The gradient flow is a concept which provides a potential bridge between perturbative and non-perturbative physics. The crucial parameter switching between these two regimes is the flow time t.

In this project, you will learn the concepts of the gradient flow and develop methods to extrapolate the perturbative small-t region to the non-perturbative large-t regime. This will help to combine perturbative and lattice results for the determination of fundamental QCD parameters.

• R.V. Harlander, F. Lange, T. Neumann,
  Hadronic vacuum polarization using gradient flow
  JHEP 08 (2020) 109 [arXiv:2007.01057]
  
• R.V. Harlander, Y. Kluth, and F. Lange,
  The two-loop energy-momentum tensor within the gradient-flow formalism
  Eur. Phys. J. C78 (2018) 944 [err. ibid. C79 (2019) 858]
  [arXiv:1808.09837]
  
• J. Artz, R.V. Harlander, F. Lange, T. Neumann, and M. Prausa,
  Results and techniques for higher order calculations within the gradient flow formalism
  JHEP 06 (2019) 121 [err. ibid. 10 (2019) 032]
  [arXiv:1905.00882]
  
• R.V. Harlander and T. Neumann,
  The perturbative QCD gradient flow to three loops
  JHEP 06 (2016) 161 [arXiv:1606.03756]
  

Quantum effects can tell us something about physics beyond the Standard Model. In order to fully capture such effects, one needs to develop new theoretical methods to calculate loops in Feynman diagrams. Finite Fields have turned out to be a promising avenue.

In this project, you will learn, develop, and apply modern techniques for the calculation of quantum effects in particle physics. You will contribute to the precise theoretical determination of important observables at the LHC.

• J. Klappert, F. Lange, P. Maierhöfer, J. Usovitsch,
  Integral Reduction with Kira 2.0 and Finite Field Methods
  [arXiv:2008.06494]
  
• J. Klappert, S.Y. Klein, F. Lange,
  Interpolation of Dense and Sparse Rational Functions and other Improvements in FireFly
  [arXiv:2004.01463]
  
• J. Klappert, F. Lange,
  Reconstructing rational functions with FireFly
  Comput. Phys. Commun. 247 (2020) 106951 [arXiv:1904.00009]
  

Effective Field Theories can describe physics beyond the Standard Model in a generic way. Their construction is algorithmic, but very cumbersome.

In this project, you will learn the concepts of Effective Field Theories and develop an algorithm for their construction. This will be useful for the interpretation of data collected at the LHC and future colliders, in particular in the light of possible new discoveries.

• Joshua Rosaler (June 2020, RWTH Aachen), EFTGen: An Algorithm for Automatic Generation of Higher Dimensional Operators in Effective Field Theory