to experimental data. In addition to that, we discuss how polarisation quantities, in particular, angular coefficients, are instrumental in precise W-boson mass measurements which aim to reach 0.01% level of precision. Aiming to fill the gap for precise theoretical input, we provide NNLO + NLO EW predictions, and comment on their effects and theoretical uncertainty.

Furthermore, we explore advancements in the area of fixed-order predictions in general and present results for Wbb̄ production at NNLO precision. This is the first study of a 2 → 3 process involving a massive particle at such accuracy, which marks a milestone following significant advancements in the field. We also discuss the novel proposition for a flavoured anti-kT algorithm, which aims to combine the experimental convenience of anti-kT prescription with a modification for flavoured particles, enabling IR-safe heavy flavour tagging with two real emissions. Results based on this prescription are compared with the well-established flavour-kT method and to available data.

Lastly, we introduce the new framework named HighTEA, which as we hope, will be helpful for the researchers who use the output of fixed order predictions. We present the ideas and structure of the project, the details of its current capabilities, its limitations and aspirations, and provide with user instructions to quickly bring an interested reader up to speed.