Search for a leptoquark in events with a hadronically decaying $\tau$-lepton and missing transverse momentum using $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

A search for leptoquark signals is performed in final states with a hadronically decaying $\tau$-lepton and missing transverse momentum, using data from proton–proton collisions at a centre-of-mass energy of $\sqrt{s}=13$ TeV recorded by the ATLAS detector at the Large Hadron Collider during Run 2 (2015–18), corresponding to an integrated luminosity of 140 fb${}^{-1}$. The analysis is designed to probe both resonant production and non-resonant $t$-channel exchange of the leptoquark, covering a wide range of coupling scenarios. No excess above the Standard Model background prediction is observed. Limits are set on the couplings in the benchmark $U_1$ vector-leptoquark model at 95% confidence level for masses between 1.5 TeV and 3.0 TeV.