Numerical techniques for analytical high-multiplicity scattering amplitudes

Abstract

In this thesis we employ generalised unitarity methods to compute high-multiplicity one-loop scattering amplitudes in quantum chromodynamics, and leverage the scattering equations to obtain high-multiplicity tree-level amplitudes in higher-derivative theories. We develop a set of numerical strategies, based on the study of singular limits in complex phase space and on the reconstruction of generic ansatze, to obtain compact analytical spinor expressions from numerical evaluations only. The advantages of analytical expressions for scattering amplitudes include faster evaluation and increased numerical stability in soft and collinear limits. Thus, they provide a solid foundation for phenomenological studies. The amplitudes we present include the first full set of analytical expressions for 1) six-gluon scattering at one-loop with a gluon in the loop, 2) Higgs + four-parton amplitudes with a top-quark loop retaining full mass effects, and 3) tree-level amplitudes in a theory and in conformal gravity.