Leading-Color Two-Loop Amplitudes for Four Partons and a W Boson in QCD

TL;DR

This paper computes leading-color two-loop QCD corrections for processes involving four partons and a W boson, providing analytic expressions suitable for precise theoretical predictions in particle physics.

Contribution

It introduces a novel method to derive analytic two-loop amplitudes using a Vandermonde-structured linear system and a dedicated Ansatz, enhancing computational efficiency.

Findings

Analytic expressions for two-loop amplitudes are obtained.

Efficient solution of large linear systems is demonstrated.

Results are expressed in a basis of one-mass pentagon functions.

Abstract

We present the leading-color two-loop QCD corrections for the scattering of four partons and a $W$ boson, including its leptonic decay. The amplitudes are assembled from the planar two-loop helicity amplitudes for four partons and a vector boson decaying to a lepton pair, which are also used to determine the planar two-loop amplitudes for four partons and a $Z/\gamma^*$ boson with a leptonic decay. The analytic expressions are obtained by setting up a dedicated Ansatz and constraining the free parameters from numerical samples obtained within the framework of numerical unitarity. The large linear systems that must be solved to determine the analytic expressions are constructed to be in Vandermonde form. Such systems can be very efficiently solved, bypassing the bottleneck of Gaussian elimination. Our results are expressed in a basis of one-mass pentagon functions, which opens the possibility of their efficient numerical evaluation.