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

Johannes Henn,Yingxuan Xu,Yang Zhang,Tiziano Peraro

doi:10.1007/jhep03(2022)056

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.

Highlights

Recent years have seen tremendous progress in computing five-particle Feynman integrals, scattering amplitudes at two loops, and even complete cross sections
It turned out that all relevant Feynman integrals can be described by a function space with certain symbol letters, and there are exactly 31 symbol letters, as initially conjectured in [9]
We provide a basis of master integrals that leads to canonical differential equations

Summary

Introduction

Recent years have seen tremendous progress in computing five-particle Feynman integrals, scattering amplitudes at two loops, and even complete cross sections. We see that when new results for Feynman integrals become available, this constitutes a game changer and paves the way towards obtaining scattering amplitudes, and eventually full cross sections This motivates us to aim at the two-loop six-point massless integrals, where very little is known in general. The knowledge of the function space, together with physical properties of amplitudes, makes it possible to bootstrap results to very high loop orders, as reviewed in [31, 32] This result is closely linked to additional symmetries of planar N = 4 sYM that are broken in QCD, and as a result, the corresponding integrals in QCD are considerably more complicated.

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Conclusion