Search for leptoquarks produced in lepton-quark collisions and coupling to $\tau$ leptons

A search for leptoquarks produced in lepton-quark collisions and coupling to $\tau$ leptons is presented. It is based on a data set of proton-proton collision events recorded by the CMS detector at the LHC at a center-of-mass energy of $13~\mathrm{TeV}$ and corresponding to an integrated luminosity of $138~\mathrm{fb}^{-1}$. The reconstructed final state consists of a jet, significant missing transverse momentum, and a $\tau$ lepton reconstructed through its leptonic or hadronic decays. Limits are set on the leptoquark production cross section times branching fraction and interpreted as exclusions in the plane of the leptoquark mass and the coupling strength of the leptoquark-lepton-quark vertex. These results complement the constraints on the leptoquark-$\tau$-b couplings set by previous searches in other production modes, while they are the first limits for leptoquark-$\tau$-u, leptoquark-$\tau$-d, and leptoquark-$\tau$-s couplings.