Two-loop helicity amplitudes for V+jet production including axial vector couplings to higher orders in ϵ

Abstract

We compute the two-loop Quantum Chromodynamics (QCD) corrections to all partonic channels relevant for the production of an electroweak boson V = Z, W$^{±}$, γ$^{*}$ and a jet at hadron colliders. We consider the decay of a vector boson V to three partons V → $$ q\overline{q}g $$, V → ggg with a vector and axial vector coupling in both channels, including singlet and non-singlet contributions. For the quark channel, we use a recent tensor decomposition and extend the calculation to $$ \mathcal{O} $$(ϵ$^{2}$). For the gluonic channel, we define a new tensor decomposition which allows us to compute the vector and the axial vector amplitudes at once and to perform the computation of the amplitudes to $$ \mathcal{O} $$(ϵ$^{2}$). We provide finite remainders of the helicity amplitudes analytically continued to all relevant scattering regions $$ q\overline{q} $$ → Vg, qg → Vq and gg → Vg. The axial vector contribution to the gluon-induced channel completes the set of two-loop amplitudes for this process, while the extension to $$ \mathcal{O} $$(ϵ$^{2}$) represents the first step in the calculation of next-to-next-to-next-to-leading-order (N$^{3}$LO) QCD corrections to Z+jet production at hadron colliders.