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. So far, its main application has been within QCD.

In this project, you will learn the concepts of the gradient flow, formulate the flow-equations in the Standard Model, and calculate observables in this scheme.

• J. Borgulat, R.V. Harlander, J.T. Kohnen, F. Lange,
  Short-flow-time expansion of quark bilinears through next-to-next-to-leading order QCD
  JHEP 05 (2024) 179 [arXiv:2311.16799]
  
• 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]
  

• Jonas Kohnen (October 2023, RWTH Aachen)
  
• 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 the past, we have developed a program that generates an effective field theory for general chiral fields.

In this project, you will generalize this algorithm to spontaneously broken gauge theories and derive effective theories for various phenomenologically relevant models. 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.

• R.V. Harlander, T. Kempkens, M.C. Schaaf,
  Standard Model Effective Field Theory up to Mass Dimension 12
  Phys. Rev. D 108 (2023) 055020 [arXiv:2305.06832]
  
• R.V. Harlander and M.C. Schaaf,
  AutoEFT: Automated Operator Construction for Effective Field Theories
  Comput. Phys. Commun. 300 (2024) 109198 [arXiv:2309.15783]
  

• Maximilian Rzehak (November 2023, RWTH Aachen)
  Representation of operators in effective field theories
• 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

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.

• M. Czakon, R.V. Harlander, J. Klappert, M. Niggetiedt,
  Exact top-quark mass dependence in hadronic Higgs production
  Phys. Rev. Lett. 127 (2021) 162002 [arXiv:2105.04436]
  
• 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]
  

• Ruijia Yang (October 2022), Higgs Production beyond the Standard Model
• Sebastian Rhode (April 2019), Higgs Production in Gluon Fusion with Higher-Dimensional Operators
• Lukas Simon (October 2018), CP-mixing effects in Higgs-Strahlung