A computation of two-loop six-point Feynman integrals in dimensional regularization

TL;DR

This paper analytically computes complex two-loop six-point Feynman integrals in dimensional regularization, advancing the understanding of multi-scale quantum field theory calculations.

Contribution

It provides the first analytic results for two-loop master integrals with eight scales using canonical differential equations and uniform transcendentality.

Findings

Analytic expressions for double-box, pentagon-triangle, and hexagon-bubble integrals.

Results expressed as one-fold integrals over classical polylogarithms.

Integral basis with uniform transcendentality and boundary values up to fourth order in epsilon.

Abstract

We compute three families of two-loop six-point massless Feynman integrals in dimensional regularization, namely the double-box, the pentagon-triangle, and the hegaxon-bubble family. This constitutes the first analytic computation of two-loop master integrals with eight scales. We use the method of canonical differential equations. We describe the corresponding integral basis with uniform transcendentality, the relevant function alphabet, and analytic boundary values at a particular point in the Euclidean region up to the fourth order in the regularization parameter $\epsilon$. The results are expressed as one-fold integrals over classical polylogarithms suitable for fast and high-precision evaluation.