What determines the hierarchy of the particle masses? Is there an underlying mechanism that relates the flavor and the mass eigenstates of the fermions? These and similar questions on the flavor structure are left completely unanswered by the Standard Model.

In this project, you are going to study the concept of spurions which allows one to impose a certain flavor symmetry on the effective field theory. Given a certain set of spurions, you are going to construct invariants under this flavor symmetry, ensuring the absence of redundant structures.

You will learn the physical and mathematical concepts of Effective Field Theories and the associated theoretical tools like group theory and representations.

Effective Field Theories (EFTs) describe physics beyond the Standard Model by including additional operators in the Lagrangian. AutoEFT is a program, developed within our group, that can construct independent sets of these EFT operators. The basis as well as the representation of the operators is not unique though, and AutoEFT currently makes a specific choice.

The goal of this thesis is to develop an algorithm that can translate EFT operators between different representations. One way to do this is to visualize the operators using Birdtrack diagrams. These diagrams make it much easier to understand the structure of the operators and to simplify them.

Finally, the algorithm should be implemented as a computer program.

You will learn:

• The basic concepts of Effective Field Theories
• How Birdtrack diagrams can be used to describe tensor contractions

The gradient-flow formalism provides a way relate perturbative calculations to lattice calculations in QCD. The flow equations provide additional relations beyond the usual field equations on the flowed fields. They can be used to derive non-trivial relations among observables

In this project, you will derive such relations for simple observables and verify them by doing explicit calculations.

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 develop a new game to for FeynGame.

You will learn:

• The algorithmic structure of Feynman diagrams.

Requirements:

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