Evaluating Feynman Integrals through differential equations and series expansions

TL;DR

This paper reviews a method using differential equations and series expansions to evaluate multi-loop Feynman integrals, enabling analytical continuation and handling arbitrary internal complex masses.

Contribution

It introduces a series expansion approach for solving differential equations in Feynman integral evaluation, allowing for broader applicability to complex mass scenarios.

Findings

Effective series expansion method for multi-loop integrals

Analytical continuation to complex phase-space

Handles arbitrary internal complex masses

Abstract

We review the method of the differential equations for the evaluation of multi-loop Feynman integrals. In particular, we focus on the series expansion approach for solving the system of differential equation and we discuss how to perform the analytical continuation of the result to entire (complex) phase-space. This approach allow us to consider arbitrary internal complex masses. This review is based on a lecture given by the author at the "Advanced School and Workshop on Multiloop Scattering Amplitudes" held in NISER, Bhubaneswar (India) in January 2024.