The quark and gluon form factors to three loops in QCD through to O(eps^2)

TL;DR

This paper provides explicit formulas for three-loop QCD quark and gluon form factors up to order epsilon squared, essential for higher-loop calculations and understanding QCD corrections.

Contribution

It presents the first explicit formulas for O(eps) and O(eps^2) three-loop contributions to quark and gluon form factors in QCD, including lower-loop results for completeness.

Findings

Explicit formulas for three-loop form factors up to O(eps^2)

Contributions necessary for four-loop anomalous dimension extraction

Results include lower-loop form factors for consistency

Abstract

We give explicit formulae for the O(eps) and O(eps^2) contributions to the unrenormalised three loop QCD corrections to quark and gluon form factors. These contributions have at most transcendentality weight eight. The O(eps) terms of the three-loop form factors are required for the extraction of the four-loop quark and gluon collinear anomalous dimensions. The O(eps^2) terms represent an irreducible contribution to the finite part of the form factors at four-loops. For the sake of completeness, we also give the contributions to the one and two loop form factors to the same transcendentality weight eight.