Calculation of the quark and gluon form factors to three loops in QCD

Understand

We describe the calculation of the three-loop QCD corrections to quark and gluon form factors.

• The relevant three-loop Feynman diagrams are evaluated and the resulting three-loop Feynman integrals are reduced to a small set of known master integrals by using integration-by-parts relations.
• Our calculation confirms the recent results by Baikov et al.\ for the three-loop form factors.
• In addition, we derive the subleading ${\cal O}(\epsilon)$ terms for the fermion-loop type contributions to the three-loop form factors which are required for the extraction of the fermionic contributions to the four-loop quark and gluon collinear anomalous dimensions.