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Marzucca, Robin
[UCL]
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In this thesis we are investigating the mathematical dependence of scattering amplitudes on kinematical invariants. In particular, we are analyzing the underlying geometries of scattering amplitudes in order to predict the resulting function space. We then use this knowledge of the function space to find suitable, more efficient ways to perform the computation of scattering amplitudes. First, we consider the forward-scattering limit of amplitudes in N=4 supersymmetric Yang-Mills theory (SYM), where scattering amplitudes can be written as linear combinations of building blocks that can be expressed in terms of single-valued multiple polylogarithms. Further, we introduce a novel mathematical formalism for the computation of these building blocks exploiting their single-valuedness that allows us to compute scattering amplitudes very efficiently. Finally, we find relations among building blocks for different numbers of external particles, generalizing the factorization of scattering amplitudes observed at two loops. This allows us to compute scattering amplitudes for any number of external particles. Lastly, we show that the formalism introduced for computations in N=4 SYM can be used for the computation of scattering amplitudes in other theories like quantum chromo dynamics. As a second part we consider a family of three-loop Feynman integrals called the banana integral family. We show that the equal-mass case of the banana family can be related to the elliptic curve underlying the well-studied sunrise integral family. We relate the solutions for the banana integral family to the functions defined on the elliptic curve of the sunrise integral and subsequently solve the banana integral family in terms of these functions.

Bibliographic reference |
Marzucca, Robin. *Novel paths from special functions to scattering amplitudes.* Prom. : Duhr, Claude |

Permanent URL |
http://hdl.handle.net/2078.1/222558 |