Methods for the Reduction of Three-Loop QCD Form Factors

2009/03/03 by Beat Toedtli, Toedtli, Beat
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions

paper · pdf · doi:10.48550/arxiv.0903.0540

openalex publication_date 2009/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Electroweak radiative corrections at high energies
• Differential equations for two-loop four-point functions

Related

• Master integrals for massless three-loop form factors
• Three loop heavy quark form factors and their asymptotic behavior
• Three loop master integrals for O (αα_s²) corrections to quark form factor
• Massive three loop form factors in the planar limit
• Challenges for analytic calculations of the massive three-loop form factors