# All master integrals for three-jet production at NNLO

## TL;DR

This paper analytically computes all previously unknown nonplanar master integrals for massless five-particle scattering at two loops, enabling more precise theoretical predictions for collider experiments.

## Contribution

It provides the complete set of two-loop Feynman integrals for massless 2→3 scattering, using differential equations and identifying integrals with constant leading singularities.

## Key findings

- Integrals evaluate to multiple polylogarithms of uniform weight.
- Results agree with previous conjectures for nonplanar pentagon functions.
- Complete set of integrals enhances precision in collider phenomenology.

## Abstract

We evaluate analytically all previously unknown nonplanar master integrals for massless five-particle scattering at two loops, using the differential equations method. A canonical form of the differential equations is obtained by identifying integrals with constant leading singularities, in $D$ space-time dimensions. These integrals evaluate to $\mathbb{Q}$-linear combinations of multiple polylogarithms of uniform weight at each order in the expansion in the dimensional regularization parameter, and are in agreement with previous conjectures for nonplanar pentagon functions. Our results provide the complete set of two-loop Feynman integrals for any massless $2\to 3$ scattering process, thereby opening up a new level of precision collider phenomenology.