Structural Relations between Harmonic Sums up to w=6

TL;DR

This paper explores the algebraic and structural relations of harmonic sums up to weight 6, with applications to quantum field theory calculations like Bhabha-scattering corrections.

Contribution

It provides a detailed analysis of the relations among harmonic sums up to weight 6 and demonstrates their application in high-order quantum field theory computations.

Findings

Identified algebraic relations among harmonic sums up to weight 6

Applied these relations to simplify calculations in Bhabha-scattering

Enhanced understanding of the structure of harmonic sums in quantum calculations

Abstract

Multiply nested finite harmonic sums $S_{a_1 ... a_n}(N)$ occur in many single scale higher order calculations in Quantum Field Theory. We discuss their algebraic and structural relations to weight {\sf w=6}. As an example, we consider the application of these relations to the soft and virtual corrections for Bhabha-scattering to $O(\alpha^2)$.