# Evaluating multi-loop Feynman integrals numerically through differential equations

## TL;DR

This paper introduces a numerical method for evaluating multi-loop Feynman integrals using differential equations, improving efficiency in complex quantum field theory calculations.

## Contribution

It presents a novel approach combining differential equations and sector decomposition for efficient multi-loop integral evaluation in the physical region.

## Key findings

- Successfully computed two-loop integrals for key scattering processes
- Completed master integrals for non-planar diagrams in relevant particle interactions
- Demonstrated the method's effectiveness in complex multi-loop calculations

## Abstract

The computation of Feynman integrals is often the bottleneck of multi-loop calculations. We propose and implement a new method to efficiently evaluate such integrals in the physical region through the numerical integration of a suitable set of differential equations, where the initial conditions are provided in the unphysical region via the sector decomposition method. We present numerical results for a set of two-loop integrals, where the non-planar ones complete the master integrals for $gg\to\gamma\gamma$ and $q\bar{q}\to\gamma\gamma$ scattering mediated by the top quark.