Renormalization of extensions of the Standard Model: Towards automation

• Applicant: Professorin Dr. Heidi A. Rzehak
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 442089660

In the second part of the project, we continue the investigations of extensions of the Standard Model: While the Standard Model conforms very well with the results of the experiments at colliders, there are open questions the Standard Model cannot answer. Therefore, extensions of the Standard Model are studied. To test these extensions against the upcoming results of the experiments at the Large Hadron Collider (LHC) at CERN, precise theoretical predictions are needed that include quantum corrections not only of strong but also of electroweak interactions at least at next-to-leading order of the perturbation series. The focus of this project, the first as well as the second part, is on a crucial part of the calculation, the renormalization procedure. A renormalization scheme defines the relation between the parameters of the theory and the physical observables and fixes the expansion point of the perturbation series. The convergence behaviour of the perturbation series depends on the chosen expansion point. A fast convergence is important, such that truncating the perturbation series after the first terms leads to reliable accurate results. In general, a chosen renormalization scheme and hence the corresponding expansion point can lead to a fast convergence for some part of the allowed values of the model parameters, while it fails to do so in other parameter regions. In the first part of the project, we started to investigate Standard Model extensions, such as the general Two-Higgs-Doublet Model, and to formulate test criteria for a fast convergence. The goal is to find model-independent test criteria that can be automated. Such test criteria are a first step towards complete automation of the renormalization procedure, which is needed to study many different Standard Model extensions. In the second part of the project, we will continue these investigations and apply the insights from the first part to further Standard Model extensions. Furthermore, we work on solutions of conceptional problems that occur in the renormalization procedure. In the first part, we formulated a method to avoid gauge dependences. In the second part, we will develop this method and adapt it to further models, for example Higgs-triplet models.

• DFG Programme: Research Grants