Planar three-loop QCD helicity amplitudes for $V$+jet production at hadron colliders

TL;DR

This paper presents the calculation of three-loop planar QCD helicity amplitudes for vector boson plus jet production, providing essential ingredients for high-precision collider predictions.

Contribution

It offers the first complete computation of three-loop planar QCD helicity amplitudes for V+jet processes, including finite remainders in a compact, numerically efficient form.

Findings

Finite remainders expressed in multiple polylogarithms

Amplitudes valid across all kinematic regions

Enhances precision in collider phenomenology

Abstract

We compute the planar three-loop Quantum Chromodynamics (QCD) corrections to the helicity amplitudes involving a vector boson $V=Z,W^\pm,\gamma^*$, two quarks and a gluon. These amplitudes are relevant to vector-boson-plus-jet production at hadron colliders and other precision QCD observables. The planar corrections encompass the leading colour factors $N^3$, $N^2 N_f$, $N N_f^2$ and $N_f^3$. We provide the finite remainders of the independent helicity amplitudes in terms of multiple polylogrithms, continued to all kinematic regions and in a form which is compact and lends itself to efficient numerical evaluation.