The two-loop helicity amplitudes for gg → V1V2 → 4 leptons

We compute the two-loop massless QCD corrections to the helicity amplitudes for the production of two electroweak gauge bosons in the gluon fusion channel, gg -> V1V2, keeping the virtuality of the vector bosons V-1 and V-2 arbitrary and taking their decays into leptons into account. The amplitudes are expressed in terms of master integrals, whose representation has been optimised for fast and reliable numerical evaluation.