Lattice analysis of the SU(2) scalar-fermion-gauge system

The discovery of the Higgs particle in 2012 has been a major milestone in our understanding of the fundamental laws of physics. However, a deeper understanding of its theoretical underpinnings reveals even more tantalizing insights. One of these insights yields the prediction that almost all known particles, including very prominent ones like the electron, should have a self-similar substructure. This was predicted in ground- breaking works in the early 1980ies. In the recent decade, large-scale numerical simulations have provided substantial support of this prediction. However, experimentally, the effect is elusive, as the corrections to a non-self-similar structure are often small. The aim of this project is to investigate the possibility that the effect could be discovered in the proposed next generation of large-scale lepton colliders. To this end, extensive numerical simulations on supercomputers will be performed. While not yet providing a final number to be tested, the project is a major stepping stone in this direction. Especially, it will provide a measure for the necessary experimental effort needed to discover the effect at such a collider. To this end, a simplified version of the standard model of particle physics will be simulated. The interaction rate of two simplified electrons, the simplest of leptons, will be calculated. The self- similar structure is expected to create an extent of these particles, which will modify the interaction rate in an observable way. In addition, and in contrast to current experiments like the large hadron collider at CERN, such processes are very clean, and thus should make it easy to identify the relevant structure. This project will in this course also quantify the self-similar structure of particles like the simplified electrons. These are unambiguous predictions of the theory. If the standard model of particle physics is an accurate description of nature, its theoretical consistency requires these to be observable. Thus, this project offers a touch stone for the test of our formal theoretical understanding of our current most fundamental theory of nature.