# Elliptic polylogarithms and Feynman parameter integrals

## TL;DR

This paper explores the use of elliptic polylogarithms to evaluate complex multiloop Feynman integrals that are not reducible to traditional multiple polylogarithms, providing new computational techniques.

## Contribution

It demonstrates how certain two- and three-point functions in quantum field theory can be expressed using elliptic polylogarithms through direct Feynman parameter integration.

## Key findings

- Elliptic polylogarithms effectively evaluate complex Feynman integrals.
- A basis of pure Feynman integrals can be identified for these cases.
- The method applies to higher order corrections in QED, QCD, and electroweak theory.

## Abstract

In this paper we study the calculation of multiloop Feynman integrals that cannot be expressed in terms of multiple polylogarithms. We show in detail how certain types of two- and three-point functions at two loops, which appear in the calculation of higher order corrections in QED, QCD and in the electroweak theory (EW), can naturally be expressed in terms of a recently introduced elliptic generalisation of multiple polylogarithms by direct integration over their Feynman parameter representation. Moreover, we show that in all examples that we considered a basis of pure Feynman integrals can be found.