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Novel structures in scattering amplitudes

Periodic Reporting for period 3 - AMPLITUDES (Novel structures in scattering amplitudes)

Reporting period: 2020-04-01 to 2022-01-31

The aim of this ERC funded project is to improve our understanding of Nature. We develop theoretical physics methods to study elementary particles, the fundamental building blocks of all matter. The focus of the ERC group is on scattering amplitudes, which help predict the outcome of particle collider experiments. This research has already produced novel results in several areas:

- We investigated to what extent scattering amplitudes are determined from conformal symmetry, an extension of space-time translation and rotation symmetry. This powerful symmetry governs the interactions of gluons, the force carriers that hold atoms together. Quantum effects obscure its consequences, especially for scattering amplitudes. This ongoing research was started in the first reporting period, and has now given first results. In particular, we obtained quantitative predictions in a toy model, which allowed to find the result for otherwise prohibitively complicated calculations in quantum field theory.

- We settled a long-standing open question by computing the effects of exchanges of low-energetic gluons between two partons at an unprecedented theoretical precision. In obtaining this result we developed several universal tools for quantum field theory computations

- We developed novel ways of evaluating Feynman integrals, thereby removing a bottleneck in quantum field theory calculations. In the first reporting period, we developed new tools and algorithms to facilitate the automation of such calculations. We refined those methods further and applied them to several cutting edge problems, producing completely new results. As a particular highlight, building upon the identification of the relevant function space in the first reporting period, we determined for the first time a full five-gluon scattering amplitude at the so-called two-loop level, including all planar and complicated non-planar contributions.

- In a novel line of research, we studied the energy-energy correlation, an important observable at particle colliders. It measures the correlation between the energy deposited at two detectors, as a function of their relative angle. Our group pioneered a new approach using methods from conformal field theory, thereby avoiding divergences at intermediate steps. In this way we obtained novel results in maximally supersymmetric Yang-Mills theory, as well as a proof of principle for applications in quantum chromodynamics.

A description of the project for the general public can be found at
During the first year of the project, work on the project focused on mainly the following areas:
- development of novel methods for the computation of loop integrals (algorithm for a canonical choice of basis for differential equations, novel methods for integration-by-parts relations)
- applications of the above methods to determine the function space for multi-jet scattering amplitudes at the next-to-next-to leading order in perturbation theory
- reserach into the consequences of conformal symmetry for scattering amplitudes
In this period, research results were published in peer-reviewed journal articles, including one publication in the prestigious journal Physical Review Letters. Team members presented the research results at various international conferences.
Our results will help measure fundamental parameters of Nature, such as, for example, couplings of the Higgs boson, with unprecedented precision. Moreover, by accurately predicting backgrounds from known physics, our results will also be invaluable for searches of new particles.