Two-loop leading colour helicity amplitudes for $W^\pm\gamma+j$ production at the LHC

TL;DR

This paper computes advanced two-loop QCD helicity amplitudes for W gamma plus jet production at the LHC, providing analytic expressions and demonstrating their efficient numerical evaluation for practical use.

Contribution

It introduces a complete reduction and analytic extraction of two-loop amplitudes including W decay, using finite field methods and special functions, advancing precision calculations for collider phenomenology.

Findings

Efficient numerical evaluation of two-loop finite remainders.

Analytic expressions simplified via permutation and partial fractioning.

Demonstrated applicability for LHC phenomenology.

Abstract

We present the two-loop leading colour QCD helicity amplitudes for the process $pp\to W(\to l\nu)\gamma+j$. We implement a complete reduction of the amplitudes, including the leptonic decay of the $W$-boson, using finite field arithmetic, and extract the analytic finite remainders using a recently identified basis of special functions. Simplified analytic expressions are obtained after considering permutations of a rational kinematic parametrisation and multivariate partial fractioning. We demonstrate efficient numerical evaluation of the two-loop colour and helicity summed finite remainders for physical kinematics, and hence the suitability for phenomenological applications.