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We outline the computational details to obtain mixed EW-QCD corrections toon-shell production of a single vector boson at the LHC at two-loop level. Weuse the method of differential equation to obtain the pure virtual,real-virtual and double-real master integrals. Finally, we obtain the ${\calO}(\alpha \alpha_s)$ corrections to the total partonic cross section of theprocess $q \bar{q} \rightarrow Z + X$.

NNLO mixed EW-QCD corrections to single vector boson production