Search for heavy neutrinos and third-generation leptoquarks in final states with two hadronically decaying $\tau$ leptons and two jets in proton-proton collisions at $\sqrt{s} = 13~\mathrm{TeV}$

A search for new particles has been conducted using events with two high transverse momentum ($p_{\textrm{T}}$) $\tau$ leptons that decay hadronically, at least two high-$p_{\textrm{T}}$ jets, and missing transverse momentum from the $\tau$ lepton decays. The analysis is performed using data from proton-proton collisions, collected by the CMS experiment at the LHC in 2016 at $\sqrt{s} = 13~\mathrm{TeV}$, corresponding to an integrated luminosity of $35.9~\mathrm{fb}^{-1}$. The observed data are consistent with the standard model expectation. The results are interpreted with two physics models. The first model involves right-handed charged bosons, $\textrm{W}_\mathrm{R}$, that decay to heavy right-handed neutrinos, $N_{\ell}$ $(\ell = \textrm{e},\mu,\tau)$, arising in a left-right symmetric extension of the standard model. The model considers that $\textrm{N}_{\textrm{e}}$ and $\textrm{N}_{\mu}$ are too heavy to be detected at the LHC. Assuming that the $\textrm{N}_{\tau}$ mass is half of the $\textrm{W}_\mathrm{R}$ mass, masses of the $\textrm{W}_\mathrm{R}$ boson below $3.5~\mathrm{TeV}$ are excluded at a $95\%$ confidence level (expected exclusion of $3.35~\mathrm{TeV}$). Exclusion bounds are also presented considering different scenarios for the mass ratio between $\textrm{N}_{\tau}$ and $\textrm{W}_\mathrm{R}$ as function of $\textrm{W}_\mathrm{R}$ mass. In the second model, pair production of third-generation scalar leptoquarks that decay into $\tau\tau\textrm{b}\textrm{b}$ is considered, resulting in an observed (expected) exclusion region with leptoquark masses below 1.02 $(1.0)~\mathrm{TeV}$, 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.