Advancing Predictions: This is what we found out

The overall goal of research in fundamental physics is to improve our understanding of Nature. Particle collider experiments provide a valuable source of experimental data. To fully exploit this data, it is vital to understand well the theory predicting outcomes of such scattering experiments. This was the focus of this ERC-funded project.

The research done within this project provided the research community with novel methods and algorithms for making precise predictions for scattering amplitudes needed for phenomenological studies of collider physics experiments. Employing novel methods from supersymmetric toy models, the most accurate formulas to date for predicting the physics of soft exchanges in those amplitudes were derived. In addition, new structural properties of scattering amplitudes were found that have the potential to lead to completely different ways of thinking about quantum field theory.

An overall highlight of this project are the results for two-loop five-particle scattering processes, pioneered by our group. The relevant function space was identified, and the two-loop non-planar Feynman integrals required to describe five-particle scattering were computed. This allowed us, for the first time, to compute full five-particle two-loop amplitudes, both in supersymmetric toy models, and in quantum chromodynamics, for a certain helicity configuration; moreover, the analytic function representation made it possible to study the Regge behavior of the answer. Our streamlined approach to computing scattering amplitudes, including finite fields methods, has become state of the art, and has since been used for a number of phenomenological applications. These crucially build upon the Feynman integrals computed within this ERC project.

The work was organized according to four interconnected themes, (1) Novel structures in loop integrands, (2) Novel methods for computing Feynman integrals, (3) Applications to scattering amplitudes and collider physics, and (4) Long-distance singularities. The focus of themes (1) and (2) was to develop new methodology and algorithms, while themes (3) and (4) focuses on specific applications to state-of-the-art problems in scattering amplitudes, including the calculation of amplitudes for processes of phenomenological relevance.

The research results led to more than 70 scientific articles published in peer-reviewed journal articles, including eleven in the prestigious journal Physical Review Letters. Team members presented the research results at various international conferences. Examples of research results are:

- Obtained predictions from conformal symmetry — an extension of space-time translation and rotation symmetry — for scattering amplitudes.
- Calculated the four-loop cusp anomalous dimension in QCD, which settles a longstanding open question.
- Pioneered a new approach to computing energy-energy correlations, which are an important observable at particle colliders.
- Developed novel algorithmic ways of evaluating Feynman integrals, thereby removing a bottleneck in quantum field theory calculations.
- Explored geometric representations of scattering amplitudes and found a duality that relates observables in a supersymmetric theory to all-plus helicity amplitudes in QCD.
- Used integrability methods to obtain non-perturbative predictions for form factors in maximally supersymmetric Yang-Mills theory.

Image: Josh Worth
January 29, 2024