# Quark and gluon form factors in four loop QCD: the $N_f^2$ and $N_{q\gamma} N_f$ contributions

## TL;DR

This paper presents the first four-loop QCD corrections to quark and gluon form factors with two closed quark lines, providing new analytic results and cusp anomalous dimensions using advanced integral techniques.

## Contribution

It introduces novel integral reduction and direct integration methods to compute four-loop massless QCD corrections for quark and gluon form factors.

## Key findings

- First-time four-loop corrections for gluon and singlet quark form factors.
- Analytic expressions for form factors and cusp anomalous dimensions.
- Application of new integral reduction techniques.

## Abstract

We calculate the four-loop massless QCD corrections with two closed quark lines to quark and gluon form factors. The results for the gluon form factor and the singlet part of the quark form factor are given for the first time. From our analytic expressions for the form factors, we determine the corresponding cusp anomalous dimensions. The relevant Feynman integrals are obtained with novel integral reduction techniques and direct integration methods.