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Loop amplitudes in quantum field theory

Periodic Reporting for period 3 - CutLoops (Loop amplitudes in quantum field theory)

Reporting period: 2018-10-01 to 2020-03-31

Discoveries in particle physics have consistently relied on high-energy collision experiments. In colliders, new particles can be produced, and properties of known particles and their interactions can be probed in detail. At the Large Hadron Collider (LHC), the experiments ATLAS and CMS are exploring phenomena at the TeV scale through proton-proton collisions. Evidence supports the recent discovery of the Higgs boson, whose properties remain to be described in the years to come. Searches for low-scale supersymmetry and other exotic scenarios of physics beyond the Standard Model are underway. It is thus of utmost importance to compute scattering processes to high precision.
Particle colliders involve complicated scattering configurations, where the traditional method of computing probability amplitudes by Feynman rules fails to be feasibly implementable on a reasonable time scale. Recently, a set of methods have been developed to construct these mathematical functions recursively, based on newly-discovered symmetries in quantum field theory.
The objective of the CutLoops project is to explore the mathematics of singularities in particle scattering, discover algebraic relations among them, thereby to reveal deeper structure and fundamental principles in quantum field theory, and to apply these tools to specific particle scattering processes relevant to current collider experiments.
CutLoops has established an algebraic framework for a large group of scattering functions, which exposes relationships among them governed by singularities and differential equations. The team has also found definitions for the singularities and methods for computing them.
In the second half of the project, the team will work to extend the algebraic framework to more complicated types of scattering events, and to use these results to outline and implement efficient computation for specific components of physical processes that have remained out of reach so far.