All master integrals for three-jet production at NNLO
D. Chicherin, T. Gehrmann, J. M. Henn, P. Wasser, Y. Zhang, S. Zoia
TL;DR
The paper tackles the analytic computation of all master integrals for massless five-point two-loop scattering, enabling NNLO predictions for three-jet production. It introduces a refined strategy to obtain a uniform transcendental weight basis using D-dimensional leading singularities in Baikov representation and a new criterion for pure integrals; this yields canonical differential equations for the full double-pentagon family. The authors confirm the pentagon function alphabet and the second-entry condition, providing complete analytic results in terms of Goncharov polylogarithms along with boundary values. The work delivers the first complete analytic set of master integrals for this multi-scale, nonplanar topology and showcases a general, scalable method for multi-jet amplitudes at NNLO.
Abstract
We evaluate analytically all previously unknown nonplanar master integrals for massless five-particle scattering at two loops, using the differential equations method. A canonical form of the differential equations is obtained by identifying integrals with constant leading singularities, in $D$ space-time dimensions. These integrals evaluate to $\mathbb{Q}$-linear combinations of multiple polylogarithms of uniform weight at each order in the expansion in the dimensional regularization parameter, and are in agreement with previous conjectures for nonplanar pentagon functions. Our results provide the complete set of two-loop Feynman integrals for any massless $2\to 3$ scattering process, thereby opening up a new level of precision collider phenomenology.