  A search for physics beyond the standard model (SM) in the final state with a
hadronically decaying tau lepton and a neutrino is presented. This analysis is
based on data recorded by the CMS experiment from proton-proton collisions at a
center-of-mass energy of 13 TeV at the LHC, corresponding to a total integrated
luminosity of 138 fb$^{=1}$. The transverse mass spectrum is analyzed for the
presence of new physics. No significant deviation from the SM prediction is
observed. Limits are set on the production cross section of a W' boson decaying
into a tau lepton and a neutrino. Lower limits are set on the mass of the
sequential SM-like heavy charged vector boson and the mass of a quantum black
hole. Upper limits are placed on the couplings of a new boson to the SM
fermions. Constraints are put on a nonuniversal gauge interaction model and an
effective field theory model. For the first time, upper limits on the cross
section of $t$-channel leptoquark (LQ) exchange are presented. These limits are
translated into exclusion limits on the LQ mass and on its coupling in the
$t$-channel. The sensitivity of this analysis extends into the parameter space
of LQ models that attempt to explain the anomalies observed in B meson decays.
The limits presented for the various interpretations are the most stringent to
date. Additionally, a model-independent limit is provided.
