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

TL;DR

This paper computes three-loop quantum chromodynamics (QCD) corrections to quark and gluon form factors, confirming previous results and providing additional terms crucial for higher-order calculations in particle physics.

Contribution

It presents the first complete calculation of three-loop QCD form factors, including subleading epsilon terms, and applies these to phenomenological processes like Drell-Yan and Higgs production.

Findings

Confirmed three-loop form factor results by Baikov et al.

Derived subleading epsilon terms for fermion-loop contributions.

Provided finite parts for use in effective theory calculations.

Abstract

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. The finite parts of the form factors are used to determine the hard matching coefficients for the Drell-Yan process and inclusive Higgs-production in soft-collinear effective theory.