Three-loop master integrals for H+jet production at N$^3$LO: Towards the non-planar topologies

TL;DR

This paper discusses recent advances in computing complex three-loop non-planar master integrals essential for precise N$^3$LO predictions of H+jet production at the LHC, focusing on their analytic structure and computational techniques.

Contribution

It presents new analytic methods and insights for calculating three-loop non-planar integrals, advancing the precision of theoretical predictions for collider processes.

Findings

Analytic structure of three-loop non-planar integrals elucidated

Canonical differential equations used for integral computation

Progress towards complete three-loop topology calculations

Abstract

We discuss the recent progress that has been made towards the computation of three-loop non-planar master integrals relevant to next-to-next-to-next-to-leading-order (N$^3$LO) corrections to processes such as H+jet production at the LHC. We describe the analytic structure of these integrals, as well as several technical issues regarding their analytic computation using canonical differential equations. Finally, we comment on the remaining steps towards the computation of all relevant three-loop topologies and their application to amplitude calculations.