An Exceptional Cluster Algebra for Higgs plus Jet Production

TL;DR

This paper demonstrates that the symbol alphabet for certain three-loop Feynman integrals in Higgs plus jet production is governed by a G_2 cluster algebra, expanding the known algebraic structures involved.

Contribution

It identifies a G_2 cluster algebra structure underlying the integrals, extending the previously known C_2 algebra for Higgs plus jet processes.

Findings

The alphabet is described by a G_2 cluster algebra.

New adjacency relations reduce the function space dimension.

Embedding G_2 in higher-rank algebras explains adjacency relations.

Abstract

A recent evaluation of three-loop nonplanar Feynman integrals contributing to Higgs plus jet production has established their dependence on two novel symbol letters. We show that the resulting alphabet is described by a $G_2$ cluster algebra, enlarging the $C_2$ cluster algebra found to cover all previously known integrals relevant for this process. The cluster algebra connection we find reveals new adjacency relations, which significantly reduce the function space dimension of the non-planar triple ladder integral. These adjacencies may be understood in part by embedding $G_2$ inside higher-rank cluster algebras.