# Analytic result for a two-loop five-particle amplitude

## TL;DR

This paper computes the complete two-loop five-particle amplitude in N=4 super Yang-Mills, including non-planar terms, and analyzes its properties and limits, advancing understanding of scattering amplitudes in quantum field theory.

## Contribution

It provides the first full-color two-loop five-particle amplitude including non-planar contributions with all-order regularization, confirming conjectures and analyzing multi-Regge limits.

## Key findings

- Amplitude expressed in terms of permutations of Parke-Taylor amplitudes
- Amplitude has correct collinear and infrared properties
- Analytic results for multi-Regge limit and leading logarithms

## Abstract

We compute the symbol of the full-color two-loop five-particle amplitude in $\mathcal{N}=4$ super Yang-Mills, including all non-planar subleading-color terms. The amplitude is written in terms of permutations of Parke-Taylor tree-level amplitudes and pure functions to all orders in the dimensional regularization parameter, in agreement with previous conjectures. The answer has the correct collinear limits and infrared factorization properties, allowing us to define a finite remainder function. We study the multi-Regge limit of the non-planar terms, analyze its subleading power corrections, and present analytically the leading logarithmic terms.