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