On Epsilon Expansions of Four-loop Non-planar Massless Propagator Diagrams

TL;DR

This paper computes four-loop non-planar massless propagator diagrams in dimensional regularization, expanding in epsilon up to weight twelve, and finds only multiple zeta values in the results.

Contribution

It introduces a method to evaluate complex four-loop diagrams in epsilon expansion, revealing the exclusive appearance of multiple zeta values.

Findings

Results expressed in terms of multiple zeta values

Expansion achieved up to transcendentality weight twelve

Method applicable to similar high-loop calculations

Abstract

We evaluate three typical four-loop non-planar massless propagator diagrams in a Taylor expansion in dimensional regularization parameter $\epsilon=(4-d)/2$ up to transcendentality weight twelve, using a recently developed method of one of the present coauthors (R.L.). We observe only multiple zeta values in our results.