# A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons

## TL;DR

This paper provides the first numerical results for two-loop helicity amplitudes involving a W-boson and four partons in QCD, using innovative finite field sampling and sector decomposition techniques.

## Contribution

It introduces a novel numerical approach to evaluate complex two-loop amplitudes with an incomplete master integral basis in QCD.

## Key findings

- First numerical results for these amplitudes
- Effective use of finite field sampling and sector decomposition
- Identification of master integrals with simple divergence structure

## Abstract

We present the first numerical results for the two-loop helicity amplitudes for the scattering of four partons and a W-boson in QCD. We use a finite field sampling method to reduce directly from Feynman diagrams to the coefficients of a set of master integrals after applying integration-by-parts identities. Since the basis of master integrals is not yet fully known analytically, we identify a set of master integrals with a simple divergence structure using local numerator insertions. This allows for accurate numerical evaluation of the amplitude using sector decomposition methods.