Four-dimensional representation of scattering amplitudes and physical observables through the application of the Loop-Tree Duality theorem

Understand

In this thesis we propose a novel method to compute higher-order corrections to physical cross sections, bypassing more traditional approaches.

• This technique, the Four-Dimensional Unsubtraction (FDU), is based on the Loop-Tree Duality (LTD) theorem, and aims at building pure four-dimensional representations of scattering amplitudes at higher orders in perturbation theory.
• This is done by locally renormalising the virtual contribution at high energies, and then mapping the kinematics of the corresponding real contribution so it matches the virtual one in the soft and collinear limits.
• This makes the ultraviolet and infrared singularities vanish at the integrand level when taking the sum of both contributions, meaning that the four-dimensional limit can be taken before integrating, thus allowing for a straightforward numerical implementation.