Leading singularities of the two-loop six-particle maximally helicity violating amplitude

Abstract

We use the leading singularity technique to determine the planar six-particle two-loop maximally helicity violating amplitude in $\mathcal{N}=4$ super Yang-Mills theory 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 [1]. 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 Anastasiou Bern Dixon Kosower/Bern Dixon Smirnov iterative structure.