The quest to understand the fundamental constituents of Nature can be traced at least as far back as the ancient Greeks. Today, experiments at the smallest length scales take place at the Large Hadron Collider (LHC). Here, pairs of protons collide at speeds close to that of light and, for the briefest of moments, generate other, short-lived, particles. These decay, converting into high-energy sprays of particles that are deposited in detectors. Researchers then study the patterns they draw in the experiment, comparing them to those predicted by theory. In the summer of 2012, this resulted in the ground-breaking discovery of the Higgs boson, which further validated the ability of the Standard Model of Particle Physics (SM) to describe Nature at short distances. Nevertheless, open questions in particle physics remain unanswered by the SM. Given the evidence for dark matter in astronomical measurements, how does it manifest at the microscopic level? What is the resolution of the hierarchy problem, that is, what causes the large divide between the Higgs mass and the Planck scale? As a scalar particle, the Higgs boson is inherently sensitive to scales of new physics. It is therefore essential to ask if its properties and interactions with heavy particles match the predictions of the SM. To answer these questions and identify signals of new physics, theorists must make precise predictions of the SM. In the coming years, with the projected increase in collision rates, experiments at the LHC will hugely increase the amount of recorded data. We will enter into an era of precision, where uncertainties will reduce to the percent level for a broad class of collision observables. To understand this data theorists must make correspondingly precise predictions. These precise predictions pose an immense theoretical challenge.
A critical step in making these predictions is the calculation of a "scattering amplitude". Scattering amplitudes are mathematically beautiful objects that encode transition probabilities of particle collisions. In a textbook approach, a scattering amplitude is thought of as a sum of Feynman diagrams. As the precision of the associated prediction rises, so does the number of closed loops of particles in a diagram. The number of diagrams in the sum grows factorially and in cases relevant for LHC physics they can number in the tens of thousands. Each one is interpreted as an integral over the unobserved internal states of the diagram. These multi-dimensional integrals are known as “Feynman integrals” and their computation is a demanding undertaking.
In recent years, a new framework for the calculation of amplitudes has emerged. Building on a deep understanding of the physical and mathematical properties of the amplitudes, one uses numerical evaluations to constrain an Ansatz for the analytic form of the amplitude. These Ansaetze are constructed from knowledge of the geometric and mathematical structures which underpin the amplitudes. The project LoopAnsatz employs and develops these methods to handle increasingly complex loop amplitude computations.
Over its duration, LoopAnsatz has produced a number of state of the art results. Firstly, it has developed geometric techniques for both the computation of amplitudes as well as real radiation contributions. Secondly, it has produced cutting-edge computations of Feynman integrals for five-particle scattering. Finally, it has both produced scattering amplitudes for W+2-jet production at the LHC as well as amplitudes for the production of three photons.
