# Four-loop quark form factor with quartic fundamental colour factor

## TL;DR

This paper presents an analytical calculation of four-loop QCD corrections to the massless non-singlet quark form factor for a specific colour structure, involving complex non-planar integrals and differential equations.

## Contribution

It introduces a novel method to compute complex non-planar master integrals using a second mass scale and differential equations, advancing high-order QCD calculations.

## Key findings

- Analytical results for cusp and collinear anomalous dimensions.
- Explicit expressions for the finite part of the form factor.
- Master integrals expanded up to weight eight are provided.

## Abstract

We analytically compute the four-loop QCD corrections for the colour structure $(d_F^{abcd})^2$ to the massless non-singlet quark form factor. The computation involves non-trivial non-planar integral families which have master integrals in the top sector. We compute the master integrals by introducing a second mass scale and solving differential equations with respect to the ratio of the two scales. We present details of our calculational procedure. Analytical results for the cusp and collinear anomalous dimensions, and the finite part of the form factor are presented. We also provide analytic results for all master integrals expanded up to weight eight.