# Framework for a novel mixed analytical/numerical approach for the computation of two-loop $N$-point Feynman diagrams

## TL;DR

This paper introduces a new mixed analytical and numerical framework for efficiently computing complex two-loop N-point Feynman diagrams by combining analytical calculations of integrand components with numerical integration.

## Contribution

It presents a novel approach that represents two-loop N-point diagrams as double-integrals with analytically computed integrand parts and numerical integration, improving computational efficiency.

## Key findings

- Framework successfully applied to scalar three- and four-point functions.
- Integrand components computed analytically, numerical integration performed over remaining variables.
- Method offers a systematic way to handle complex multi-loop Feynman diagrams.

## Abstract

A framework to represent and compute two-loop $N$-point Feynman diagrams as double-integrals is discussed. The integrands are 'generalised one-loop type" multi-point functions multiplied by simple weighting factors. The final integrations over these two variables are to be performed numerically, whereas the ingredients involved in the integrands, in particular the "generalised one-loop type" functions, are computed analytically. The idea is illustrated on a few examples of scalar three- and four-point functions.