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The algorithm developed by the CMS Collaboration to reconstruct and identify$\tau$ leptons produced in proton-proton collisions at $\sqrt{s}=$ 7 and 8 TeV,via their decays to hadrons and a neutrino, has been significantly improved.The changes include a revised reconstruction of $\pi^0$ candidates, andimprovements in multivariate discriminants to separate $\tau$ leptons from jetsand electrons. The algorithm is extended to reconstruct $\tau$ leptons inhighly Lorentz-boosted pair production, and in the high-level trigger. Theperformance of the algorithm is studied using proton-proton collisions recordedduring 2016 at $\sqrt{s}=$ 13 TeV, corresponding to an integrated luminosity of35.9 fb$^{-1}$. The performance is evaluated in terms of the efficiency for agenuine $\tau$ lepton to pass the identification criteria and of theprobabilities for jets, electrons, and muons to be misidentified as $\tau$leptons. The results are found to be very close to those expected from MonteCarlo simulation.

Performance of reconstruction and identification of $\tau$ leptons decaying to hadrons and $\nu_\tau$ in pp collisions at $\sqrt{s}=$ 13 TeV