QCD corrections to electroweak $\mathcal{l}{\nu }_{\mathcal{l}}\mathrm{jj}$ and ${\mathcal{l}}^{+}{\mathcal{l}}^{-}\mathrm{jj}$ production

The production of W or Z bosons in association with two jets is an important background to the Higgs boson search in vector-boson fusion at the CERN Large Hadron Collider (LHC). The purely electroweak component of this background is dominated by vector-boson fusion, which exhibits kinematic distributions very similar to the Higgs boson signal. We consider the next-to-leading-order QCD corrections to the electroweak production of $\mathcal{l}{\nu }_{\mathcal{l}}\mathrm{jj}$ and ${\mathcal{l}}^{+}{\mathcal{l}}^{-}\mathrm{jj}$ events at the LHC, within typical vector-boson fusion cuts. We show that the QCD corrections are modest, increasing the total cross sections by about 10%. The remaining scale uncertainties are below 2%. A fully flexible next-to-leading-order partonic Monte Carlo program allows us to demonstrate these features for cross sections within typical vector-boson-fusion acceptance cuts. Modest corrections are also found for distributions.