Symbolic Summation and Higher Orders in Perturbation Theory

TL;DR

This paper presents a systematic symbolic summation approach to evaluate complex multi-loop Feynman integrals in perturbation theory, demonstrated through examples like non-planar vertices and three-loop QCD corrections.

Contribution

It introduces algorithms for solving Feynman integrals using symbolic summation, advancing computational methods in higher-order perturbative calculations.

Findings

Successfully applied to non-planar two-loop vertex integrals

Extended to three-loop QCD structure function calculations

Demonstrated efficiency of symbolic summation algorithms

Abstract

Higher orders in perturbation theory require the calculation of Feynman integrals at multiple loops. We report on an approach to systematically solve Feynman integrals by means of symbolic summation and discuss the underlying algorithms. Examples such as the non-planar vertex at two loops, or integrals from the recent calculation of the three-loop QCD corrections to structure functions in deep-inelastic scattering are given.