On the analytic computation of massless propagators in dimensional regularization

TL;DR

This paper discusses an algorithm for computing massless Feynman integrals using hyperlogarithms, providing explicit results up to three loops and analyzing the nature of their epsilon-expansion coefficients.

Contribution

It introduces explicit computations for three-loop propagators with arbitrary insertions and proves the rational linear combination structure of their epsilon-expansion coefficients.

Findings

Explicit three-loop propagator results including epsilon^4 terms

Examples provided for four and higher loops

Coefficients are rational linear combinations of multiple zeta values and Euler sums

Abstract

We comment on the algorithm to compute periods using hyperlogarithms, applied to massless Feynman integrals in the parametric representation. Explicitly, we give results for all three-loop propagators with arbitrary insertions including order $\varepsilon^4$ and show examples at four and more loops. Further we prove that all coefficients of the $\varepsilon$-expansion of these integrals are rational linear combinations of multiple zeta values and in some cases possibly also alternating Euler sums.