High-energy behaviour of scattering amplitudes in the standard model effective field theory

Our current understanding of the fundamental interactions among the elementary constituents of matter is encapsulated in a theoretical framework called the standard model. Most of its predictions have been experimentally verified, some to a very high degree of accuracy, in a experimental effort which spans a large number of experiments conducted over several decades at different scales. Notwithstanding its amazing success, observations as well as theoretical arguments point to the existence of new physics at higher scales. A consistent and model-independent approach that can be used to systematically study interactions at very short distances, i.e. at high energy, is that of an effective field theory. In this work, I present the study of several scattering processes at very high energy involving the heaviest degrees of freedom of the standard model, i.e. the top quark, the vector bosons W and Z, and the Higgs boson. I employ the framework of the standard model effective field theory, where the standard model is extended to include higher order operators of dimension six which are compatible with the local and global symmetries at dimension four. The main motivation for this work is to explore the possibly increased sensitivity to new physics of 2 to N scattering amplitudes with respect to 2 to 2 processes which have been already considered. The analysis is divided in two parts. In the first more theoretical part, the high-energy behaviour of the helicity amplitudes is evaluated for every core process, looking for footprints of S-matrix unitarity violation. In the second more phenomenological part, core processes are embedded in realistic initial-final states that can appear at future very high-energy lepton collider. This allows to estimate their sensitivity to a selected set of the standard model effective field theory operators and determine whether they can be useful to improve on the current (or expected) constraints on the corresponding Wilson coefficients.