Subleading effects of soft emissions: A study of next-to-leading power threshold corrections to scattering amplitudes

Accurate and precise theory predictions for collider observables are instrumental for the discovery of new physics. To improve the quality of these predictions, increasingly complex contributions to scattering amplitudes must be evaluated. In certain kinematic regimes this approach no longer suffices due to the occurrence of large logarithmic contributions at every order, which spoil the perturbative series. One such regime is when the final state particle is produced at threshold, rendering additional radiation soft. In this instance, the threshold expansion can be applied to simplify the structure of the scattering process by keeping only leading-power (LP) terms in the soft momenta, allowing for the factorisation of the amplitude and the identification of the all-order result. In this procedure the large logarithms are resummed and a well behaved result is obtained. In this thesis we aim to improve this approach by retaining also next-to-leading power (NLP) terms in the threshold expansion, thereby enhancing the performance of the approximation further away from threshold. Firstly, we study the factorisation properties of scattering amplitudes in QED at NLP, revealing a finite set of functions with more complex interplay, which nevertheless capture the studied NLP behaviour at the one- and two-loop level. Secondly, we provide a detailed analysis of the various sources of NLP terms in case of multiple emissions, using a method of regions approach. Thirdly, we develop a framework for the resummation of leading-logarithmic (LL) NLP terms in colour singlet production processes. Finally, we study the numerical effects of NLP terms, at both fixed- and all-order using the developed resummation approach. Results indicate that NLP effects can indeed be sizeable, such that a consistent inclusion of NLP effects would benefit particle physics phenomenology