First look at the evaluation of three-loop non-planar Feynman diagrams for Higgs plus jet production

TL;DR

This paper presents pioneering three-loop non-planar Feynman integral computations for Higgs plus jet production, revealing new structural insights and counterexamples to existing conjectures, with results expressed in generalized polylogarithms.

Contribution

First computation of non-planar three-loop Feynman integrals for Higgs plus jet production, including differential equations and structural analysis.

Findings

Counterexample to adjacency conjecture in planar integrals

Discovery of two new alphabet letters in non-planar integrals

Expressions in terms of generalized polylogarithms up to weight six

Abstract

We present new computations for Feynman integrals relevant to Higgs plus jet production at three loops, including first results for a non-planar class of integrals. The results are expressed in terms of generalised polylogarithms up to transcendental weight six. We also provide the full canonical differential equations, which allows us to make structural observations on the answer. In particular, we find a counterexample to previously conjectured adjacency relations, for a planar integral of the tennis-court type. Additionally, for a non-planar triple ladder diagram, we find two novel alphabet letters. This information may be useful for future bootstrap approaches.