Search for associated production of a Higgs boson and two vector bosons via vector boson scattering at $\sqrt{s}$ = 13 TeV

A search for Higgs boson (H) production in association with two vector bosons (V = W, Z) via vector boson scattering (VBS) is presented using proton-proton collision data collected at $\sqrt{s}$ = 13 TeV by the CMS experiment, corresponding to an integrated luminosity of 138 fb${}^{-1}$. Events containing two forward jets consistent with VBS, a large-radius jet from the decay of a boosted H to a pair of b quarks, and 0, 1, or 2 charged leptons coming from V decays are selected. The process is excluded at 95% CL for observed (expected) values of the VVHH coupling modifier ${\kappa }_{\mathrm{V}\mathrm{V}}$ outside the interval 0.40 $<$ ${\kappa }_{\mathrm{V}\mathrm{V}}$ $<$ 1.60 (0.34 $<$ ${\kappa }_{\mathrm{V}\mathrm{V}}$ $<$ 1.66), assuming standard model values for all other couplings, thus establishing a novel probe of the VVHH interaction. Constraints are also set on the individual ${\kappa }_{2\mathrm{W}}$ and ${\kappa }_{2\mathrm{Z}}$ coupling modifiers, and on the allowed region in the ${\kappa }_{2\mathrm{W}}$-${\kappa }_{2\mathrm{Z}}$ plane.