Search for a W' boson decaying to a $\tau$ lepton and a neutrino in proton-proton collisions at $\sqrt{s} =$ 13 TeV

A search for a new high-mass resonance decaying to a tau lepton and a neutrino is reported. The analysis uses proton-proton collision data collected by the CMS experiment at the LHC at $\sqrt{s} =$ 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The search utilizes hadronically decaying tau leptons. No excess in the event yield is observed at high transverse masses of the $\tau$ and missing transverse momentum. An interpretation of results within the sequential standard model excludes W' boson masses below 4.0 TeV at 95% confidence level. Existing limits are also improved on models in which the W' boson decays preferentially to fermions of the third generation. Heavy W' bosons with masses less than 1.7-3.9 TeV, depending on the coupling in the non-universal G(221) model, are excluded at 95% confidence level. These are the most stringent limits on this model to date.