Master Integrals for Four-Loop Massless Propagators up to Transcendentality Weight Twelve

TL;DR

This paper computes all four-loop massless propagator master integrals' epsilon expansions up to weight twelve, revealing they contain only multiple zeta values, thus extending previous results significantly.

Contribution

It introduces a new method to evaluate four-loop master integrals up to weight twelve, surpassing previous weight seven results, and confirms the exclusive presence of multiple zeta values.

Findings

All four-loop massless propagator integrals contain only multiple zeta values up to weight twelve.

The method extends previous calculations from weight seven to weight twelve.

Results support the conjecture that these integrals are expressible solely in terms of multiple zeta values.

Abstract

We evaluate a Laurent expansion in dimensional regularization parameter $\epsilon=(4-d)/2$ of all the master integrals for four-loop massless propagators up to transcendentality weight twelve, using a recently developed method of one of the present coauthors (R.L.) and extending thereby results by Baikov and Chetyrkin obtained at transcendentality weight seven. We observe only multiple zeta values in our results. Therefore, we conclude that all the four-loop massless propagator integrals, with any integer powers of numerators and propagators, have only multiple zeta values in their epsilon expansions up to transcendentality weight twelve.