Two-loop scattering amplitudes for top-pair production in association with a jet at hadron colliders

The Large Hadron Collider (LHC) at CERN allows us to investigate the fundamental laws of nature at unprecedentedly high energy.

Our capability to harness this stunning potential relies on our ability to compute theoretical predictions to be compared against the experimental measurements.

Keeping the theoretical uncertainties in line with the experimental ones requires computing theoretical predictions at least at the next-to-next-to-leading order (NNLO) in Quantum Chromodynamics (QCD), the quantum field theory which describes the strong interactions.

A fundamental ingredient entering the theoretical predictions are the scattering amplitudes, which encode the probability distribution of the scattering processes observed in the experiments.

The project targets the computation of the two-loop amplitudes for the production of a top-quark pair in association with a jet.

These amplitudes are the main bottleneck towards obtaining NNLO predictions for this process, which is a high priority of the LHC physics programme.

The presence of the top-quark mass in a process involving so many particles represents a substantial step up in complexity with respect to the state of the art.

The main difficulty lies in the appearance of classes of special functions whose systematic treatment and efficient evaluation are still open problems. Overcoming this bottleneck will require a close interplay between physics and mathematics. The algebraic complexity of the amplitudes themselves also represents a formidable challenge.

I will tackle it by employing cutting-edge techniques based on numerical sampling over finite fields and advanced algorithms of rational reconstruction based on algebraic geometry and physical properties.

The success of the project will not only open the door to NNLO predictions for this important process, but will improve significantly our capability of computing high-precision predictions for high-multiplicity processes in general.