Analytic QCD Amplitudes using Finite Field Evaluation Techniques

Abstract

In this thesis we present the analytic expressions of different high-multiplicity one-loop scattering amplitudes in Quantum Chromodynamics. The scattering amplitudes are decomposed into combinations of colour-ordered amplitudes. The colour-ordered amplitudes are represented as scalar integrals multiplied by coefficients, which are functions of the kinematics of the external particles. We parametrised the kinematics using momentum-twistor variables, in order to express the coefficients as rational functions. We found the analytic form of the rational coefficients by employing numerical interpolation techniques, which make it possible to reconstruct analytic expressions by sampling their value over finite fields. We computed the expressions of the one-loop corrections to
up to second order in the dimensional regulator. We also computed the expressions of the Maximally-Helicity-Violating six-gluon one-loop amplitudes in an arbitrary number of dimensions. We studied different techniques for optimising the reconstruction process, developing original methods for directly reconstructing polynomial expressions of high degree into simpler, partial-fractioned forms.