In order to understand the composition of the universe and the properties of matter within it, we consider its smallest building blocks, such as electrons, photons and quarks, and try to understand how they interact with each other. After the Higgs boson has recently been discovered, its properties are of particular interest to the scientific community, as it is the key ingredient to the mechanism which gives all other particles their mass. This property could also be a gateway to understanding dark matter, which we have so far only observed through the influence of its mass on light rays travelling through the universe and which appears to be invisible otherwise.
To learn about the properties of particles, we formulate a mathematical model of their interactions (like the Standard Model) and calculate the probabilities of producing a certain particle in collision experiments such as the one taking place at the Large Hadron Collider (LHC) at CERN. By comparing the calculated probabilities to the measured ones, we can infer whether our model represents the laws of nature or not. Mathematically, we encode these probabilities in so-called scattering amplitudes. These can generally not be calculated exactly, but we have to approximate them using a technique called perturbation theory, where we consider ever-more 'perturbations' of the underlying process. With each additional perturbation, our result becomes more accurate, while the calculation becomes more and more complicated.
In this project, we consider the calculation of scattering amplitudes as functions of the masses of the Z- and W-bosons, the Higgs boson as well as the top quark, which constitute the heavy particles of the Standard Model. Generally, calculations become much more difficult, when keeping track of the masses of particles, and we often encounter new mathematical functions which are not yet well understood. The goal of this project is to understand the mathematical properties of these functions in order to enable the calculation of scattering amplitudes to very high orders in perturbation theory, resulting in very precise theoretical predictions for collider experiments. In particular, we consider the production of a Higgs boson at the Large Hadron Collider, which is an important ingredient to understanding the properties of the Higgs boson and potentially to illuminating the hidden features of dark matter.
