# Simplifying differential equations for multi-scale Feynman integrals beyond multiple polylogarithms

## TL;DR

This paper introduces a method leveraging Picard-Fuchs operator factorization to simplify and decouple differential equations for multi-scale Feynman integrals, facilitating their solution beyond multiple polylogarithms.

## Contribution

The authors develop an algorithm that reduces complex differential equations to smaller blocks based on Picard-Fuchs operator factors, enabling easier analysis of multi-scale Feynman integrals.

## Key findings

- Decouples differential equations into blocks of size related to irreducible factors
- Facilitates conversion of equations to epsilon-form for polylogarithmic integrals
- Provides a systematic approach for multi-scale Feynman integral analysis

## Abstract

In this paper we exploit factorisation properties of Picard-Fuchs operators to decouple differential equations for multi-scale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the irreducible factors of the Picard-Fuchs operator. As a side product, our method can be used to easily convert the differential equations for Feynman integrals which evaluate to multiple polylogarithms to $\varepsilon$-form.