Evidence for WW/WZ vector boson scattering in the decay channel $\ell\nu$qq produced in association with two jets in proton-proton collisions at $\sqrt{s} =$ 13 TeV

Evidence is reported for electroweak (EW) vector boson scattering in the decay channel $\ell\nu$qq of two weak vector bosons WV (V = W or Z), produced in association with two parton jets. The search uses a data set of proton-proton collisions at 13 TeV collected with the CMS detector during 2016-2018 with an integrated luminosity of 138 fb$^{-1}$. Events are selected requiring one lepton (electron or muon), moderate missing transverse momentum, two jets with a large pseudorapidity separation and a large dijet invariant mass, and a signature consistent with the hadronic decay of a W/Z boson. The cross section is computed in a fiducial phase space defined at parton level requiring all parton transverse momenta $p_\mathrm{T}$ $\gt$ 10 GeV and at least one pair of outgoing partons with invariant mass $m_\mathrm{qq}$ $\gt$ 100 GeV. The measured and expected EW WV production cross sections are 1.90 $^{+0.53}_{-0.46}$ pb and 2.23 $^{+0.08}_{-0.11}$ (scale) $\pm$ 0.05 (PDF) pb, respectively, where PDF is the parton distribution function. The observed EW signal strength is $m_\mathrm{EW}$ = 0.85 $\pm$ 0.12 (stat) $^{+0.19}_{-0.17}$ (syst), corresponding to a signal significance of 4.4 standard deviations with 5.1 expected, and it is measured keeping the quantum chromodynamics (QCD) associated diboson production fixed to the standard model prediction. This is the first evidence of vector boson scattering in the $\ell\nu$qq decay channel at LHC. The simultaneous measurement of the EW and QCD associated diboson production agrees with the standard model prediction.