Search for heavy neutrinos and third-generation leptoquarks in hadronic states of two $\tau$ leptons and two jets in proton-proton collisions at $\sqrt{s} =$ 13 TeV

A search for new particles has been conducted using events with two high transverse momentum $\tau$ leptons that decay hadronically and at least two energetic jets. The analysis is performed using data from proton-proton collisions at $\sqrt{s} =$ 13 TeV, collected by the CMS experiment at the LHC in 2016 and corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The observed data are consistent with standard model expectations. The results are interpreted in the context of two physics models. The first model involves right-handed charged bosons, W$_\mathrm{R}$, that decay to heavy right-handed Majorana neutrinos, N$_\ell$ $(\ell = $e, $\mu, \tau)$, arising in a left-right symmetric extension of the standard model. The model considers that N$_\mathrm{e}$ and N$_\mu$ are too heavy to be detected at the LHC. Assuming that the N$_\tau$ mass is half of the W$_\mathrm{R}$ mass, masses of the W$_\mathrm{R}$ boson below 3.50 TeV are excluded at 95% confidence level. Exclusion limits are also presented considering different scenarios for the mass ratio between N$_\tau$ and W$_\mathrm{R}$, as a function of W$_\mathrm{R}$ mass. In the second model, pair production of third-generation scalar leptoquarks that decay into $\tau\tau$bb is considered, resulting in an observed exclusion region with leptoquark masses below 1.02 TeV, assuming a 100% branching fraction for the leptoquark decay to a $\tau$ lepton and a bottom quark. These results represent the most stringent limits to date on these models.