Methods for the Reduction of Three-Loop QCD 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.

PhD thesis, 90 Pages

References in corpus (4)

• Quark and gluon form factors to three loops
• Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• Master Integrals for Fermionic Contributions to Massless Three-Loop Form Factors

Cited by in corpus (1)

• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors