Model-independent on-shell amplitude methods for one-loop Higgs production via gluon fusion

An amplitude-based description of new physics can serve as an alternative to the traditional frameworks of Standard Model Effective Field Theory (SMEFT) and Higgs Effective Field Theory (HEFT), by constructing scattering amplitudes directly through bootstrap methods without reference to an explicit Lagrangian. This approach provides a new model-independent description of electroweak symmetry breaking that remains valid beyond truncated EFT expansions, while fully capturing the helicity structure of the interactions. A key advantage of this framework is that it is intrinsically on shell, gauge invariant, and free from field-redefinition ambiguities. So far, however, it has been formulated only at tree level. The goal of this thesis is to explore its extension to one loop, making use of techniques such as generalized unitarity, which are well established in QCD. As an illustrative example, Higgs production through gluon fusion is studied. While conceptually simple, this process already requires a one-loop treatment in order for an EFT description to reproduce the Standard Model contribution.