Methods for the Reduction of Three-Loop QCD Form Factors

TL;DR

This thesis explores methods for reducing complex three-loop QCD form factors, detailing integral classification, reduction attempts, and partial results, advancing computational techniques in high-order quantum chromodynamics calculations.

Contribution

It introduces a new reduction code and classification scheme for three-loop QCD form factors, identifying the small set of topologies resistant to reduction.

Findings

Reduction code fails on only 11 topologies

Classification of integrals into irreducible, reducible, and loop-by-loop topologies

Partial results provided for complex three-loop form factors

Abstract

In this thesis, we study the three-loop QCD form factors. After an introduction and a discussion of the physics motivation, we generate the quark form factor using Qgraf. We then show how to bring the Feynman integrals into a unique form by using various trivial symmetries such as shifts in loop momenta. We then try (and fail) to reduce it to master integrals using the Laporta algorithm. After a discussion of our implementation of the Laporta algorithm (called "Solve") we perform an extensive classification of all the integrals into irreducible, reducible and loop-by-loop integrable topologies. We devise methods to deal with each of these cases. We show that our reduction code fails to reduce only a small set of 11 topologies. We finally give some partial results, and in the appendix we collect some already known master integrals.