Looping the loops: a tale of elliptic dual Feynman integrals

TL;DR

This paper reviews a loop-by-loop method for deriving differential equations for complex multi-scale Feynman integrals, demonstrated on the elliptic sunrise example, advancing computational techniques in quantum field theory.

Contribution

Introduces a loop-by-loop approach to generate differential equations for elliptic dual Feynman integrals, enhancing analytical tools for multi-scale problems.

Findings

Effective application to the elliptic sunrise integral

Simplifies the derivation of differential equations for complex integrals

Provides a framework adaptable to other multi-scale Feynman integrals

Abstract

In this talk, we review a loop-by-loop approach used to generate differential equations for multi-scale (dual) Feynman integrals. We illustrate the method on a well-established example: the unequal mass elliptic sunrise.