Nf-contribution to the virtual correction for electroweak vector boson production at NNLO

Multi-loop scattering amplitudes are difficult to evaluate due to singularities of the integrals involved, especially with increasing number of loops, external legs, and mass scales. For the first time for hadronic collisions at two loops, we enable the combined numerical integration over loop momentum and phase space by tackling infrared, ultraviolet and threshold singularities simultaneously using local subtractions. We demonstrate the feasibility of our approach by calculating previously unknown perturbative corrections for processes of interest to the Large Hadron Collider, namely the N_f -part of the finite remainder of the phase-space integrated virtual corrections at next-to-next-to-leading order (NNLO) in QCD for the production of up to three massive electroweak vector bosons in proton-proton collisions.