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.

There are several topics that can be worked on during a master's thesis, among them the definition of QCD ghosts at finite flow time, or the asymptotic expansion in the limit of large flow times.

• R.V. Harlander and F. Lange,
  The effective electroweak Hamiltonian in the gradient-flow formalism
  Phys. Rev. D 105 (2022) L071504 [arXiv:2201.08618]
  
• 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. C 78 (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]
  

• Janosch Borgulat (April 2022, RWTH Aachen)
  Towards the Full Energy-Momentum Tensor in the Gradient Flow Formalism
• Yannick Kluth (September 2018, RWTH Aachen)
  Gradient Flow and the Energy-Momentum Tensor
• Fabian Lange (September 2017, RWTH Aachen):
  The Perturbative Gradient Flow at Higher Orders
• Johannes Artz (June 2017, RWTH Aachen):
  Automatic approach to the perturbative gradient flow

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 develop an algorithm for transformations between different operator bases for EFTs. 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.

• Tim Kempkens (October 2021, RWTH Aachen)
  Automated Generation of EFT Operators
• Joshua Rosaler (June 2020, RWTH Aachen)
  EFTGen: An Algorithm for Automatic Generation of Higher Dimensional Operators in Effective Field Theory

• Hao-Lin Li et al., Complete Set of Dimension-8 Operators in the Standard Model Effective Field Theory
• Coenraad B. Marinissen et al., ..., 83106786, 114382724, 1509048322, 2343463290, 27410087742, ... efficient Hilbert series for effective theories

Effective Field Theories are a way to parametrize unknown physics. A proper theoretical description requires the renormalization of the higher-dimensional operators at higher orders in perturbation theory.

In this project, you will learn the concepts of Effective Field Theories and operator renormalization. You will develop a method to systematically determine the renormalization matrix to higher orders in perturbation theory.

Previous master's theses on this topic:

• Joshua Schophoven (November 2020, RWTH Aachen)
  Methods for Higher Order Renormalisation of Quantum Field Theories

• Weiguang Cao et al., Renormalization and non-renormalization of scalar EFTs at higher orders

The Higgs mechanism of the Standard Model is the minimal implementation of spontaneous symmetry breaking. A careful study of the underlying phenomenology may shed light into regions beyond the Standard Model.

In this project, you will build on long experience of our group in this field. You will theoretically study the production mechanisms of Higgs bosons beyond the Standard Model, in particular supersymmetric models, 2-Higgs-doublet models, or effective field theories.

• R.V. Harlander, J. Klappert, S. Liebler, and L. Simon,
  vh@nnlo-v2: New physics in Higgs Strahlung
  JHEP 05 (2018) 089 [arXiv:1802.04817]
  
• R.V. Harlander, S. Liebler, and H. Mantler,
  SusHi Bento: Beyond NNLO and the heavy-top limit
  Comput. Phys. Commun. 212 (2017) 239-257 [arXiv:1605.03190]
  
• R.V. Harlander,
  Higgs production in heavy quark annihilation through next-to-next-to-leading order QCD
  Eur. Phys. J. C 76 (2016) 252 [arXiv:1512.04901]
  
• R.V. Harlander, S. Liebler, and H. Mantler,
  SusHi: A program for the calculation of Higgs production in gluon fusion and bottom-quark annihilation in the Standard Model and the MSSM
  Comput. Phys. Commun. 184 (2013) 1605-1617 [arXiv:1212.3249]
  

• Sebastian Rhode (April 2019), Higgs Production in Gluon Fusion with Higher-Dimensional Operators
• Lukas Simon (October 2018), CP-mixing effects in Higgs-Strahlung