# Analytic form of the full two-loop five-gluon all-plus helicity amplitude

## TL;DR

This paper presents a complete analytic calculation of the full-color two-loop five-gluon amplitude for the all-plus helicity configuration, including master integrals, divergence structure, and finite parts, validated through factorization checks.

## Contribution

It provides the first fully analytic expression for the two-loop five-gluon all-plus helicity amplitude, including master integrals and divergence analysis.

## Key findings

- Verified divergence structure of the amplitude
- Extracted a finite hard function
- Expressed the result in a compact form with special functions

## Abstract

We compute the full-color two-loop five-gluon amplitude for the all-plus helicity configuration. In order to achieve this, we calculate the required master integrals for all permutations of the external legs, in the physical scattering region. We verify the expected divergence structure of the amplitude, and extract the finite hard function. We further validate our result by checking the factorization properties in the collinear limit. Our result is fully analytic and valid in the physical scattering region. We express it in a compact form containing logarithms, dilogarithms and rational functions.