Quark and gluon form factors to four loop order in QCD: the $N_f^3$ contributions

TL;DR

This paper presents the first four-loop QCD calculations of quark and gluon form factors with three quark lines, utilizing a novel integration method to evaluate master integrals for any space-time dimension.

Contribution

It introduces a new modular arithmetic-based integration by parts algorithm for calculating four-loop form factors in QCD, including the first gluon form factor at this order.

Findings

Successful computation of four-loop corrections for quark and gluon form factors.

First-time calculation of a gluon form factor at four-loop order in QCD.

Development of a novel method for evaluating master integrals in arbitrary dimensions.

Abstract

We calculate the four-loop massless QCD corrections with three closed quark lines to quark and gluon form factors. We apply a novel integration by parts algorithm based on modular arithmetic and compute all relevant master integrals for arbitrary values of the space-time dimension. This is the first calculation of a gluon form factor at this perturbative order in QCD.