  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.
