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

Abstract

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 ϵ. The results are expressed as one-fold integrals over classical polylogarithms. We provide a set of supplementary files containing our results in machine-readable form, including a proof-of-concept implementation for numerical evaluations of the one-fold integrals valid within a subset of the Euclidean region.

Keywords

• Higher-Order Perturbative Calculations
• Scattering Amplitudes
• Differential and Algebraic Geometry