Leading Singularities of the Two-Loop Six-Particle MHV Amplitude

TL;DR

This paper computes the two-loop six-particle MHV amplitude in N=4 super Yang-Mills theory using leading singularities, providing both known and new results and testing iterative structures.

Contribution

It introduces a leading singularity method to determine the amplitude, including the first explicit calculation of the parity-odd part.

Findings

Parity-even part matches previous results

Parity-odd part is newly computed

Tested ABDK/BDS iterative structure numerically

Abstract

We use the leading singularity technique to determine the planar six-particle two-loop MHV amplitude in N=4 super Yang-Mills in terms of a simple basis of integrals. Our result for the parity even part of the amplitude agrees with the one recently presented in arXiv:0803.1465. The parity-odd part of the amplitude is a new result. The leading singularity technique reduces the determination of the amplitude to finding the solution to a system of linear equations. The system of equations is easily found by computing residues. We present the complete system of equations which determines the whole amplitude, and solve the two-by-two blocks analytically. Larger blocks are solved numerically in order to test the ABDK/BDS iterative structure.