The context of the project is the study of the fundamental particles and interactions of nature. This is done in the framework of Quantum Field Theory (QFT), which treats elementary particles as excited quantum states of fields. The study of elementary particles and their interactions is mainly driven by high-energy collision experiments, where particles are collided at very high energies. The Large Hadron Collider (LHC) at CERN is the largest and most powerful particle collider ever built and it is collecting an unprecedented amount of data of particle collisions, probing previously unexplored energy scales and interactions.
All interactions and particles observed so far in collision experiments are compatible with the Standard Model (SM), namely a QFT which describes the strong interactions of quantum chromodynamics (QCD), weak and electromagnetic interactions. The SM is currently the most accurate and successful theory of the fundamental interactions of nature. The SM has however several important shortcomings and scientists are putting great effort in the search of new physics Beyond the Standard Model (BSM). Our ability to test the SM as accurately as possible is crucial for detecting possible deviations representing BSM signals and therefore the discovery of new particles and interactions.
Scattering amplitudes are essential ingredients for theoretical predictions for high-energy experiments. They are related to the probability of interactions between fundamental particles. They are computed in perturbation theory and next-to-next-to-leading-order (NNLO) accuracy is typically needed to match the one of the experimental data. This involves the calculation of complicated integrals, called Feynman integrals. The calculation of amplitudes is especially difficult for processes with many external particles (or legs), which are however very common at the LHC, due to the high centre-of-mass energy of the collisions. Multi-particle scattering amplitudes are therefore a crucial objective of current high-energy phenomenology.
The main goal of this project is a breakthrough in our capability of computing complicated multi-loop quantities, focusing on two-loop corrections to five-point scattering amplitudes in QCD. This involves theoretical work for better understanding multi-loop integrals, the development of new computational tools and techniques capable of tackling these complex calculations, as well as the explicit computation of important multi-loop results relevant for modern phenomenology, such as two-loop five-point amplitudes.
The usage of finite fields is an important innovative aspect of this project. Finite fields are numerical fields with a finite number of elements that can be represented by machine-size integers. Operations over finite fields are therefore relatively fast but also exact and free of numerical errors. Multivariate reconstruction algorithms allow to infer full numerical or analytic results out of several numerical evaluations over finite fields. This allows to sidestep the appearance of large analytic expressions in intermediate stages, which are often the main bottleneck of amplitude calculations, since only the final result is reconstructed analytically. These methods are very general and have a huge range of possible applications in science, even outside physics.
