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

Abstract

We evaluate three typical four-loop non-planar massless propagator diagrams in a Taylor expansion in dimensional regularization parameter $ε=(4-d)/2$ 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.

Figures (1)

• Figure 1: Diagrams considered in Ref. Brown:2008um as possible candidates for the presence of sixth roots of unity in the $\epsilon$-expansion.