Mixed QCD$\otimes$QED corrections to exclusive Drell Yan production using the $q_T$-subtraction method

In this work we extend the qT -subtraction formalism, originally developed for QCD corrections, to the case of mixed QCD⊗QED corrections, and apply it to the fully exclusive calculation of the $$ \mathcal{O}\left({\alpha}_s\alpha \right) $$ contribution to the production of an off-shell Z boson in hadronic collisions. We present explicit results for the subtraction term and the hard factor, therefore providing all the ingredients needed for the application of the formalism up to $$ \mathcal{O}\left({\alpha}_s\alpha \right) $$ . To study the phenomenological impact we consider the decay of the off-shell Z boson into a pair of neutrinos, and present kinematical distributions for the final-state leptons at LHC energies.