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

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 → qq¯ 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 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 O (ϵ ²). We provide finite remainders of the helicity amplitudes analytically continued to all relevant scattering regions qq¯ → 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 O (ϵ ²) represents the first step in the calculation of next-to-next-to-next-to-leading-order (N³LO) QCD corrections to Z+jet production at hadron colliders.