Search for new physics in the tau plus missing transverse momentum final state in proton-proton collisions at $\sqrt{s}= 13\,\mathrm{TeV}$

A search for physics beyond the standard model (SM) in the final state with a hadronically decaying tau lepton and 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$~\mathrm{fb}^{-1}$. No significant deviation from the SM prediction is observed. Model independent limits are set on the production cross section of W$^{\prime}$ bosons decaying into tau lepton plus neutrino final states. 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 the new resonance with the SM fermions. Limits are additionally set on non-universal gauge interaction models and an effective field theory model. Upper limits on the cross section of $t$-channel leptoquark exchange are presented and are translated into exclusion limits on the mass and coupling of leptoquarks; the sensitivity of this analysis reaches into the parameter space of leptoquark models that could explain the anomalies measured in B-meson decays. The limits presented are the most stringent to date.