# Planar master integrals for four-loop form factors

## TL;DR

This paper provides a comprehensive set of planar master integrals for four-loop massless QCD form factors, offering analytic Laurent expansions up to weight eight to facilitate high-precision calculations.

## Contribution

It introduces a complete basis of finite integrals and their analytic Laurent expansions for four-loop three-point functions in massless QCD.

## Key findings

- Analytic results for Laurent expansions up to weight eight.
- Complete set of planar master integrals for four-loop form factors.
- Method employing direct parametric integrations for finite integrals.

## Abstract

We present the complete set of planar master integrals relevant to the calculation of three-point functions in four-loop massless Quantum Chromodynamics. Employing direct parametric integrations for a basis of finite integrals, we give analytic results for the Laurent expansion of conventional integrals in the parameter of dimensional regularization through to terms of weight eight.