Search for heavy resonances decaying to WW, WZ, or WH boson pairs in the lepton plus merged jet final state at $\sqrt{s}=13~\mathrm{TeV}$

A search for new heavy resonances decaying to pairs of bosons (WW, WZ, or WH) is presented. The analysis uses data from proton-proton collisions collected by the CMS detector from 2016 to 2018 at a centre-of-mass energy of $13~\mathrm{TeV}$, corresponding to an integrated luminosity of $137~\mathrm{fb}^{-1}$. One of the bosons is required to be a W boson decaying to an electron or muon and a neutrino, while the other boson is required to be reconstructed as a single massive jet with substructure compatible with a quark pair from a W or Z boson decay, or a bottom quark pair from a Higgs boson decay. The search is performed in the resonance mass range between 1.0 and $4.5~\mathrm{TeV}$, and includes a specific search for resonances produced via vector boson fusion. The signal is extracted using a two-dimensional maximum likelihood fit to the jet mass and the diboson invariant mass distributions. No significant excess is observed above the estimated background. Model-independent upper limits on the production cross section of spin-0, spin-1, or spin-2 heavy resonances are derived as a function of the resonance mass, and are interpreted in the context of bulk radion, heavy vector triplet, and bulk graviton models.