So far, the standard model has been an enormous success and even after years of experimental measurements no significant discrepancy between the predictions from computations assuming the standard model and experimental observations has been registered. In order to find an indication of new physics beyond the standard model, we will therefore need to improve the accuracy of both experimental data and theoretical predictions. While experimental predictions are automatically improved with each new measurement, there are various ways in which theoretical predictions can be refined. Most theoretical predictions for the Large Hadron Collider (LHC) are computed as an expansion in the strong coupling constant, as QCD corrections dominate scattering processes at hadron colliders. Due to the high energy in the collision, the mass of some particles is negligible in comparison, and computations are often performed considering all particles to be massless. To improve theoretical predictions, one can compute the scattering amplitudes describing a scattering event at the LHC to higher orders in the coupling constant. This requires us to compute scattering amplitudes with more and more loops as well as more and more external particles and is the standard approach to improve theoretical predictions. Another way to improve theoretical predictions is to relax some of the common approximations, like considering all particles to be massless, that are done in order to make the computations more manageable. In the proposed project, I will analyse the mathematical properties of scattering amplitudes with mixed QCD-electroweak corrections in order to improve current computational methods for such observables. In particular, I will compute corrections to Higgs production through gluon fusion at the LHC including both strong- and electroweak interactions at next-to-next-to leading order (NNLO) with a full dependence on the mass of electro-weak gauge bosons.
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