A first look at the function space for planar two-loop six-particle Feynman integrals

TL;DR

This paper explores the mathematical function space of planar two-loop six-particle Feynman integrals, deriving their differential equations, identifying symbol letters, and connecting to known alphabets from supersymmetric theories, advancing analytic calculations.

Contribution

It introduces a systematic study of the function space for these integrals, deriving differential equations, and identifying the symbol alphabet including known dual conformally invariant letters.

Findings

Derived differential equations for all genuine six-particle integrals.

Identified the symbol alphabet including the hexagon alphabet from supersymmetric theories.

Established a basis for future analytic calculations of two-loop six-particle processes.

Abstract

Two-loop corrections to scattering amplitudes are crucial theoretical input for collider physics. Recent years have seen tremendous advances in computing Feynman integrals, scattering amplitudes, and cross sections for five-particle processes. In this paper, we initiate the study of the function space for planar two-loop six-particle processes. We study all genuine six-particle Feynman integrals, and derive the differential equations they satisfy on maximal cuts. Performing a leading singularity analysis in momentum space, and in Baikov representation, we find an integral basis that puts the differential equations into canonical form. The corresponding differential equation in the eight independent kinematic variables is derived with the finite-field reconstruction method and the symbol letters are identified. We identify the dual conformally invariant hexagon alphabet known from maximally supersymmetric Yang-Mills theory as a subset of our alphabet. This paper constitutes an important step in the analytic calculation of planar two-loop six-particle Feynman integrals.