Effective Field Theories (EFTs) are used to describe physics beyond the Standard Model in a model-independent way. The operators that appear in the effective Lagrangian can be constructed algorithmically, but they may have an unnecessarily complicated form. They can often be simplified using symmetries of the involved operators.

Recently, a method was proposed to bring any operator to a minimal form. The goal of this project is to investigate the usefulness and efficiency of this method, and to apply it to realistic cases of operators in the Standard Model EFT (SMEFT).

In this project, you will learn the basic physical and mathematical concepts of Effective Field Theories. Ideally, you will contribute to the efficiency of the automatic generation of EFTs.

The gradient flow formalism provides a way relate perturbative calculations to lattice calculations in QCD. Up to now, the perturbative calculations have been mostly restricted to massless quarks. However, quark mass effects can become important for large flow times.

The goal of this project is to study the gradient flow of QCD with massive quarks. While such problems can be dealt with in a purely numerical way, you are going to approach the problem analytically at the level of asymptotic expansions.

You will learn:

• The general method of the gradient flow.
• Approaches to calculating non-standard Feynman integrals.

FeynGame is a tool to learn about the concept of Feynman diagrams in a playful way. It allows to easily produce high-quality images of Feynman diagrams. In this project, you will use FeynGame to develop a tutorial on Feynman diagrams directed at high-school students.

You will learn:

• The algorithmic structure of Feynman diagrams.

Requirements:

• Interest in Feynman diagrams.
• Possibly some affinity to computer programming.