CERN-LHC. This paper reports on a search for the electroweak diboson ($WW/WZ/ZZ$) production in association with a high-mass dijet system, using data from proton--proton collisions at a center-of-mass energy of $\sqrt{s}=13$ TeV. The data, corresponding to an integrated luminosity of 35.5 fb$^{-1}$, were recorded with the ATLAS detector in 2015 and 2016 at the Large Hadron Collider. The search is performed in final states in which one boson decays leptonically, and the other boson decays hadronically. The hadronically decaying $W/Z$ boson is reconstructed as either two small-radius jets or one large-radius jet using jet substructure techniques. The electroweak production of $WW/WZ/ZZ$ in association with two jets is measured with an observed (expected) significance of 2.7 (2.5) standard deviations, and the fiducial cross section is measured to be $45.1 \pm 8.6(\mathrm{stat.}) ^{+15.9} _{-14.6} (\mathrm{syst.})$ fb. The predicted fiducial cross sections for EW $VVjj$ ($V=W,Z$) processes are calculated with MadGraph5_aMC@NLO 2.4.3 with amplitudes of $\mathcal{O}(\alpha_{\mathrm{EW}}^6\alpha_{\mathrm{S}}^0)$, where $\alpha_{\mathrm{EW}} (\alpha_{\mathrm{S}})$ is the EW (strong) coupling constant. Both the VBS amplitudes and non-VBS amplitudes of the $VVjj$ process with one boson decaying hadronically and the other leptonically are included, using factorized on-shell decays for the gauge bosons. The NNPDF30LO PDF set is used. The parton showers and hadronization are modeled with Pythia 8.186 using the A14 set of tuned parameters for the underlying event. The interference between EW- and QCD-induced $VVjj$ processes is not included in the predictions, while it is considered as an uncertainty for the measured fiducial cross sections.

Summary of predicted and measured fiducial cross sections for EW $VVjj$ production. The three lepton channels are combined. For the measured fiducial cross sections in the merged and resolved categories, two signal-strength parameters are used in the combined fit, one for the merged category and the other one for the resolved category; while for the measured fiducial cross section in the inclusive fiducial phase space, a single signal-strength parameter is used. For the SM predicted cross section, the error is the theoretical uncertainty (theo.). For the measured cross section, the first error is the statistical uncertainty (stat.), and the second error is the systematic uncertainty (syst.).