Electroweak corrections to lepton pair production in association with two hard jets at the LHC

We compute the next-to-leading order corrections of $O({\alpha }_s^2{\alpha }^3)$ to the hadronic production of two oppositely charged leptons and two hard jets, $pp\to jj{l}^{-}{l}^{+}$, using Recola and Collier. We include electroweak and QCD corrections at the given order and all off-shell effects. We provide detailed predictions for the LHC operating at 13 TeV and obtain per-cent-level corrections for the total cross section. For differential distributions we find significant non-uniform distortions in high-energy tails at the level of several ten per cent due to electroweak Sudakov logarithms and deformations at the level of a few per cent for angular variables.