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

Abstract

We compute the planar three-loop Quantum Chromodynamics (QCD) corrections to the helicity amplitudes involving a vector boson $V=Z,W^{\pm },{\gamma }^{\ast }$, 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.

Comments: 8 pages, 1 figure, 1 table, ancillary files are available https://xjetamps.hepforge.org