Amplitude techniques for Physics Beyond the Standard Model

The Standard Model is known to be incomplete, motivating a sustained effort in particle physics to search for new physics beyond it, for instance through the framework of effective field theories. Amplitude techniques built on the spinor-helicity formalism provide a natural avenue for bottom-up constructions of effective field theories. \\ Effective field theory extensions of the Standard Model can be formulated in this approach directly in terms of the physical observables of interest, namely, the scattering amplitudes of the known SM particles, with a mapping of EFT operators and contact-term amplitudes. \\ In this thesis, we present an overview of the spinor-helicity formalism both for massless and massive particles. We then construct renormalizable and non-renormalizable three-particle vertices using Little Group scaling.\\ We compute in leading order, using amplitude methods, the partonic processes relevant to top pair production both in QCD and in an EFT involving quarks and gluons up to the order $1/\Lambda^2$.\\ We also produce a matching of the new terms' coefficients with SMEFT's Wilson coefficients using amplitudes computed in the literature.