Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM

TL;DR

This paper presents a method to construct local, dual-conformally invariant two-loop scattering amplitudes in planar SYM, revealing the structure of divergences and providing a computational tool.

Contribution

It introduces a novel integrand-level approach for all two-loop amplitudes in planar SYM, aligning with BCFW recursion and including a practical Mathematica package.

Findings

Explicit local integrand formulas for all two-loop amplitudes

Clear separation of finite and divergent contributions at the integrand level

Validation against all-loop BCFW recursion relations

Abstract

We use generalized unitarity at the integrand-level to directly construct local, manifestly dual-conformally invariant formulae for all two-loop scattering amplitudes in planar, maximally supersymmetric Yang-Mills theory (SYM). This representation separates contributions into manifestly finite and divergent terms---in a way that makes manifest the exponentiation of infrared divergences at the integrand-level. These results perfectly match the all-loop BCFW recursion relations, to which we provide a closed-form solution valid through two-loop-order. Finally, we describe and document a Mathematica package which implements these results, available as part of this work's source files on the arXiv.