Two-loop leading colour helicity amplitudes for W ^± γ + j production at the LHC

Abstract

<jats:title>A<jats:sc>bstract</jats:sc> </jats:title><jats:p>We present the two-loop leading colour QCD helicity amplitudes for the process <jats:italic>pp → W</jats:italic> (<jats:italic>→ lν</jats:italic>)<jats:italic>γ</jats:italic> + <jats:italic>j</jats:italic>. We implement a complete reduction of the amplitudes, including the leptonic decay of the <jats:italic>W</jats:italic>-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.</jats:p>