Novel Computational Methods for Scattering Amplitudes

The discovery of the Higgs boson at CERN's Large Hadron Collider (LHC) experiment has opened a new era in the quest of particle physics to find what the fundamental constituents of matter are, and how they interact. By looking at what is produced in high-energy collisions of protons, many of the interactions of the Higgs boson with other elementary particles have been observed.

In the coming years, the LHC will accumulate 10 times more data from these collisions, enabling among other things the measurement of the strength of these interactions to an unprecedented precision.

In order to determine fundamental constants of nature from them, as well as to tell apart the subtle signature of new phenomena beyond our those we currently understand, the theoretical description of these measurements must accomplish a corresponding level of accuracy. At the core of this description lie physical quantities known as scattering amplitudes, which encode the probability of particular outcomes of particle collisions.

When the colliding particles interact weakly they can be computed approximately by Feynman diagrams, which elegantly visualise all possible ways for the colliding particles to transform to the particular outcome, and correspond to mathematical expressions known as Feynman integrals. One of the greatest challenges, however, is that these Feynman integrals become notoriously hard to evaluate as the precision of the approximation increases.

The main goal of the proposed research will thus be to push the forefront of the analytic evaluation technology of Feynman integrals and scattering amplitudes, so as to cope with the increased experimental precision the LHC and its High-Luminosity upgrade are expected to reach in the years to come. The first step towards achieving this goal will be to leverage recent theoretical and algorithmic advances in the prediction of the integrals' singularities, namely the values of their parameters for which they become singular.

This will then be used to drastically simplify the determination of the differential equations obeyed by the basis integrals contributing to relevant physical processes. Ultimately, the function spaces expressing these integrals as well as the associated scattering amplitudes will be obtained by bootstrap approaches that avoid the difficulties of direct integration.