Glue-and-Cut at Five Loops

TL;DR

This paper computes five-loop massless propagator integrals' epsilon-expansions in dimensional regularization using the glue-and-cut method, revealing results consistent with conjectures involving pi-dependent terms.

Contribution

It provides the first complete epsilon-expansion of five-loop master integrals in massless propagator calculations using a recursive glue-and-cut approach.

Findings

All expansion coefficients determined up to weight nine.

Results compatible with pi-dependent conjectures.

Method reduces complex integrals to simpler one-loop calculations.

Abstract

We compute epsilon-expansions around 4 dimensions of a complete set of master integrals for momentum space five-loop massless propagator integrals in dimensional regularization, up to and including the first order with contributions of transcendental weight nine. Our method is the glue-and-cut technique from Baikov and Chetyrkin, which proves extremely effective in that it determines all expansion coefficients to this order in terms of recursively one-loop integrals and only one further integral. We observe that our results are compatible with conjectures that predict $\pi$-dependent contributions.