Scattering amplitudes provide a window on the mathematical structure of Quantum Field Theory and serve as a bridge between theoretical predictions and experimental data. Because of this, their computation is of interest to many different research areas. Although much progress has been made in the last few decades, it remains very difficult to compute scattering amplitudes at higher orders in perturbation theory. I will describe mathematical methods for the analytic computation of amplitudes in a general QFT. These rely on the decomposition of amplitudes on their fundamental building blocks, which are much simpler and can be tackled one by one. As a direct example and application, I will present three-loop results in QCD which allowed to confirm for the first time the quadrupole radiation contribution to the infrared structure of QCD. I will conclude with a description of the high-energy (Regge) limit and the first computation of the three-loop gluon Regge trajectory.
Andrea Pelloni, Tanjona Rabemananjara, Tommaso Giani