# Numerical Evaluation of Six-Photon Amplitudes

## TL;DR

This paper demonstrates an improved amplitude reduction method applied to six-photon scattering processes, including massive fermion loops, with strategies for rational part reconstruction and handling vanishing Gram-determinants.

## Contribution

It introduces enhancements to the integrand-level amplitude reduction technique for complex scattering processes involving photons and fermion loops.

## Key findings

- Successful computation of 2 photons -> 4 photons scattering amplitudes.
- Effective strategies for reconstructing rational parts of one-loop amplitudes.
- Methods to address vanishing Gram-determinants in calculations.

## Abstract

We apply the recently proposed amplitude reduction at the integrand level method, to the computation of the scattering process 2 photons -> 4 photons, including the case of a massive fermion loop. We also present several improvements of the method, including a general strategy to reconstruct the rational part of any one-loop amplitude and the treatment of vanishing Gram-determinants.