PhD project: Feynman Graph Expansions

Project description

This project aims to develop a new methodology for doing high-order perturbative QFT calculations to obtain high-precision predictions for LHC observables, such as cross sections involving Higgs bosons, top quarks and jets in the final states. The methodology to be developed will be based on asymptotic expansions to obtain sufficiently accurate approximations for the scattering amplitudes and their corresponding cross sections.

The core idea of the project is to use graph theory to formalize the asymptotic expansions via the method of regions, which is the general method to obtain these expansions. This provides an efficient method for doing calculations in momentum/ loop-momentum space. The project will also make heavy use of the Feynman polytope approach, which provides an alternative geometric formulation for the method of regions for loop integrals in the Feynman parametric representation. The prospective PhD candidate will have to master several different areas:

  • Particle Physics: Deepening the understanding of the relevant aspects of the standard model, as well as the collider physics involved.
  • Mathematical aspects: how to compute Feynman integrals, e.g. solving of systems of differential equations or via direct integration techniques. For the method of regions: graph theory and convex geometry.
  • Computational aspects: using computer algebra software (FORM, Maple, Mathemtica) to compute scattering amplitudes, or their integrands and using software to solve very large systems of equations.

Project supervisor

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