Experiments at particle colliders are the most effective way of probing the most fundamental constituents of nature - the elementary particles - and the way they interact with each other. The Large Hadron Collider (LHC) at CERN is the most powerful collider ever built. Data collected by the LHC, including future runs and upgrades, will have an unprecedented reach and accuracy. Theoretical predictions with a similar level of precision, often at the per-cent level, are thus needed to fully exploit its potential. The Standard Model (SM), which describes the strong interactions of quantum chromodynamics (QCD) and the electroweak (EW) interactions, currently provides the most accurate description of the observed fundamental particles and interactions. It has been validated by a huge number of experiments and observations but it is an incomplete theory, which lacks a high-energy description of gravity, dark energy and dark matter, and has other undesirable features when extrapolated at high energies. The search for new physics is thus one of the main objectives of modern high-energy experiments. High-precision predictions in the SM are crucial for detecting signals of new particles and interactions, which might be hidden by the large SM background. In particular, new data collected in Run 3 of LHC will allow to perform high-precision tests involving multi-particle final states as well as massive particles, which are of great importance e.g. for jet physics, top physics and Higgs physics. This data needs to be compared to similarly accurate theoretical predictions.
At the core of theoretical predictions in collision experiments are scattering amplitudes. They encode the probability of the interactions and are computed perturbatively in the coupling constants. In order to match the expected experimental precision, we often need to reach next-to-next-to-leading order (NNLO) in perturbation theory. This requires the calculation of complex integrals over the momenta of unresolved virtual particles. These integrals are known as loop integrals or Feynman integrals. NNLO predictions usually require two-loop amplitudes, which involve the integration over two independent loop momenta. Computing these integrals and combining them in scattering amplitudes is however beyond the state of the art for complex multi-leg processes involving internal and external masses.
The main objective of this project is a breakthrough in our ability to make high-precision predictions for collider experiments for processes involving massive internal and external particles, as well as multi- particle final states. This relies on new methods for scattering amplitudes and Feynman integrals, as well as finite fields and functional reconstruction techniques. The objectives include the development of a highly automated framework for the semi-numerical calculation of multi-loop amplitudes which can be systematically used for theoretical predictions for complex scattering processes at the LHC of high relevance for top physics and Higgs physics. These include top pair production in association with a Higgs boson and top pair production in association with a vector boson at NNLO. These will lead us to a deeper understanding of the top quark and the symmetry breaking mechanism of the SM.
The project is developing ground-breaking new methods for theoretical predictions in high-energy physics for the efficient reduction of loop integrals to independent master integrals, the analytic or semi-numerical integration of Feynman integrals, and will make NNLO phenomenological predictions involving top quark and massive bosons (Higgs, W and Z).
