Renormalization of extensions of the Standard Model: Towards automation

• Applicant: Privatdozentin 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

Extensions of the Standard Model are investigated in order to address open questions the Standard Model cannot answer. 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 (NLO) of the perturbation series. The current experimental situation does not give a clear hint about which type of new physics can be expected. For this reason, to make the investigation of many different extensions feasible, automation of the calculation of the predictions is needed.The goal of this project is therefore to advance the automation of these calculations focusing on the renormalization procedure, which is a crucial part of the calculation. 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 this project, on the one hand, we will develop general criteria to evaluate whether, for a considered scenario, the chosen renormalization scheme results in a fast convergence and, hence, the perturbative approximation leads to a reliable, accurate result. We will automate the test of these criteria and develop a corresponding computer tool. In a second step, criteria for how to change the renormalization conditions in order to obtain a fast convergence will be searched for and implemented into the computer tool. On the other hand, we will also search and study possible solutions to the conceptual problems such as the treatment of mixing angles and of quark masses. A further conceptual question is how to treat particles that appear in the initial or final state of a production or decay process, in case their masses cannot be chosen independently from the other particles’ masses because the number of independent model parameters is smaller than the number of massive particles in the considered extension of the Standard Model.

• DFG Programme: Research Grants