Automated NLO Electroweak Corrections to Processes at Hadron and Lepton Colliders

The aim of this thesis is the completion of the NLO automated framework of the MC program WHIZARD, accounting for NLO corrections in the full SM for cross sections and distributions of processes at hadron and lepton colliders. Specifically, it builds on the implemented FKS subtraction scheme for NLO QCD calculations, and extends it to automated NLO EW and QCD-EW mixed corrections. To that end, the implemented FKS scheme is generalised to systematically subtract QED and QCD infrared (IR) divergences in mixed coupling expansions. The automated computation of NLO contributions is validated for a set of benchmark processes at the LHC, including e.~g. $t\bar{t}~(+H/W/Z)$ production. Cross-checks for $e^+e^-$ processes likewise show that WHIZARD can be used for predictions at lepton colliders including fixed $\mathcal{O}(\alpha)$ corrections. This framework is applied to the study of NLO EW cross sections and differential distributions for multi-boson processes at a future multi-TeV muon collider. For some high-energy lepton-collider setups, tiny initial-state masses jeopardise the reliability of fixed-order expansions of observables in QED perturbation theory. In order to recover meaningful predictions for NLO EW observables, QED parton-distribution functions (PDFs) must be applied guaranteeing a universal treatment of collinear ISR effects. This however causes computational challenges for MC integration measures. Methods to cope with these difficulties are presented in this thesis. With the automation of NLO EW corrections for hadron and lepton collision processes, WHIZARD offers a powerful tool for EW precision studies at current and future colliders and provides the desired accuracy level of predictions for new physics searches.