High-precision multi-leg Higgs and top physics with finite fields

Modern experiments at the Large Hadron Collider will yield measurements of several important observables with percent-level accuracy. Similarly accurate theoretical predictions are however needed for comparison with data, unlocking its outstanding potential to test the Standard Model of fundamental interactions, its symmetry braking mechanism and its limitations, hence giving us important hints about new physics. High-precision predictions in high-energy physics are however affected by high complexity. This is currently preventing high-precision studies for crucial interactions, such as multi-particle interactions involving the top quark and the Higgs boson, due to the presence of a large number of external particles and massive external and internal states. At the core of these predictions is the perturbative calculation of scattering amplitudes, which need to be computed at least at next-to-next to leading order to match the experimental uncertainty. This task, for multi-leg massive processes, is beyond the capabilities of existing techniques and tools. FFHiggsTop aims to achieve a breakthrough in high-precision predictions for high-energy scattering processes involving many external particles and massive internal and external final states. This will be achieved thanks to the development of new revolutionary methods for scattering amplitudes, building on top of cutting-edge technology based on finite fields and functional reconstruction techniques. Its main objectives are: 1. Develop ground-breaking techniques for computing scattering amplitudes at higher orders in perturbation theory 2. Perform new high-precision phenomenological predictions for top - anti-top pair production in association with an electroweak vector boson or a Higgs boson. FFHiggsTop will unlock a range of new possibilities for studying fundamental interactions and develop new technology with a broad spectrum of possible applications in physics and other sciences.