Semi-numerical power expansion of Feynman integrals

TL;DR

This paper introduces a semi-numerical algorithm combining sector decomposition and Mellin-Barnes techniques to efficiently expand Feynman integrals in powers, providing both numerical coefficients and aiding analytic solutions.

Contribution

It presents a novel semi-numerical method for power expanding Feynman integrals, integrating sector decomposition with Mellin-Barnes techniques for improved analysis.

Findings

Enables numerical calculation of expansion coefficients

Facilitates obtaining full analytic power expansions from differential equations

Provides a numerical check for method of regions independent of power counting

Abstract

I present an algorithm based on sector decomposition and Mellin-Barnes techniques to power expand Feynman integrals. The coefficients of this expansion are given in terms of finite integrals that can be calculated numerically. I show in an example the benefit of this method for getting the full analytic power expansion from differential equations by providing the correct ansatz for the solution. For method of regions the presented algorithm provides a numerical check, which is independent from any power counting argument.